From 73a1c95ca3d420667abbfaf7ba0512132cc6e417 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Thu, 6 Feb 2020 17:09:41 -0500 Subject: [PATCH] updated 01 and 02 problems --- .../fallingtennisball02-checkpoint.txt | 2500 +++++++++++++++++ .../therocket-checkpoint.txt | 151 - data/projectile_coords.npz | Bin 0 -> 1348 bytes data/therocket.txt | 151 - .../space-garbage-checkpoint.png | Bin 0 -> 48363 bytes .../space_garbage_traj-checkpoint.png | Bin 0 -> 100733 bytes .../spacecraft-checkpoint.png | Bin 0 -> 18744 bytes .../spring-mass-checkpoint.png | Bin 0 -> 15562 bytes .../spring_pendulum_traj-checkpoint.png | Bin 0 -> 212971 bytes .../trajectory_spacecraft-checkpoint.png | Bin 0 -> 43620 bytes .../two-euler-steps-checkpoint.png | Bin 0 -> 22019 bytes .../van_der_pol-checkpoint.png | Bin 0 -> 94282 bytes images/freefall.png | Bin 0 -> 38559 bytes images/projectile.png | Bin 0 -> 67769 bytes .../01_Catch_Motion-checkpoint.ipynb | 673 ++--- .../02_Step_Future-checkpoint.ipynb | 651 ++--- notebooks/01_Catch_Motion.ipynb | 670 ++--- notebooks/02_Step_Future.ipynb | 686 +++-- notebooks/03_Get_Oscillations.ipynb | 26 +- notebooks/Projectile_Motion.mp4 | Bin 0 -> 10718913 bytes 20 files changed, 3728 insertions(+), 1780 deletions(-) create mode 100644 data/.ipynb_checkpoints/fallingtennisball02-checkpoint.txt delete mode 100644 data/.ipynb_checkpoints/therocket-checkpoint.txt create mode 100644 data/projectile_coords.npz delete mode 100644 data/therocket.txt create mode 100644 images/.ipynb_checkpoints/space-garbage-checkpoint.png create mode 100644 images/.ipynb_checkpoints/space_garbage_traj-checkpoint.png create mode 100644 images/.ipynb_checkpoints/spacecraft-checkpoint.png create mode 100644 images/.ipynb_checkpoints/spring-mass-checkpoint.png create mode 100644 images/.ipynb_checkpoints/spring_pendulum_traj-checkpoint.png create mode 100644 images/.ipynb_checkpoints/trajectory_spacecraft-checkpoint.png create mode 100644 images/.ipynb_checkpoints/two-euler-steps-checkpoint.png create mode 100644 images/.ipynb_checkpoints/van_der_pol-checkpoint.png create mode 100644 images/freefall.png create mode 100644 images/projectile.png create mode 100644 notebooks/Projectile_Motion.mp4 diff --git a/data/.ipynb_checkpoints/fallingtennisball02-checkpoint.txt b/data/.ipynb_checkpoints/fallingtennisball02-checkpoint.txt new file mode 100644 index 0000000..82427ad --- /dev/null +++ b/data/.ipynb_checkpoints/fallingtennisball02-checkpoint.txt @@ -0,0 +1,2500 @@ + 0.0000000000000000e+00 1.6000000000000001e+00 + 1.0000000000000020e-03 1.5999950510001959e+00 + 2.0000000000000044e-03 1.5999803020031378e+00 + 3.0000000000000070e-03 1.5999557530158828e+00 + 4.0000000000000053e-03 1.5999214040501974e+00 + 4.9999999999999645e-03 1.5998772551225511e+00 + 5.9999999999999238e-03 1.5998233062541209e+00 + 6.9999999999998831e-03 1.5997595574707895e+00 + 7.9999999999998423e-03 1.5996860088031455e+00 + 8.9999999999998016e-03 1.5996026602864835e+00 + 9.9999999999997608e-03 1.5995095119608016e+00 + 1.0999999999999720e-02 1.5994065638708064e+00 + 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b/notebooks/.ipynb_checkpoints/01_Catch_Motion-checkpoint.ipynb index 8d8ca10..0e2d1f4 100644 --- a/notebooks/.ipynb_checkpoints/01_Catch_Motion-checkpoint.ipynb +++ b/notebooks/.ipynb_checkpoints/01_Catch_Motion-checkpoint.ipynb @@ -33,7 +33,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -51,7 +51,7 @@ " " ], "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -82,13 +82,13 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ - "import imageio\n", - "import numpy\n", - "from matplotlib import pyplot" + "import imageio \n", + "import numpy as np\n", + "import matplotlib.pyplot as plt" ] }, { @@ -102,7 +102,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 31, "metadata": {}, "outputs": [], "source": [ @@ -111,7 +111,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 32, "metadata": {}, "outputs": [ { @@ -120,7 +120,7 @@ "imageio.plugins.ffmpeg.FfmpegFormat.Reader" ] }, - "execution_count": 28, + "execution_count": 32, "metadata": {}, "output_type": "execute_result" } @@ -131,7 +131,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 33, "metadata": {}, "outputs": [ { @@ -162,10 +162,9 @@ " - download by calling (in Python): imageio.plugins.ffmpeg.download()\n", "```\n", "\n", - "If you do, we suggest to install `imageio-ffmpeg` package, an ffmpeg wrapper for Python that includes the `ffmpeg` executable. You can install it via `pip` or `conda`:\n", + "If you do, we suggest to install `imageio-ffmpeg` package, an ffmpeg wrapper for Python that includes the `ffmpeg` executable. You can install it via `conda`:\n", "\n", - "- `pip install --upgrade imageio-ffmpeg`\n", - "- `conda install imageio-ffmpeg -c conda-forge`" + " `conda install imageio-ffmpeg -c conda-forge`" ] }, { @@ -183,13 +182,13 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "%matplotlib notebook\n", "\n", - "pyplot.rc('font', family='serif', size='18')" + "plt.rc('font', family='serif', size='18')" ] }, { @@ -201,7 +200,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 40, "metadata": {}, "outputs": [ { @@ -210,7 +209,7 @@ "(1080, 1440, 3)" ] }, - "execution_count": 8, + "execution_count": 40, "metadata": {}, "output_type": "execute_result" } @@ -222,7 +221,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 41, "metadata": {}, "outputs": [ { @@ -231,7 +230,7 @@ "imageio.core.util.Array" ] }, - "execution_count": 9, + "execution_count": 41, "metadata": {}, "output_type": "execute_result" } @@ -244,7 +243,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Naturally, `imageio` plays well with `pyplot`. You can use [`pyplot.imshow()`](https://matplotlib.org/devdocs/api/_as_gen/matplotlib.pyplot.imshow.html) to show the image in a figure. We chose to show frame 1100 after playing around a bit and finding that it gives a good view of the long-exposure image of the falling ball.\n", + "Naturally, `imageio` plays well with `pyplot`. You can use [`plt.imshow()`](https://matplotlib.org/devdocs/api/_as_gen/matplotlib.plt.imshow.html) to show the image in a figure. We chose to show frame 1100 after playing around a bit and finding that it gives a good view of the long-exposure image of the falling ball.\n", "\n", "##### Explore:\n", "\n", @@ -253,7 +252,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 42, "metadata": {}, "outputs": [ { @@ -1039,7 +1038,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -1050,7 +1049,7 @@ } ], "source": [ - "pyplot.imshow(image, interpolation='nearest');" + "plt.imshow(image, interpolation='nearest');" ] }, { @@ -1066,7 +1065,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 43, "metadata": {}, "outputs": [], "source": [ @@ -1078,7 +1077,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 64, "metadata": {}, "outputs": [ { @@ -1864,7 +1863,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -1875,8 +1874,8 @@ } ], "source": [ - "fig = pyplot.figure()\n", - "pyplot.imshow(image, interpolation='nearest')\n", + "fig = plt.figure()\n", + "plt.imshow(image, interpolation='nearest')\n", "\n", "coords = []\n", "connectId = fig.canvas.mpl_connect('button_press_event', onclick)" @@ -1886,28 +1885,30 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Notice that in the previous code cell, we created an empty list named `coords`, and inside the `onclick()` function, we are appending to it the $(x,y)$ coordinates of each mouse click on the figure. After executing the cell above, you have a connection to the figure, via the user interface: try clicking with your mouse on the endpoints of the white lines of the metered panel (click on the edge of the panel to get approximately equal $x$ coordinates), then print the contents of the `coords` list below." + "Notice that in the previous code cell, we created an empty list named `coords`, and inside the `onclick()` function, we are appending to it the $(x,y)$ coordinates of each mouse click on the figure. After executing the cell above, you have a connection to the figure, via the user interface: \n", + "\n", + "## Exercise \n", + "Click with your mouse on the endpoints of the white lines of the metered panel (click on the edge of the panel to get approximately equal $x$ coordinates), then print the contents of the `coords` list below." ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[[607.5022321428571, 117.32366071428555],\n", - " [607.5022321428571, 242.97301136363626],\n", - " [610.4243100649351, 365.700284090909],\n", - " [607.5022321428571, 497.1937905844155],\n", - " [610.4243100649351, 616.9989853896103],\n", - " [610.4243100649351, 745.5704139610389],\n", - " [613.3463879870129, 862.4535308441557],\n", - " [613.3463879870129, 982.2587256493506]]" + "[[613.6203327922078, 118.4194399350647],\n", + " [613.6203327922078, 244.0687905844154],\n", + " [607.7761769480519, 366.79606331168816],\n", + " [613.6203327922078, 495.3674918831167],\n", + " [613.6203327922078, 618.0947646103895],\n", + " [616.5424107142857, 740.8220373376623],\n", + " [616.5424107142857, 866.4713879870129]]" ] }, - "execution_count": 13, + "execution_count": 65, "metadata": {}, "output_type": "execute_result" } @@ -1925,43 +1926,43 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([607.50223214, 607.50223214, 610.42431006, 607.50223214,\n", - " 610.42431006, 610.42431006, 613.34638799, 613.34638799])" + "array([613.62033279, 613.62033279, 607.77617695, 613.62033279,\n", + " 613.62033279, 616.54241071, 616.54241071])" ] }, - "execution_count": 14, + "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "numpy.array(coords)[:,0]" + "np.array(coords)[:,0]" ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "2.2810463468175857" + "2.705318473361352" ] }, - "execution_count": 15, + "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "numpy.array(coords)[:,0].std()" + "np.array(coords)[:,0].std()" ] }, { @@ -1980,23 +1981,23 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([117.32366071, 242.97301136, 365.70028409, 497.19379058,\n", - " 616.99898539, 745.57041396, 862.45353084, 982.25872565])" + "array([118.41943994, 244.06879058, 366.79606331, 495.36749188,\n", + " 618.09476461, 740.82203734, 866.47138799])" ] }, - "execution_count": 16, + "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "y_lines = numpy.array(coords)[:,1]\n", + "y_lines = np.array(coords)[:,1]\n", "y_lines" ] }, @@ -2017,16 +2018,16 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "123.56215213358072" + "124.6753246753247" ] }, - "execution_count": 17, + "execution_count": 69, "metadata": {}, "output_type": "execute_result" } @@ -2040,7 +2041,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "##### Discuss with your neighbor\n", + "## Discussion \n", "\n", "* Why did we slice the `y_lines` array like that? If you can't explain it, write out the first few terms of the sum above and think!" ] @@ -2062,7 +2063,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 70, "metadata": {}, "outputs": [ { @@ -2848,7 +2849,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -2859,34 +2860,42 @@ } ], "source": [ - "fig = pyplot.figure()\n", - "pyplot.imshow(image, interpolation='nearest')\n", + "fig = plt.figure()\n", + "plt.imshow(image, interpolation='nearest')\n", "\n", "coords = []\n", "connectId = fig.canvas.mpl_connect('button_press_event', onclick)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise\n", + "\n", + "Click on the locations of the _ghost_ ball locations in the image above to populate `coords` with x-y-coordinates for the ball's location. " + ] + }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[[724.385349025974, 61.11931818181802],\n", - " [724.385349025974, 87.41801948051943],\n", - " [724.385349025974, 128.3271103896102],\n", - " [724.385349025974, 180.9245129870128],\n", - " [724.385349025974, 253.9764610389609],\n", - " [721.4632711038961, 344.56087662337654],\n", - " [721.4632711038961, 452.6777597402596],\n", - " [718.5411931818181, 581.2491883116882],\n", - " [721.4632711038961, 718.5868506493506],\n", - " [721.4632711038961, 879.3011363636363]]" + "[[724.6592938311688, 88.65077110389598],\n", + " [730.5034496753246, 120.79362824675309],\n", + " [724.6592938311688, 188.00142045454527],\n", + " [724.6592938311688, 258.1312905844154],\n", + " [724.6592938311688, 351.637784090909],\n", + " [721.7372159090909, 456.8325892857142],\n", + " [724.6592938311688, 579.5598620129869],\n", + " [724.6592938311688, 719.8196022727271],\n", + " [721.7372159090909, 883.4559659090908]]" ] }, - "execution_count": 19, + "execution_count": 71, "metadata": {}, "output_type": "execute_result" } @@ -2908,27 +2917,27 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 72, "metadata": {}, "outputs": [], "source": [ - "y_coords = numpy.array(coords)[:,1]\n", + "y_coords = np.array(coords)[:,1]\n", "delta_y = (y_coords[1:] - y_coords[:-1]) *0.25 / gap_lines.mean()" ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([0.89391892, 1.39054054, 1.78783784, 2.48310811, 3.07905405,\n", - " 3.675 , 4.37027027, 4.66824324, 5.46283784])" + "array([1.0828125, 2.2640625, 2.3625 , 3.15 , 3.54375 , 4.134375 ,\n", + " 4.725 , 5.5125 ])" ] }, - "execution_count": 21, + "execution_count": 73, "metadata": {}, "output_type": "execute_result" } @@ -2940,17 +2949,17 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([ 8.34324324, 6.67459459, 11.68054054, 10.01189189, 10.01189189,\n", - " 11.68054054, 5.00594595, 13.34918919])" + "array([19.845 , 1.65375, 13.23 , 6.615 , 9.9225 , 9.9225 ,\n", + " 13.23 ])" ] }, - "execution_count": 22, + "execution_count": 74, "metadata": {}, "output_type": "execute_result" } @@ -2962,16 +2971,16 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "9.77351351351352" + "9.095624999999998" ] }, - "execution_count": 23, + "execution_count": 79, "metadata": {}, "output_type": "execute_result" } @@ -2984,7 +2993,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Yikes! That's some wide variation on the acceleration estimates. Our average measurement for the acceleration of gravity is not great, but it's not far off… In case you don't remember, the actual value is $9.8\\rm{m/s}^2$." + "Yikes! That's some wide variation on the acceleration estimates. Our average measurement for the acceleration of gravity is not great, but it's not far off. The actual value we are hoping to find is $9.81\\rm{m/s}^2$." ] }, { @@ -2998,7 +3007,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 80, "metadata": {}, "outputs": [ { @@ -3016,7 +3025,7 @@ " " ], "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3038,7 +3047,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 81, "metadata": {}, "outputs": [ { @@ -3076,7 +3085,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 82, "metadata": {}, "outputs": [], "source": [ @@ -3094,16 +3103,16 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "('Projectile_Motion.mp4', )" + "('Projectile_Motion.mp4', )" ] }, - "execution_count": 27, + "execution_count": 83, "metadata": {}, "output_type": "execute_result" } @@ -3116,7 +3125,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 84, "metadata": {}, "outputs": [], "source": [ @@ -3125,27 +3134,7 @@ }, { "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "3531" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(reader)" - ] - }, - { - "cell_type": "code", - "execution_count": 30, + "execution_count": 86, "metadata": {}, "outputs": [ { @@ -3154,7 +3143,7 @@ "(720, 1280, 3)" ] }, - "execution_count": 30, + "execution_count": 86, "metadata": {}, "output_type": "execute_result" } @@ -3166,7 +3155,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 88, "metadata": {}, "outputs": [ { @@ -3952,7 +3941,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -3963,35 +3952,46 @@ } ], "source": [ - "fig = pyplot.figure()\n", - "pyplot.imshow(image, interpolation='nearest')\n", + "fig = plt.figure()\n", + "plt.imshow(image, interpolation='nearest')\n", "\n", "coords = []\n", "connectId = fig.canvas.mpl_connect('button_press_event', onclick)" ] }, { - "cell_type": "code", - "execution_count": 32, + "cell_type": "markdown", "metadata": {}, + "source": [ + "## Exercise \n", + "\n", + "Grab the coordinates of the 0, 10, 20, 30, 40, ..., 100-cm vertical positions so we can create a vertical conversion from pixels to centimeters with `gap_lines2`. " + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": { + "scrolled": true + }, "outputs": [ { "data": { "text/plain": [ - "[[723.8145161290322, 117.54032258064524],\n", - " [723.8145161290322, 169.1532258064516],\n", - " [723.8145161290322, 223.3467741935484],\n", - " [723.8145161290322, 277.5403225806451],\n", - " [723.8145161290322, 329.1532258064516],\n", - " [723.8145161290322, 385.92741935483866],\n", - " [723.8145161290322, 437.5403225806451],\n", - " [723.8145161290322, 489.1532258064516],\n", - " [723.8145161290322, 540.766129032258],\n", - " [723.8145161290322, 594.9596774193548],\n", - " [723.8145161290322, 651.7338709677418]]" + "[[300.8306451612903, 112.90322580645159],\n", + " [298.25, 169.67741935483878],\n", + " [298.25, 223.8709677419355],\n", + " [298.25, 272.9032258064516],\n", + " [298.25, 327.0967741935484],\n", + " [298.25, 381.2903225806451],\n", + " [300.8306451612903, 438.0645161290322],\n", + " [300.8306451612903, 489.67741935483866],\n", + " [298.25, 559.3548387096773],\n", + " [300.8306451612903, 595.4838709677418],\n", + " [300.8306451612903, 649.6774193548385]]" ] }, - "execution_count": 32, + "execution_count": 92, "metadata": {}, "output_type": "execute_result" } @@ -4002,39 +4002,39 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 93, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([117.54032258, 169.15322581, 223.34677419, 277.54032258,\n", - " 329.15322581, 385.92741935, 437.54032258, 489.15322581,\n", - " 540.76612903, 594.95967742, 651.73387097])" + "array([112.90322581, 169.67741935, 223.87096774, 272.90322581,\n", + " 327.09677419, 381.29032258, 438.06451613, 489.67741935,\n", + " 559.35483871, 595.48387097, 649.67741935])" ] }, - "execution_count": 33, + "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "y_lines2 = numpy.array(coords)[:,1]\n", + "y_lines2 = np.array(coords)[:,1]\n", "y_lines2" ] }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "53.41935483870966" + "53.6774193548387" ] }, - "execution_count": 34, + "execution_count": 94, "metadata": {}, "output_type": "execute_result" } @@ -4066,7 +4066,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 95, "metadata": {}, "outputs": [ { @@ -4852,7 +4852,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -4864,7 +4864,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "7d91a6c017334f98835351d139242191", + "model_id": "17b0ac17bda34cbfacf4790889d9a31d", "version_major": 2, "version_minor": 0 }, @@ -4885,10 +4885,10 @@ "\n", "def catchclick(frame):\n", " image = reader.get_data(frame)\n", - " pyplot.imshow(image, interpolation='nearest');\n", + " plt.imshow(image, interpolation='nearest');\n", "\n", "\n", - "fig = pyplot.figure()\n", + "fig = plt.figure()\n", "\n", "connectId = fig.canvas.mpl_connect('button_press_event',onclick)\n", "\n", @@ -4897,41 +4897,41 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 124, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[[298.008064516129, 116.25],\n", - " [321.2338709677419, 118.83064516129036],\n", - " [344.4596774193548, 121.41129032258061],\n", - " [370.2661290322581, 123.99193548387098],\n", - " [393.4919354838709, 129.1532258064516],\n", - " [416.71774193548384, 139.47580645161293],\n", - " [439.94354838709677, 149.79838709677426],\n", - " [463.1693548387097, 160.1209677419355],\n", - " [488.97580645161287, 173.02419354838707],\n", - " [509.62096774193543, 185.92741935483878],\n", - " [532.8467741935483, 198.83064516129036],\n", - " [558.6532258064517, 219.47580645161293],\n", - " [581.8790322580644, 234.95967741935488],\n", - " [607.6854838709678, 255.60483870967744],\n", - " [628.3306451612902, 273.66935483870964],\n", - " [654.1370967741934, 296.89516129032256],\n", - " [674.7822580645161, 320.1209677419355],\n", - " [698.008064516129, 345.92741935483866],\n", - " [723.8145161290322, 376.89516129032256],\n", - " [744.4596774193549, 402.70161290322574],\n", - " [767.6854838709678, 431.0887096774193],\n", - " [790.9112903225807, 462.0564516129032],\n", - " [816.7177419354839, 495.6048387096774],\n", - " [837.3629032258063, 531.733870967742],\n", - " [860.5887096774193, 567.8629032258063],\n", - " [886.3951612903224, 606.5725806451612]]" + "[[300.8306451612903, 101.33064516129036],\n", + " [326.6370967741936, 98.75],\n", + " [347.28225806451616, 103.91129032258073],\n", + " [367.9274193548387, 106.49193548387098],\n", + " [393.7338709677419, 116.81451612903231],\n", + " [414.37903225806446, 124.55645161290329],\n", + " [442.7661290322581, 132.29838709677426],\n", + " [465.9919354838709, 139.26612903225805],\n", + " [488.27496735503223, 157.78872660443972],\n", + " [510.56059873289166, 167.69345166126618],\n", + " [535.3224113749577, 180.07435798229915],\n", + " [557.6080427528171, 199.88380809595208],\n", + " [582.3698553948833, 219.6932582096049],\n", + " [607.1316680369493, 237.0265270590511],\n", + " [629.4172994148088, 256.835977172704],\n", + " [654.1791120568748, 279.12160855056345],\n", + " [676.4647434347343, 303.8834211926295],\n", + " [701.2265560768004, 331.12141509890216],\n", + " [721.0360061904532, 355.8832277409682],\n", + " [745.7978188325193, 383.1212216472409],\n", + " [768.0834502103787, 415.31157808192677],\n", + " [792.8452628524448, 445.02575325240605],\n", + " [815.1308942303043, 477.21610968709194],\n", + " [839.8927068723702, 514.3588286501911],\n", + " [864.6545195144364, 549.0253663490835],\n", + " [886.940150892296, 583.6919040479761]]" ] }, - "execution_count": 37, + "execution_count": 124, "metadata": {}, "output_type": "execute_result" } @@ -4949,17 +4949,17 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 125, "metadata": {}, "outputs": [], "source": [ - "x = numpy.array(coords)[:,0] *0.1 / gap_lines2.mean()\n", - "y = numpy.array(coords)[:,1] *0.1 / gap_lines2.mean()" + "x = np.array(coords)[:,0] *0.1 / gap_lines2.mean()\n", + "y = np.array(coords)[:,1] *0.1 / gap_lines2.mean()" ] }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 126, "metadata": {}, "outputs": [ { @@ -5745,7 +5745,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -5757,8 +5757,8 @@ ], "source": [ "# make a scatter plot of the projectile positions\n", - "fig = pyplot.figure()\n", - "pyplot.scatter(x,-y);" + "fig = plt.figure()\n", + "plt.scatter(x,-y);" ] }, { @@ -5770,23 +5770,23 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 127, "metadata": {}, "outputs": [], "source": [ - "delta_y = (y[1:] - y[:-1])" + "delta_y = (y[1:] - y[0:-1])" ] }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 128, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The acceleration in the y direction is: 10.14\n" + "The acceleration in the y direction is: 8.60\n" ] } ], @@ -5798,14 +5798,14 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 129, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The acceleration in the x direction is: 0.72\n" + "The acceleration in the x direction is: -0.98\n" ] } ], @@ -5820,7 +5820,30 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "##### Discuss\n", + "## Saving our hard work\n", + "\n", + "We have put a lot of effort into processing these images so far. Let's save our variables `time`, `x`, and `y` so we can load it back later. \n", + "\n", + "Use the command `np.savez(file_name, array1,array2,...)` to save our arrays for use later.\n", + "\n", + "The x-y-coordinates occur at 1/60 s, 2/60s, ... len(y)/60s = `np.arange(0,len(y))/60`" + ] + }, + { + "cell_type": "code", + "execution_count": 152, + "metadata": {}, + "outputs": [], + "source": [ + "t = np.arange(0,len(y))/60\n", + "np.savez('projectile_coords.npz',t=t,x=x,y=y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Discussion\n", "\n", "* What did you get for the $x$ and $y$ accelerations? What did your neighbor get?\n", "* Do the results make sense to you? Why or why not?" @@ -5855,27 +5878,17 @@ "\n", "Suppose we had some high-resolution experimental data of a falling ball. Might we be able to compute the acceleration of gravity, and get a value closer to the actual acceleration of $9.8\\rm{m/s}^2$?\n", "\n", - "You're in luck! Physics professor Anders Malthe-Sørenssen of Norway has some high-resolution data on the website to accompany his book [3]. We contacted him by email to ask for permission to use the data set of a falling tennis ball, and he graciously agreed. _Thank you!_ His data was recorded with a motion detector on the ball, measuring the $y$ coordinate at tiny time intervals of $\\Delta t = 0.001\\rm{s}$. Pretty fancy.\n", - "\n", - "We have the data in our repository for this course, but you may have to download it first, if you got this Jupyter notebook by itself. If so, add a code cell below, and execute:\n", - "\n", - "```Python\n", - "filename = 'fallingtennisball02.txt'\n", - "url = 'http://go.gwu.edu/engcomp3data1'\n", - "urlretrieve(url, filename)\n", - "```\n", - "\n", - "You already imported `urlretrieve` above to get the video. Remember to then comment the assignment of the `filename` variable below. " + "You're in luck! Physics professor Anders Malthe-Sørenssen of Norway has some high-resolution data on the website to accompany his book [3]. We contacted him by email to ask for permission to use the data set of a falling tennis ball, and he graciously agreed. _Thank you!_ His data was recorded with a motion detector on the ball, measuring the $y$ coordinate at tiny time intervals of $\\Delta t = 0.001\\rm{s}$. Pretty fancy." ] }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 130, "metadata": {}, "outputs": [], "source": [ "filename = '../data/fallingtennisball02.txt'\n", - "t, y = numpy.loadtxt(filename, usecols=[0,1], unpack=True)" + "t, y = np.loadtxt(filename, usecols=[0,1], unpack=True)" ] }, { @@ -5887,7 +5900,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 131, "metadata": {}, "outputs": [ { @@ -6673,7 +6686,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -6684,8 +6697,8 @@ } ], "source": [ - "fig = pyplot.figure(figsize=(6,4))\n", - "pyplot.plot(t,y);" + "fig = plt.figure(figsize=(6,4))\n", + "plt.plot(t,y);" ] }, { @@ -6697,7 +6710,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 132, "metadata": {}, "outputs": [ { @@ -6708,18 +6721,18 @@ " 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057])" ] }, - "execution_count": 45, + "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "numpy.where( y < 0 )[0]" + "np.where( y < 0 )[0]" ] }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 133, "metadata": {}, "outputs": [], "source": [ @@ -6728,7 +6741,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 134, "metadata": {}, "outputs": [ { @@ -6737,7 +6750,7 @@ "0.001000000000000002" ] }, - "execution_count": 47, + "execution_count": 134, "metadata": {}, "output_type": "execute_result" } @@ -6749,7 +6762,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 135, "metadata": {}, "outputs": [ { @@ -6775,7 +6788,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 136, "metadata": {}, "outputs": [ { @@ -7561,7 +7574,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -7572,15 +7585,15 @@ } ], "source": [ - "fig = pyplot.figure(figsize=(6,4))\n", - "pyplot.plot(ay);" + "fig = plt.figure(figsize=(6,4))\n", + "plt.plot(ay);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "##### Discuss with your neighbor\n", + "## Discussion\n", "\n", "* What do you see in the plot of acceleration computed from the high-resolution data?\n", "* Can you explain it? What do you think is causing this?" @@ -7598,6 +7611,7 @@ "* Observed acceleration of falling bodies is less than $9.8\\rm{m/s}^2$.\n", "* Capture mouse clicks on several video frames using widgets!\n", "* Projectile motion is like falling under gravity, plus a horizontal velocity.\n", + "* Save our hard work as a numpy .npz file __Check the Problems for loading it back into your session__\n", "* Compute numerical derivatives using differences via array slicing.\n", "* Real data shows free-fall acceleration decreases in magnitude from $9.8\\rm{m/s}^2$." ] @@ -7615,179 +7629,62 @@ "3. _Elementary Mechanics Using Python_ (2015), Anders Malthe-Sorenssen, Undergraduate Lecture Notes in Physics, Springer. Data at http://folk.uio.no/malthe/mechbook/" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problems\n", + "\n", + "1. Instead of using $\\frac{\\Delta v}{\\Delta t}$, we can use the [numpy polyfit](https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html) to determine the acceleration of the ball. \n", + "\n", + " a. Use your coordinates from the saved .npz file you used above to load your projectile motion data\n", + " \n", + " ```python\n", + " npz_coords = np.load('projectile_coords.npz')\n", + " t = npz_coords['t']\n", + " x = npz_coords['x']\n", + " y = npz_coords['y']```\n", + " \n", + " b. Calculate $v_x$ and $v_y$ using a finite difference again, then do a first-order polyfit to $v_x-$ and $v_y-$ vs $t$. What is the acceleration now?\n", + " \n", + " c. Now, use a second-order polynomial fit for x- and y- vs t. What is acceleration now?\n", + " \n", + " d. Plot the polyfit lines for velocity and position (2 figures) with the finite difference velocity data points and positions. Which lines look like better fits to the data?" + ] + }, { "cell_type": "code", - "execution_count": 50, + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "execution_count": 50, - "metadata": {}, - "output_type": "execute_result" - } - ], "source": [ - "# Execute this cell to load the notebook's style sheet, then ignore it\n", - "from IPython.core.display import HTML\n", - "css_file = '../style/custom.css'\n", - "HTML(open(css_file, \"r\").read())" + "2. Not only can we measure acceleration of objects that we track, we can look at other physical constants like [coefficient of restitution](https://en.wikipedia.org/wiki/Coefficient_of_restitution), $e$ . \n", + "\n", + " During a collision with the ground, the coefficient of restitution is\n", + " \n", + " $e = -\\frac{v_{y}'}{v_{y}}$ . \n", + " \n", + " Where $v_y'$ is y-velocity perpendicular to the ground after impact and $v_y$ is the y-velocity after impact. \n", + " \n", + " a. Calculate $v_y$ and plot as a function of time from the data `'../data/fallingtennisball02.txt'`\n", + " \n", + " b. Find the locations when $v_y$ changes rapidly i.e. the impact locations. Get the maximum and minimum velocities closest to the impact location. _Hint: this can be a little tricky. Try slicing the data to include one collision at a time before using the `np.min` and `np.max` commands._\n", + " \n", + " c. Calculate the $e$ for each of the three collisions\n", + " " ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/notebooks/.ipynb_checkpoints/02_Step_Future-checkpoint.ipynb b/notebooks/.ipynb_checkpoints/02_Step_Future-checkpoint.ipynb index 86ed457..bde138e 100644 --- a/notebooks/.ipynb_checkpoints/02_Step_Future-checkpoint.ipynb +++ b/notebooks/.ipynb_checkpoints/02_Step_Future-checkpoint.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "###### Content under Creative Commons Attribution license CC-BY 4.0, code under BSD 3-Clause License © 2017 L.A. Barba, N.C. Clementi" + "###### Content modified under Creative Commons Attribution license CC-BY 4.0, code under BSD 3-Clause License © 2020 Ryan C. Cooper" ] }, { @@ -13,134 +13,30 @@ "source": [ "# Step to the future\n", "\n", - "Welcome to Lesson 2 of the course module \"Tour the dynamics of change and motion,\" in _Engineering Computations_. The previous lesson, [Catch things in motion](http://go.gwu.edu/engcomp3lesson1), showed you how to compute velocity and acceleration of a moving body whose positions were known. \n", + "Welcome to Lesson 2 of the course module \"Initial Value Problems (IVPs),\" in _Computational Mechanics_ The previous lesson, [Catch things in motion](http://go.gwu.edu/engcomp3lesson1), showed you how to compute velocity and acceleration of a moving body whose positions were known. \n", "\n", - "Time history of position can be captured on a long-exposure photograph (using a strobe light), or on video. But digitizing the positions from images can be a bit tedious, and error-prone. Luckily, we found online a data set from a fancy motion-capture experiment of a falling ball, with high resolution [1]. You computed acceleration and found that it was not only smaller than the theoretical value of $9.8 \\rm{m/s}^2$, but it _decreased_ over time. The effect is due to air resistance and is what leads to objects reaching a _terminal velocity_ in freefall.\n", - "\n", - "In general, not only is [motion capture](https://en.wikipedia.org/wiki/Motion_capture) (a.k.a., _mo-cap_) expensive, but it's inappropriate for many physical scenarios. Take a roller-coaster ride, for example: during design of the ride, it's more likely that the engineers will use an _accelerometer_. It really is the acceleration that makes a roller-coaster ride exciting, and they only rarely go faster than highway speeds (say, 60 mph) [2].\n", - "How would an engineer analyze data captured with an accelerometer?" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## A roller-coaster ride\n", - "\n", - "Prof. Anders Malthe-Sorenssen has a file with accelerometer data for a roller-coaster ride called \"The Rocket\" (we don't know if it's real or made up!). He has kindly given permission to use his data. So let's load it and have a look. We'll first need our favorite numerical Python libraries, of course." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, - "outputs": [], - "source": [ - "import numpy\n", - "from matplotlib import pyplot" + "Time history of position can be captured on a long-exposure photograph (using a strobe light), or on video. But digitizing the positions from images can be a bit tedious, and error-prone. Luckily, we found online a data set from a motion-capture experiment of a falling ball, with high resolution [1]. You computed acceleration and found that it was smaller than the theoretical value of $9.8 \\rm{m/s}^2$ and _decreased_ over time. The effect is due to air resistance and is what leads to objects reaching a _terminal velocity_ in freefall." ] }, { "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "\n", - "pyplot.rc('font', family='serif', size='14')" - ] - }, - { - "cell_type": "markdown", + "execution_count": 11, "metadata": {}, - "source": [ - "If you don't have the data file in the location we assume below, you can get it by adding a code cell and executing this code in it, then commenting or deleting the `filename` assignment before the call to `numpy.loadtxt()`.\n", - "\n", - "```Python\n", - "from urllib.request import urlretrieve\n", - "URL = 'http://go.gwu.edu/engcomp3data2?accessType=DOWNLOAD'\n", - "urlretrieve(URL, 'therocket.txt')\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, "outputs": [], "source": [ - "filename = '../data/therocket.txt'\n", - "t, a = numpy.loadtxt(filename, usecols=[0,1], unpack=True)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We'll take a peek at the data by printing the first five pairs of $(t, a)$ values, then plot the whole set below. Time is given in units of seconds, while acceleration is in $\\rm{m/s}^2$." + "import numpy as np\n", + "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 147, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.0 0.2731644\n", - "0.1 1.4411079\n", - "0.2 2.6693138\n", - "0.3 4.2383806\n", - "0.4 5.6499504\n" - ] - } - ], - "source": [ - "for i in range(0,5): print(t[i],a[i])" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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QH2gDtD/kXBKRmUtWk5KcRPvmxwQdikRR1UoV6XxsY76ZtzToUEREoiaSpOFS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\nAABJRU5ErkJggg==\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ - "# plot the acceleration over time\n", - "fig = pyplot.figure(figsize=(8, 3))\n", - "\n", - "pyplot.plot(t, a, color='#004065', linestyle='-', linewidth=1) \n", - "pyplot.title('Acceleration of roller-coster ride data, from [1]. \\n')\n", - "pyplot.xlabel('Time [s]')\n", - "pyplot.ylabel('[m/s$^2$]');" + "%matplotlib inline\n", + "plt.rcParams.update({'font.size': 22})\n", + "plt.rcParams['lines.linewidth'] = 3" ] }, { @@ -149,7 +45,7 @@ "source": [ "### Set things up to compute velocity and position\n", "\n", - "Our challenge now is to find the motion description—the position $x(t)$—from the acceleration data. In the [previous lesson](http://go.gwu.edu/engcomp3lesson1), we did the opposite: with position data, get the velocity and acceleration, using _numerical derivatives_:\n", + "Our challenge now is to find the motion description—the position $x(t)$—from a function of acceleration. In the [previous lesson](http://go.gwu.edu/engcomp3lesson1), we did the opposite: with position data, get the velocity and acceleration, using _numerical derivatives_:\n", "\n", "\\begin{equation}\n", "v(t_i) = \\frac{dx}{dt} \\approx \\frac{x(t_i+\\Delta t)-x(t_i)}{\\Delta t}\n", @@ -159,86 +55,76 @@ "a(t_i) = \\frac{dv}{dt} \\approx \\frac{v(t_i+\\Delta t)-v(t_i)}{\\Delta t}\n", "\\end{equation}\n", "\n", - "Since this time we're dealing with horizontal acceleration, we swapped the position variable from $y$ to $x$ in the equation for velocity, above. \n", + "Almost every problem that deals with Newton's second law is a second-order differential equation. The acceleration is a function of position, velocity, and sometimes time _if there is a forcing function f(t)_. \n", "\n", - "The key to our problem is realizing that if we have the initial velocity, we can use the acceleration data to find the velocity after a short interval of time. And if we have the initial position, we can use the known velocity to find the new position after a short interval of time. Let's rearrange the equation for acceleration above, by solving for the velocity at $t_i + \\Delta t$:\n", + "The key to solving a second order differential equation is realizing that if we have the initial velocity, we can use the acceleration to find the velocity after a short interval of time. And if we have the initial position, we can use the known velocity to find the new position after a short interval of time. Let's rearrange the equation for acceleration above, by solving for the velocity at $t_i + \\Delta t$:\n", "\n", "\\begin{equation}\n", " v(t_i+\\Delta t) \\approx v(t_i) + a(t_i) \\Delta t\n", "\\end{equation}\n", "\n", - "We need to know the velocity and acceleration at some initial time, $t_0$, and then we can compute the velocity $v(t_i + \\Delta t)$. For the roller-coaster ride, it's natural to assume that the initial velocity is zero, and the initial position is zero with respect to a convenient reference system. We're actually ready to solve this!\n", + "Consider our first computational mechanics model of a freefalling object that is dropped.\n", + "\n", + " \n", + "\n", + "An object falling is subject to the force of \n", + "\n", + "- gravity ($F_g$=mg) and \n", + "- drag ($F_d=cv^2$)\n", "\n", - "Let's save the time increment for our data set in a variable named `dt`, and compute the number of time increments in the data. Then, we'll initialize new arrays of velocity and position to all-zero values, with the intention of updating these to the computed values." + "Acceleration of the object:\n", + "\n", + "$\\sum F=ma=F_g-F_d=cv^2 - mg = m\\frac{dv}{dt}$\n", + "\n", + "so,\n", + "\n", + "$a=\\frac{c}{m}v(t_{i})^2-g$\n", + "\n", + "then, our acceleration is defined from Newton's second law and position is defined through its definition, $v=\\frac{dx}{dt}$. \n", + "\n", + "_Note: the direction of positive acceleration was changed to up, so that a positive $x$ is altitude, we will still have the same speed vs time function from [Module_01-03_Numerical_error](https://github.uconn.edu/rcc02007/CompMech01-Getting-started/blob/master/notebooks/03_Numerical_error.ipynb)_" ] }, { - "cell_type": "code", - "execution_count": 6, + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0.10000000000000001" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], "source": [ - "#time increment\n", - "dt = t[1]-t[0]\n", - "dt" + "### Step through time\n", + "\n", + "In the code cell below, we define acceleration as a function of velocity and add two parameters `c` and `m` to define drag coefficient and mass of the object. " ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 163, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "151" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "#number of time increments\n", - "N = len(t)\n", - "N" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, "outputs": [], "source": [ - "#initialize v and x arrays to zero\n", - "v = numpy.zeros(N)\n", - "x = numpy.zeros(N)" + "def a_freefall(v,c=0.25,m=60):\n", + " '''Calculate the acceleration of an object given its \n", + " drag coefficient and mass\n", + " \n", + " Arguments:\n", + " ---------\n", + " v: current velocity (m/s)\n", + " c: drag coefficient set to a default value of c=0.25 kg/m\n", + " m: mass of object set to a defualt value of m=60 kg\n", + " \n", + " returns:\n", + " ---------\n", + " a: acceleration of freefalling object under the force of gravity and drag\n", + " '''\n", + " a=-c/m*v**2*np.sign(v)-9.81\n", + " return a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Step through time\n", + "Now we use a `for` statement to step through the sequence of acceleration values, each time computing the velocity and position at the subsequent time instant. We first have to __initialize__ our variables `x` and `v`. We can use initial conditions to set `x[0]` and `v[0]`. The rest of the values we will overwrite based upon our stepping solution.\n", "\n", - "In the code cell below, we use a `for` statement to step through the sequence of acceleration values, each time computing the velocity and position at the subsequent time instant. We are applying the equation for $v(t_i + \\Delta t)$ above, and a similar equation for position:\n", + "We are applying the equation for $v(t_i + \\Delta t)$ above, and a similar equation for position:\n", "\n", "\\begin{equation}\n", " x(t_i+\\Delta t) \\approx x(t_i) + v(t_i) \\Delta t\n", @@ -247,56 +133,92 @@ }, { "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 164, + "metadata": {}, "outputs": [], "source": [ - "for i in range(N-1):\n", - " v[i+1] = v[i] + a[i]*dt\n", - " x[i+1] = x[i] + v[i]*dt" + "N = 100 # define number of time steps\n", + "t=np.linspace(0,12,N) # set values for time (our independent variable)\n", + "dt=t[1]-t[0]\n", + "x=np.zeros(len(t)) # initialize x\n", + "v=np.zeros(len(t)) # initialize v\n", + "\n", + "x[0] = 440 # define initial altitude of the object\n", + "v[0] = 0\n", + "\n", + "for i in range(1,N):\n", + " dvdt = a_freefall(v[i-1])\n", + " v[i] = v[i-1] + dvdt*dt\n", + " x[i] = x[i-1] + v[i-1]*dt" + ] + }, + { + "cell_type": "code", + "execution_count": 165, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-9.393333333333334" + ] + }, + "execution_count": 165, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a_freefall(-10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "And there you have it. You have computed the velocity and position over time from the acceleration data. We can now make plots of the computed variables. Note that we use the Matplotlib [`subplot()`](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplot.html?highlight=matplotlib%20pyplot%20subplot#matplotlib.pyplot.subplot) function to get the two plots in one figure. The argument to `subplot()` is a set of three digits, corresponding to the number of rows, number of columns, and plot number in a matrix of sub-plots. " + "And there you have it. You have computed the velocity __and position__ over time from Newton's second law. We can now make plots of the computed variables. Note that we use the Matplotlib [`subplot()`](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplot.html?highlight=matplotlib%20pyplot%20subplot#matplotlib.pyplot.subplot) function to get the two plots in one figure. The argument to `subplot()` is a set of three digits, corresponding to the number of rows, number of columns, and plot number in a matrix of sub-plots. " ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 166, "metadata": {}, "outputs": [ { "data": { - "image/png": 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dIshJT+HaCQN4YcYIHlxSwaEPLOU/ZVuiDktEpMMpsRPpQH96ZwP/+HATz0wf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\nvmbWEvgVMJY4/ACujuBYpAGNzewVoCdQAIx393+GmS0s7v6SmbUAlpp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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ "# plot velocity and position over time\n", - "fig = pyplot.figure(figsize=(10,6))\n", + "fig = plt.figure(figsize=(8,6))\n", + "\n", + "plt.subplot(211)\n", + "plt.plot(t, v, color='#0096d6', linestyle='-', linewidth=1) \n", + "plt.title('Velocity and position of \\nfreefalling object m=60-kg and c=0.25 kg/s. \\n')\n", + "plt.ylabel('$v$ (m/s) ')\n", "\n", - "pyplot.subplot(211)\n", - "pyplot.plot(t, v, color='#0096d6', linestyle='-', linewidth=1) \n", - "pyplot.title('Velocity and position of roller-coster ride (data from [1]). \\n')\n", - "pyplot.ylabel('$v$ [m/s] ')\n", + "plt.subplot(212)\n", + "plt.plot(t, x, color='#008367', linestyle='-', linewidth=1) \n", + "plt.xlabel('Time (s)')\n", + "plt.ylabel('$x$ (m)');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise\n", "\n", - "pyplot.subplot(212)\n", - "pyplot.plot(t, x, color='#008367', linestyle='-', linewidth=1) \n", - "pyplot.xlabel('Time [s]')\n", - "pyplot.ylabel('$x$ [m]');" + "The initial height is 440 m, the height of the tip of the [Empire State Building](https://en.wikipedia.org/wiki/Empire_State_Building). How long would it take for the object to reach the ground from this height? How accurate is your estimation e.g. what is the error bar for your solution?" ] }, { @@ -305,7 +227,9 @@ "source": [ "## Euler's method\n", "\n", - "The method we used above to compute the velocity and position from acceleration data is known as _Euler's method_. The eminent Swiss mathematician Leonhard Euler presented it in his book _\"Institutionum calculi integralis,\"_ published around 1770 [3].\n", + "We first used Euler's method in [Module_01: 03_Numerical_error](https://github.uconn.edu/rcc02007/CompMech01-Getting-started/blob/master/notebooks/03_Numerical_error.ipynb). Here we will look at it with more depth. \n", + "\n", + "The eminent Swiss mathematician Leonhard Euler presented it in his book _\"Institutionum calculi integralis,\"_ published around 1770 [3].\n", "\n", "You can understand why it works by writing out a Taylor expansion for $x(t)$:\n", "\n", @@ -315,7 +239,11 @@ "\n", "With $v=dx/dt$, you can see that the first two terms on the right-hand side correspond to what we used in the code above. That means that Euler's method makes an approximation by throwing away the terms $\\frac{d^2 x}{dt^2}\\frac{\\Delta t^2}{2} + \\frac{d^3 x}{dt^3}\\frac{\\Delta t^3}{3!}+\\cdots$. So the error made in _one step_ of Euler's method is proportional to $\\Delta t^2$. Since we take $N=T/\\Delta t$ steps (for a final time instant $T$), we conclude that the error overall is proportional to $\\Delta t$. \n", "\n", - "#### **Euler's method is a first-order method** because the error in the approximation goes with the first power of the time increment $\\Delta t$." + "#### **Euler's method is a first-order method** because the error in the approximation goes is proportional to the first power of the time increment $\\Delta t$.\n", + "\n", + "i.e.\n", + "\n", + "error $\\propto$ $\\Delta t$" ] }, { @@ -330,14 +258,14 @@ "Consider the differential equation corresponding to an object in free fall:\n", "\n", "\\begin{equation}\n", - "\\ddot{y}=-g,\n", + "\\ddot{y}=\\frac{c}{m}v^2-g,\n", "\\end{equation}\n", "\n", "where the dot above a variable represents the time derivative, and $g$ is the acceleration of gravity. Introducing the velocity as intermediary variable, we can write:\n", "\n", "\\begin{eqnarray}\n", "\\dot{y} &=& v \\nonumber\\\\\n", - "\\dot{v} &=& -g\n", + "\\dot{v} &=& \\frac{c}{m}v^2-g\n", "\\end{eqnarray}\n", "\n", "The above is a system of two ordinary differential equations, with time as the independent variable. For its numerical solution, we need two initial conditions, and Euler's method:\n", @@ -359,7 +287,7 @@ "\n", "\\begin{equation}\n", "\\dot{\\mathbf{y}} = \\begin{bmatrix}\n", - "v \\\\ -g\n", + "v \\\\ \\frac{c}{m}v^2-g\n", "\\end{bmatrix}.\n", "\\end{equation}\n", "\n", @@ -370,46 +298,38 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Study the code below: the function `freefall()` computes the right-hands side of the equation, and the function `eulerstep()` takes the state and applies Euler's method to update it one time increment." + "Study the code below: the function `freefall()` computes the right-hand side of the equation, and the function `eulerstep()` takes the state and applies Euler's method to update it one time increment." ] }, { "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 197, + "metadata": {}, "outputs": [], "source": [ - "def freefall(state):\n", + "def freefall(state,c=0,m=60):\n", " '''Computes the right-hand side of the freefall differential \n", " equation, in SI units.\n", " \n", " Arguments\n", " ---------- \n", " state : array of two dependent variables [y v]^T\n", + " c : drag coefficient for object; default set to 0 kg/m (so no drag considered)\n", + " m : mass of falling object; default set to 60 kg\n", " \n", " Returns\n", " -------\n", - " derivs: array of two derivatives [v -g]^T\n", + " derivs: array of two derivatives [v, c/m*v**2-g]\n", " '''\n", " \n", - " derivs = numpy.array([state[1], -9.8])\n", + " derivs = np.array([state[1], -c/m*state[1]**2*np.sign(state[1])-9.81])\n", " return derivs" ] }, { "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 198, + "metadata": {}, "outputs": [], "source": [ "def eulerstep(state, rhs, dt):\n", @@ -437,31 +357,29 @@ "source": [ "## Numerical solution vs. experiment\n", "\n", - "Here's an idea! Let's use the `freefall()` and `eulerstep()` functions to obtain a numerical solution with the same initial conditions as the falling-ball experiment from [Lesson 1](http://go.gwu.edu/engcomp3lesson1), and compare with the experimental data. \n", + "Use the `freefall()` and `eulerstep()` functions to obtain a numerical solution with the same initial conditions as the falling-ball experiment from [Lesson 1](./01_Catch_Motion.ipynb), and compare with the experimental data. \n", "\n", - "You can grab the data from its location online running the following code in a new cell:\n", - "```Python\n", - "filename = 'fallingtennisball02.txt'\n", - "url = 'http://go.gwu.edu/engcomp3data1'\n", - "urlretrieve(url, filename)\n", - "```\n", + "In [Lesson 1](./01_Catch_Motion.ipynb), we had considered only the acceleration due to gravity. So before we get into the specifics of the effects on drag, leave c=0 so that we have a constant acceleration problem, \n", "\n", - "You already imported `urlretrieve` above. Remember to then comment the assignment of the `filename` variable below. We'll load it from our local copy." + "$\\ddot{y} = -g$\n", + "\n", + "and our vector form is \n", + "\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{y}} = \\begin{bmatrix}\n", + "v \\\\ -g\n", + "\\end{bmatrix}.\n", + "\\end{equation}\n" ] }, { "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 199, + "metadata": {}, "outputs": [], "source": [ "filename = '../data/fallingtennisball02.txt'\n", - "t, y = numpy.loadtxt(filename, usecols=[0,1], unpack=True)" + "t, y = np.loadtxt(filename, usecols=[0,1], unpack=True)" ] }, { @@ -473,13 +391,8 @@ }, { "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 200, + "metadata": {}, "outputs": [], "source": [ "#time increment\n", @@ -488,13 +401,8 @@ }, { "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 201, + "metadata": {}, "outputs": [], "source": [ "y0 = y[0] #initial position\n", @@ -511,44 +419,41 @@ }, { "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 202, + "metadata": {}, "outputs": [], "source": [ "#initialize array\n", - "num_sol = numpy.zeros([N,2])" + "num_sol = np.zeros([N,2])" ] }, { "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true + "execution_count": 203, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1.6 , -0.00981])" + ] + }, + "execution_count": 203, + "metadata": {}, + "output_type": "execute_result" } - }, - "outputs": [], + ], "source": [ "#Set intial conditions\n", "num_sol[0,0] = y0\n", - "num_sol[0,1] = v0" + "num_sol[0,1] = v0\n", + "eulerstep(num_sol[0],freefall,dt)" ] }, { "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 204, + "metadata": {}, "outputs": [], "source": [ "for i in range(N-1):\n", @@ -564,59 +469,74 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 205, "metadata": {}, "outputs": [ { "data": { - "image/png": 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+pKqRqhrZsmXLGg3OmLoqKnIgPa55l02BffHJOcSB+bfw56fPQH6+06GZOq6u\nJZktQCsREY9hrd3Pmx2Ix5h6o0ObVoy55VXWtLmAfAW/5a+R+9XdkJ3udGimDqtrSeYbXCf5e3sM\niwQygF8ciciYeiTI34+Lr72HxEH30qFNK3y2LYaP/gkHdjgdmqmjanWSEZGHRGS1iAQAqOoaYAFw\nm3u8L3Aj8KSqHnIuUmPqDxHhzLPOp9H4V6BpJ9ifwM45V7B73WKnQzN1kNN/xvQTkVhc/3UBmCsi\n8z2KBOA6oe95eGySu+5SYAmwGLivxoM1pqEJaQ/nPc+WoL4k70tm73vXsyn2LaejMnWMaAP6A1Zk\nZKTGxcU5HYYxdcqB9Cw+eXk6J6R8iQAacQ7Hj7sPvO1qTg2BiCxT1cijrV+rD5cZY5wX0sifS67/\nL6t6/otsfGDdJyx7/kpy0/c7HZqpAyzJGGPK5ePtxaWXTWVP9KMcIBjfPX/y5zMXczDpL6dDM7Vc\nufu7IjKikm1mqurvRxmPMaYWO/2UU1jWuj3bP5hG96wdBHx2HZx6H3Qe5nRoppYq95yMiFT231gJ\nqlorL/Fi52SMqR7b96QQvGQmoTt/AhEYch30vdDpsEwNOBbnZH5QVa+KPoCtRxuMMaZu6NCqGaFn\nPQiRk0GVXV/+j40fPgh2IzRTTEWSTFL5RapU3hhTF4nAgEmsDr+eXQdzyfzjQ1a/fh1qVwgwHspN\nMqp6SWUarGx5Y0zd1jv6AjZGzuCQBpK/9VdWPX8FuWm7nQ7L1BLV1rtMRN6rrraMMXWHiHDxOWdz\n6PSn2E0L2LeJtc9dSvrOdU6HZmqBSiUZEQkRkXtFZL6ILBKR7woewKgaitEYUwecNnQgzS97hc1e\nXeBwMvGvXUnK2linwzIOq+yezHvAaGAT8CPwg8cjtXpDM8bUNf17dqbfP15jpf9A/PKzafLjDFg9\nv9x6pv6q7HUhWqrqgJJGiEhaNcRjjKnjuoQ1JfTGZ5AVb+Cz9h34ZTYcTIKoa8HL/v/d0FT2E19R\ncEXkEuyqajDGmPqhaWN/QodfDSPvQr282fnTG2yedyfk5TgdmjnGKrsncwvwmIgk4Uoqnp3i7wDm\nVldgxph6oOdo4nZD/jf3EbTmKzamp9DzsifBr5HTkZljpLJJ5jrgX0AyR97uOKxaIjLG1CuRJ53G\nm/uFLksfIDRhKetfmkz45OeQRi2cDs0cA5U9XDYFOE5Vw1S1i+cD+KkG4jPG1HEiwhXnnEbKqFns\n0hZk79lQT2zkAAAgAElEQVTIuhcuJ3dfgtOhmWOgsklmjaqWdtnV8VUNxhhTf503YiB+FzzHZjqQ\ne2Anf718BZmJfzodlqlhlU0yL4rITSLSVkSk2Djrp2iMKdPIfj3pdMWLrPKKwCfnEL4Lb4WEX5wO\ny9SgSt0Z0+OKzCVWUlXv6giqpthVmI2pHTYlpdL6z2dpHP81iBcMvxUiznI6LFOCql6FubIn/v8A\nbiopDmDW0QZhjGlYurcOhbC7YFkbdNkb7P7sQXxTkmk+bJLToZlqVtkk87Cq/lDSCBG5uxriMcY0\nFCIQeSXfJeTQYscL+H37FHmHU2l16o2ucaZeKPecjIicVvBaVd8vrZyqflG8vDHGlGfQWVfyWfMr\nycqDvb+8wa7PHoL8yt4r0dRWFTnxf0cl26xseWNMAxYc4Mut//wnC9teR2a+N/vi5pP44R2Qm+10\naKYaVORwWRcRua8SbYYebTDGmIYpwNebaVMnMeutxkRveQJd/Q35mYfoePET4BvodHimCiqSZLYC\nIyvR5oajjMUY04D5ensx7fKLePr9Rpy45mECt/6Ofn4rMuYRCGjidHjmKFWqC3NdZ12Yjan9VJV5\ni37lvJ0z8cvYC826wBlPQKPmTofWIFW1C7Ndd9sYU6uICONOHYrf+c9DaEc0JZ7kd6dCml3ovS6y\nJGOMqZ0at4RznmZlZhg7t29h65wpkLrd6ahMJVmSMcbUXoGhbIl6kHXaiQPJO0mYMwVNiXc6KlMJ\nlmSMMbXaBYPDCTpvJqu0G2kpe0iYcxW6d6PTYZkKqlSSEZHjaioQY4wpzdkDutH8gpks13AOpu4j\n4Y1r0N1rnA7LVMDR3H55tog0rZFojDGmFGP6daLD+Cf4XXtzMG0/Se/+C3audDosU47KJplBQG/g\nLxG5XkRq9VWXjTH1yyl92tNjwv/YFDyIloH5sPDfkLjM6bBMGSqVZFR1laqeClwF3ACsEpHTayQy\nY4wpQXREW8be+jw+x50JuVnol3eQG/+z02GZUhzViX9V/QjXHs0bwFwR+cLO1xhjjhXx8oYRt5Hf\n6zwSkw+Q+N408jbFOh2WKUFVepcFActwJZrRwJ8i8pSIhFRLZMYYUxYvLxLCr+KdjMGkHc4k8YPb\nLdHUQpXtXXaTiLwjIhuBfcCnwEBgNq5DaMcBa0UkqtojNcaYYrq2CmbU5Ol8SgwHDme5Es3mWKfD\nMh4quydzK+ALPA+cBISo6hBVvUVV31TV04CngNeqOU5jjCnRgM7NGT353r8TzTxLNLVJZU/8d1DV\ncao6S1V/VdWSbvjwOq49GmOMOSYiuzTntMn38ok70eywRFNr1MQ//vcCJ9dAu8YYU6qBXZpz2qR7\n+ZiRZOfmwrczYEus02E1eNWeZNTlh+pu1xhjyjOoa3POvuo+2o2cijcK395vicZhdu0yY0y90q9j\nUwKHXgMnXoZqPikf302+9TpzjCUZY0z9IwIDr+JT75NJ3J/Ojg/vQO0cjSMsyRhj6icRWsT8kwU6\nkv3pmey0ROMISzLGmHpraPeWxFx2J/N1JPsOZbJr/l2Q8IvTYTUolmSMMfVadHgrho7/Nx/ljyD5\n4GGSPrwdtv/udFgNhiUZY0y9d1qfNpx44e18lj+EPQcOsW/+bbBjudNhNQiWZIwxDcLZ/drR49w7\nWR08nFB/ha/ugqRVTodV71mSMcY0GBcN7Mj4W57Eu+doyMmAhbfDnvVOh1WvWZIxxjQo3t7eEHMH\n+V2iSdydTPK8GyB5k9Nh1VuOJxkROUdElorIjyLyi4hEllN+vYjEFnvceKziNcbUA17efBU2lYWH\nurFr9x72vX8dpMQ7HVW95GiSEZEBwLvAFao6AngY+EpEWpdRLUlVY4o9Zh+TgI0x9caY49uzf8hd\nxOX3ZGfSbvbPux5StzsdVr3j9J7MncBXqroWQFU/A3YD/3I0KmNMvSci3HZGH7YNuIM/87uwY+cO\n0j64DtJ2OR1aveJ0kjkViCs2bCkwyoFYjDENjIhw77knsqLXbazJ60hi4jYOzb8B0vc5HVq94ViS\nEZFmQAhQfLMhCehaRtVGIvKa+xxOrIjcIyIBNRaoMaZe8/ISHh4fRWzXW1mf15bknQnwxa2QmeZ0\naPWCk3syjdzPWcWGZwFBZdTbADzvPodzIXAG8EFphUXkahGJE5G4vXv3ViVeY0w95evtxczLhrF1\n4H207xLu6gTw5R2Qfdjp0Oo8J5NMuvvZv9hwf6DUT1ZVL1PVpe7XycC9wJki0q+U8i+paqSqRrZs\n2bIawjbG1EeBft7cfE4UPmfPhMZh6O415Hx5N+SWdANgU1GOJRlVTQFSgeI9yVoDmyvRVEHZ7tUR\nlzGmgWvcipzT/8eGAz5sW/UTud8+APl5TkdVZzl94v9boPj/YiLdw48gIn1F5Kpig9u5n7dVc2zG\nmAZqn3cY9+ZMYm+WD4nLvyLvh/+BqtNh1UlOJ5lHgNEiEgEgImcAbYBn3e8fEpHVHif2mwP/FpHm\n7vH+uLpBLwGWHevgjTH1U+uQAP571XnM9L6S5EzYseRD8n991hLNUXA0yajqMuBS4E0R+RG4Gxit\nqknuIgG4OgGI+/2fuE7yfyEiscAvuHqjnaOqtj9rjKk2PcKCuevKcTzBRPYdzifp57fQ5W86HVad\nI9qAMnNkZKTGxRX/W44xxpTul03JvDTnVW72mku7EH9ajv439Dnf6bCOGRFZpqplXu6rLE4fLjPG\nmFptWPcWXHDRRJ7LPZe0jFz0l9nw1zdOh1Vn+DgdgDHG1HbnnNCWQN9/0CGjJxL3IsQ+DAEh0GGQ\n06HVerYnY4wxFTCqVxh+AybACZeg+XlkLbzb7kVTAZZkjDGmEjL7T+HzzD5s3plMxie32pWby2FJ\nxhhjKsHLy5t5jS5lSW4Ptu3cRdant8LhFKfDqrUsyRhjTCX4+Xjx7MRBfNZqKqtz2rBt62ZyP5sG\n2enlV26ALMkYY0wlNfb34fnJw3ml8TVszmrK9k1/kvflXXadsxJYkjHGmKPQKjiA56acwkzfqWzP\nCGDn2l/R7/8D+flOh1arWJIxxpij1KVFIx6bPJqHuZJD+X7o5lhY/JRdfsaDJRljjKmCfh1CefSa\n8+k2cTZePr6wZgGseNvpsGoNSzLGGFNFx7cPxa/DADj5HvIRMn59EdZ/4XRYtYIlGWOMqSYZ7Yfz\nXPaZbNmTTsaiR2D7UqdDcpwlGWOMqSb+Pl6sa3YK7+cOJyH5ENlf3gPJm5wOy1F27TK3nJwcEhMT\nyczMdDoUY6qdt7c3oaGhtGjRAi8v27asKV5ewhPjTuCyl8fx3c79+CStpcsXt+Nz/gvQuGHe/t2S\njFtiYiLBwcF07twZESm/gjF1hKqSk5PD7t27SUxMpGPHjk6HVK8F+Hrz0hWDGPfsYZqlPYdv4jY6\nfnEbXuc+A/6NnQ7vmLNNGrfMzEyaN29uCcbUOyKCn58f7dq1Iz3d/pV+LDRr5MfLVw7jWd9JrMsI\nYVf8WvSb+yAv1+nQjjlLMh4swZj6zA6THVtdWjTiyStG8B+dzH5thO5YBj893uD+Q2PfOmOMqSGR\nnZvxzDVnctykZ/Hy8YcNC2H5G06HdUxZkjHGmBrUr0MoPq17wSnTyRcvMn97FTZ86XRYx4wlmTrq\nyy+/JCYmBhHhiiuuOGL8KaecQuvWrenXrx+PPPKIAxFWXP/+/Zk/f361tLVhw4bC5RIbG1stbRY3\ne/ZsjjvuODp37lzpujNmzCAhIaHIsPnz59O/f//qCc7UWgdbD2L24TFs2ZtO9nePQOIyp0M6JizJ\n1FFjxowp/BF98803+eCDD4qMX7RoEWPGjOHJJ5/kjjvucCDCiuvZsyfNmjWrlrbCw8NrLLkUuPHG\nG496md5///1HJJlmzZrRs2fPaojM1GYBvt7ENY5mXs5QEpIPkvfVPbBvs9Nh1ThLMnVcp06dOOOM\nM7jmmmvYuXOn0+Eclblz5xITE+N0GI6JiYlh7ty5TodhapivtxfPTRjAj6Hnsygrgu27k9GFd9T7\nG55ZkqkHXn/9dXx9fZk8eTJaSs+Vzz//nH79+hXpQTd58mRCQ0OZMWMGUPRQ08svv8y4ceOIiIjg\noosuIiMjg/vvv58RI0bQt29fVqxYUaT9uLg4oqOjGTp0KMOGDWP69Onk5rq6a3oeXnrzzTc588wz\nadmyJZMmTeLSSy+ldevWTJo0qUh7M2fO5Pjjj2f48OH079+fO++8k4yMDAA+/PBDhg4dysiRI4mK\niuLmm28mKyurUstsy5YtjBkzhhEjRjB8+HDGjRvHhg0bCscvXbqU6OhoBg4cSJ8+fbjzzjsL56e4\nHTt2HHGIbvbs2XTu3Lkwee7du7fw9U033URMTAzTp0/nm2++YfDgwYhIkT2cv/76izPOOIMBAwbQ\nt29frrnmmsLuxz/88ENhnffee4+xY8cSERHBJZdcUunlYI6tkCBfXpkcxSs+l/D74TYk7dwGX90F\nufX4c1PVBvMYMGCAlmbt2rVHDOt0+2elPt75bWthuXd+21pmWU9nPvVjhcpVVKdOnVRVdeHChSoi\nOnv27MJxV1xxhX7//feF77///nt1feR/i46O1unTpxcZBuh5552nubm5mpmZqV26dNHTTjtN//rr\nL1VVvf322zUmJqaw/N69ezU0NFQ/+eQTVVU9fPiwDh48WO+9997CMq+//roGBgbq008/raqqv/32\nm15zzTWFcV5xxRWFZV988UVt166d7tq1S1VVExISNCQkROPj41VVdfz48frxxx+rqmp2draOHj1a\n77///iPmwXPeizv99NOLxHf55Zfr66+/rqqqe/bs0ZCQEH3jjTdUVTUtLU2PP/54veuuu4rMT8Gy\nL22a06dP1+jo6HLjio+PV6Bw/gqWecE8ZWdn66hRo3TChAlH1PnHP/6hqq5l3q5dO33ttddKnWfV\nkr/n5tj7ZdNe7X/ne/r1PTG6b+Zg1a/vU83LczqsEgFxWoXfXduTqSfGjBnDjTfeyO23387atWur\n3N4FF1yAt7c3/v7+REZGkpeXR/fu3QEYPnx4kT2ZZ555hrCwMM4++2wAAgMDueyyy3jmmWeKtJmb\nm8vVV18NQFRUFC+88EKJ0/7Pf/7DxIkTad26NeA6JHj//ffTuLHr39KPP/544bR8fX0ZO3YsCxcu\nrNT87dixg+3bt5OXl1c4zVGjRhXOT1BQEBMnTgQgODiYf/zjH8ycObNwb6omvfvuuyQmJnLLLbcA\nrnm85ZZb+L//+z/i4+OLlL3kkksA1zIfNGgQK1eurPH4TNUN7daCW88dzAO5E0nJ9kG3xMKy15wO\nq0bYZWXKkPDImRUqNyGqIxOiKnapjs+uH16VkMr0yCOPEBsby2WXXcaSJUuq1FabNm0KXwcFBeHv\n71/4vlGjRhw4cKDw/apVq9izZ0+R8yrp6ek0adKEtLQ0mjRpAkBYWBh+fn5lTvfgwYNs27atMKEV\nuPHGGwtfHzhwgNtuu42tW7fi5+dHUlJSpQ8T3X///UycOJHvv/+eiy++mCuvvLLw5Pvq1avp1q1b\nkUOL3bt3JzMzk02bNtG3b99KTauyVq9eTVhYWGFSLZi+qrJ69Wq6dOlSOLxt27aFr4ODg0lLS6vR\n2Ez1mRDVkbAmZ9I1qBfy1Z2w/C0I6Qg9T3M6tGplezL1iL+/P++++y7r16/nvvvuO2J8SVc0KNiS\nL87b27vM98VFREQQGxtb+Fi6dCkJCQmFCaYibVREeno6J598Mk2bNuWnn34iNjaWO+64o9RzUaU5\n77zzSExM5M4772TRokX07t2bjz76qMrxeSpt2VYnz2UqIpVeDsZZp0SE4dVpMAy9nnyFvNhHYdef\nTodVrSzJ1DMRERHMnDmTxx57jN9//73IuODgYMC1t1Bgx44dVZ5m37592bx5c5Ef1f379zN16tRK\ntxUcHEzHjh3ZtKno5dHfeusttmzZwvr169mzZw8XXXRR4Q9sdnZ2pafzwQcfEBISwjXXXMPSpUsZ\nO3Ysr776KgB9+vRhy5YtRX6wN2/eTEBAwBF7WMVjL2/ZeiZ6z7Ke+vTpw+7duzl06FCR6YsIffr0\nqfhMmjpjT6czePNgf7YlHyD/q7vhQNXXy9rCkkw9dO2113LOOeewbt26IsN79OhBo0aNWLx4MeD6\nL82ePXuqPL3rrruO7OxsXnzxxcJh//nPf2jevPlRtXf33Xfz1ltvkZSUBLh6vc2YMYPWrVvTuXNn\nAgMDWbRoEeDaW/j0008rPY3i565ycnIKD5ddd911pKen88477wBw6NAhnn/+eW655RYCAwNLbbNf\nv36Fy3b37t18//33R5Rp1aoVKSkp5OTk0K9fvxLbmTBhAu3bt+fJJ58EXOeyZs2axSWXXFLkUJmp\nP7Jy8nkmYzSxh7uStGcPfHkHZJW8EVLnVKXXQF17VLZ3WW22cOFCjY6OVn9/f42OjtYVK1YUGZ+c\nnKzt2rU7oifTa6+9pt27d9eTTz5ZH374YY2OjtZOnTrp3XffrYmJiRodHa2AnnDCCbpo0SK97bbb\nNCwsTMPCwvS2227TRYsW6QknnKCARkdHa2JioqqqxsXF6YgRI7Rfv3560kkn6bRp0zQnJ0dVVV95\n5RUNDw8vjHXRokWF8UyYMKGw/SlTphQOf+KJJ7RPnz46fPhwHTlypMbFxRWOW7BggYaHh+vAgQP1\nvPPO08mTJxe2vX79+iLzMG/evBKX3+zZs3Xw4ME6cuRIHTRokE6ePFkPHjxYOH7JkiU6fPhwjYyM\n1N69e+vtt99eOD9PPvlkkfkpqLd06VLt06ePDh06VKdOnarTpk3TkJAQPfPMMwvbffbZZzU8PFyj\noqL0+eef16+//lqjoqIU0KioKP3pp59UVXXjxo06ZswY7d+/v/bu3VunTp1aOJ24uLgiddasWaN3\n3HFH4XK88cYbS/3e1LXveUPye/w+Pf6u+frpPadp8hODVT+9WTU3x+mwqty7TLQBHcONjIzUuLi4\nEsetW7eOiIiIYxyRMceWfc9rtw+WJfLovFhm+b3AiS2h0QnnwfBbwcErxIvIMlWNPNr6drjMGGNq\niQsHtOfck/rzQM5lbNqXRfbqj2HVB+VXrMUsyRhjTC1yx+nHEdb9RP6XfQEp6dnw23Ow/ffyK9ZS\nlmSMMaYW8fH24ulLTuSUM8cTFnMNaD58ez+kbnM6tKNiScYYY2qZ0CA/Jg/rggyYBF2Go9mH4Ms7\n62SPM0syxhhTW3l5sfPEm/lpXxPSdifAogcgP9/pqCrFkowxxtRin65NZVraeNamCJnxv8GSkq/5\nV1tZkjHGmFps6vCuDOgTwYPZFxO/L4PcP+bWqds3W5IxxphazMtLePyiE8gLO54nM89ie8ph9MfH\nIWm106FViCUZY4yp5Rr5+/Dy5ZEsCRjK3PRIklIPwtf3wKG9TodWLksydVR8fDwxMTEEBAQU3oHR\n8xEQEOB0iIWWLl1Khw4dyMzMdDoUUlNTmTFjBqmpqRWu43nH0II7X1bEPffcU+TumBU1Z86cSk3H\nNAwdmgXx3IT+vK5nsuhAO9IPJMPXd0OO8+tVWSzJ1FFdunQhNja28NbFnpfZLxheWwQHBxMeHo6v\nr6/ToZCamsr9999fqSQTHh5+VD/6Dz300BG3la4ISzKmNEO7t+Ces/uSe/J0glp0gL0b4IdHoRZf\nHsxuWlZPvfHGG06HUOi4447j22+/dToMY+qFy4d0dr1I+S989E/Y/B007wYnXuZoXKWxPZl6JiEh\ngZiYGKKjowGYPXs2bdu2JSAggOnTp5OUlMSJJ55ImzZtmD59Ou+99x79+vVDRHj77bc57bTT6Nmz\nJ2eccUbhpfYLzJw5k379+hEdHc2IESP47rvvCsedfvrphIaGcvvtt/PPf/6T6OhovLy8ePrpp484\n1HTnnXcWHkZ67LHHGDlyJD169OCLL77gjz/+YNy4cYSHh3PDDTcUmX5ubi533nkn/fr1IyYmhlNP\nPbXwdsMHDhwoPEz42GOPMXHiRAYOHMiQIUMKb1m8atUqLr74YgAuvvhiYmJieP755wH48MMPGTp0\nKCNHjiQqKoqbb7650nfbBHj55Zfp2rUrJ510ElOmTClyTxiAbdu2MW7cOIYMGcKIESM49dRTi9xy\n4NJLL2XlypXMmTOHmJgYzj333ArVMw1Qsy7sGTiNnWlZ6NJXYOtipyMqWVUu4VzXHpW61P8LI5x5\nVFKnTp10+vTphe/j4+M1Ojq6SJklS5aot7e3fvLJJ6qqevHFF+vixYsLx3///fcK6A033KCqqrm5\nuXrmmWfq6NGjC8u88sor2r17d01JSVFV12Xt/f39dcOGDYVloqOjtX379pqQkKCqqtdff73++OOP\nqqoKFLntwPTp07Vx48b6ww8/qKrqSy+9pGFhYfrYY4+pqutWBUFBQRobG1tY55577tFhw4ZpRkaG\nqqrOnz9fQ0NDdd++fUWWx8CBAwsviz927Fi9/PLLiywfQOPj44sso/Hjx+vHH3+sqqrZ2dk6evRo\nvf/++4uUKT4PxS1evFi9vb11yZIlqqq6adMmDQsLK/J5LFy4UC+44ALNz89XVdU333xTe/bsWXgb\ngYLl6PmZVrReRdil/uuPnNw8HfHYdzrtrmma9L8o1ddOV92/rdqnQxUv9W97MvVAwVZvTExM4Za6\np0GDBnHTTTcxdepUnnvuOcLCwhgyZMgR5Qr2HLy9vbnhhhv46quv2LhxIwAPPvggU6ZMoWnTpgBE\nRkbSt29fXnih6B/DTjnlFDp16gTAU089xfDhw0uNOywsjBEjRgAwbNgwdu/eXRhX8+bN6dWrFytW\nrAAgIyODJ554guuuu66wU8PYsWPx8fHh7bffLtLu2WefTePGjQGIiYkp3Nspy+OPP87ZZ58NgK+v\nL2PHjmXhwoXl1vP09NNPM2TIEAYNGgRAt27dGDVqVJEyJ510Ei+99FLhHTLHjRvHxo0b2bx5c5lt\nH209U3/5eHsx45zefJAfzYLU7qQdPODqCJCd7nRoRdg5mdJc84PTEVTYpEmTmDFjBuA6XFbSyeYH\nH3yQjz76iAceeKDUH6aC5ACuH0hw3X+kTZs2bN26lTfffJMvv/z7T2CHDh064nBQhw4dKhx3mzZt\nCl8HBQUdMaxRo0YcOHAAgE2bNpGRkcFjjz1WJLGFhoYecRK/bdu2ha+Dg4NJS0srN5YDBw5w2223\nsXXrVvz8/EhKSqr04bJ169bRt2/fIsM6duzI9u3bC997e3sze/ZsvvvuO7y8vAqTRlJSEuHh4aW2\nfbT1TP02MrwVt5wazpPfnE+XlBeJ8YnH//v/wqgHwat27ENYkqlnOnfuXGLPpMDAQHr37s3nn3/O\n8uXLy9zDKM3NN9/M1KlTyyzj7e1d4fZKKlt8mBbrNfPoo48esXdQVhsickQbxaWnp3PyySdzwQUX\n8Pbbb+Pt7c2cOXMKE3dVSLGbTU2bNo3PP/+c3377rbAHYEViPNp6pv7718ju/JGYyox1l/JCykv0\n9foZr5VvQ//LnQ4NsBP/9dbnn39eZC9j7ty59O3bl6uvvpopU6aQkZFxRJ1t2/6+lHjB3k5ERATB\nwcF06tSJDRs2FCm/YMEC3nnnnRqag6K6d+9OQEDAETG8+OKLfPPNNxVux6vY1t3BgwdZv349e/bs\n4aKLLipMUNnZ2ZWOMSIigi1bthQZ5rlMAX788Ueio6MLE0VJ0/GM8fDhw+Tl5VWonmmYvLyEmeP7\nEdCiIw+kn09iagYa9xps/dXp0IBakGRE5BwRWSoiP4rILyJS5m0+RaSJiMxx11kuIo+KiO2RFfO/\n//2P5ORkAJKTk3nhhRe49957efTRR8nIyGD69OlH1Hn55ZcByMvL46mnnmL06NH07NkTgHvvvZe3\n3nqLhIQEAFJSUrj33nuPODxUUwIDA5k2bRrPPvss+/btA1yHBh9//PFKxdCiRQu8vLxISUkhKSmJ\nk08+mc6dOxMYGMiiRYsA1/x/+umnlY7x+uuv59dff+X33103mIqPj+fzzz8vUqZXr1789ttvpKe7\njpsvWLDgiHZatWpFSkoKAOeffz7r16+vUD3TcDUJ8OWFywbwl39vtnW9xPW/me8egtTt5VeuaVXp\nNVDVBzAAOAT0cr8/C9gHtC6jznzgLfdrP2Ax8N+KTK9Svctquc2bN2tUVJT6+flpu3btNCoqqsgj\nODhY4+Pjdd68edqzZ0/t2rWrxsbG6sKFC7VDhw7q7e2to0aNUtW/e5d98sknOmbMGO3Ro4eOGTNG\nd+7cWWSas2bN0oiICB02bJiOGDFCP/vss8JxF154oYaEhGinTp0K21VV/fPPPzU6OloBPeGEE3Te\nvHn60EMPaadOnTQkJEQnTpyoa9as0aioKAU0KipK16xZoxMnTixs76GHHlJVV6+3u+++W8PDw3XE\niBF6yimnFPaSy83N1ejoaPX399fw8HB95513dO7cuRoeHq7+/v5Fenjddddd2rt3bx00aJB+9NFH\nqqq6YMECDQ8P14EDB+p5552nkydPLqy3fv36I+ahNC+//LJ26dJFhw4dqhMmTNDrr79eQ0JCdMyY\nMaqqmpiYqKeffrp26dJFzznnHJ0xY0ZhuwsXLlRV1V9++UUjIiJ0+PDhOmnSpArXq4i69j03lZN6\nOFs1P1/1q3tcvVXfu1w1K71KbVLF3mWiDh7TFZEPAFHVCzyGrQU+VNV7SyjfB1gFHK+qq9zDxgFz\ngFaqeqh4HU+RkZEaFxdX4rh169YRERFxtLNSp8XGxjJy5Eg7vt8ANOTveYOSfZj096/G7+A2fLtF\nw6gHoNj5wYoSkWWqWuYRprI4fbjsVKD4r/5SoLQzu6cCmYDn5UeXAoHASdUenTHG1EFLd2Zy3qbT\n2ZiST378j7Di7fIr1RDHkoyINANCgF3FRiUBXUup1hXYrUU3uZM8xplKeu+997jpppsA139KNm3a\n5GW0M/gAAAqeSURBVHBExpiq6tKiEQf9WjP90FiSDmRB3KuQWPJRnJrm5J5MI/dz8T8jZAFBZdQp\nqTyl1RGRq0UkTkTi9u6t/ZfFPtbGjx/PypUrUVViY2Pp3r270yEZY6qoRWN/nr30RFZKBE8eOIn4\noOOh5XGOxOJkkin4W6p/seH+wOEy6pRUntLqqOpLqhqpqpEtW7Y8qkCNMaauGdCpGXefGcG8vGhe\nDrwS/Bs7EodjXX9VNUVEUoHi16RvDZR2rYwtQCsREY9DZgX1q3x9DVU94s9zxtQX1rGj4Zk0tDOd\nWzQipqdzG9hOn/j/FijeayHSPbwk3+A6yd+7WPkM4JeqBOLt7U1OTk5VmjCmVsvIyKgV9/Qxx46I\nMDK8laMbz04nmUeA0SISASAiZwBtgGfd7x8SkdUiEgCgqmuABcBt7vG+wI3Ak+V1Xy5PaGgou3fv\nJj8/vyrNGFPrqCqHDx9mx44dtGrVyulwTAPj6D/lVXWZiFwKvCkiGYA3MFpVC3qMBeA6oe+ZhicB\nT4vIUnf5b4H7qhpLixYtSExMPOKyJcbUB76+voSF/X979x4rR1mHcfz70LTFtBQBsdWKRWIU0SoI\nSlBTGm1TREOEGEJUsGKjGGmqJKSQFIOtoTVeoKLBQMCDipeCBFGIIsRTBMT0QgNCKgophkuxQMEK\nLZfm5x/zrqzTc/acmZ3Z2dPzfJLJnrmdeZ/M7L4778zOO51p06Y1XRQbZxr9MWavdfoxppmZ7Wms\n/xjTzMz2Yq5kzMysNq5kzMysNq5kzMysNq5kzMysNuPq7jJJ24BHSq7+OuCpCovTD5xpbHCm/re3\n5YFXM82KiNKPDBhXlUw3JK3v5ja+fuRMY4Mz9b+9LQ9Ul8nNZWZmVhtXMmZmVhtXMqN3edMFqIEz\njQ3O1P/2tjxQUSZfkzEzs9r4TMbMzGrjSgaQdJKkdZJul3SnpI53VEiaJmkgrbNR0jclNfpE67yi\nmdI675P0gKSBHhSxsCKZJE2XdJGkOyQNSrpH0vljeT9JmixpRcp0W8p0g6S+6jO7zLGX1psiaYuk\nwZqLWFiJz4jN6bhrH5b0qryjUfIz4ixJa9M6/5B01YgbiohxPQBHA/8BjkjjHweeBmZ0WOd64Cfp\n70nAXcBFTWfpMtNSsm4T7gcGms7QbSbgbGADsF8aPwTYBixvOksXmWYAjwPT0/g+wBpgfdNZujn2\n2tb9DrAdGGw6R7eZ+i1DRZmWAr8BJqfx9wD/GnFbTYdtegCuA36Vm/YAsGKY5d8FBDC7bdqpwAvA\n1KbzlMmU5p9E1m/PYJ9WMkX306nAablpPwAeajpLF5kmAUflpi0Gnm06S9lMbcscBdwOXN1vH9Al\n3099laHbTMBBZD0Qvy03fc5I23JzGcwD8p3MrAPmd1h+F/DX3PKvAT5UeenKKZqJiLgx0lHTpwpl\niog1EfGL3OSdwOQaylZW0UwvRcQ9rXFJM4HPAqtrK2FxhY89SfuQfQH4MtkXuH5TONMYUDTTicBz\nEfFg+8SIuH2kDY3rSkbSgcD+wBO5WVuBw4ZZ7TDgydwH8ta2eY0qmamvVZjpOLLmpcZ1k0nSTEkb\ngIfImji/XkshC+oi09nAnyLivrrKVlYXmaZIuipduxiUtKzVjXzTSmaaDTwuaZGkP0q6S9IPJY34\nuJlxXckAU9Lri7npL5J1+zzcOkMtT4d1eqlMpn7XdSZJ84A3A8srLFc3SmeKiMci4mhgFvBB4Nrq\ni1dK4UyS3gQsok8qyiGU3U9/Ay6LiDnAJ8nOBK6rvnillMl0ANmlguPJznaOB14LDEqa2Glj472S\neT695ptQJpNdYxlunaGWp8M6vVQmU7/rKpOkWcBlwEkR8WzFZSur6/0UEU8CXwFOkfThCstWVplM\n3wPOj4h+PTZL7aeI+ExErEt/PwVcAHxM0pG1lLKYMpl2AxOBCyPilYh4GfgacASwoNPGxnUlExHP\nAM+S3bXTbgZZU8RQHgZeL0m55emwTs+UzNTXuskkaTrwa2BR+/WMppXJJGmCpAm5yQ+k13dWW8Li\nimaStB9wJHBu6zZf4ATgyDS+suYij6jC91Nr2cZvNy+Z6dHcK7z6RPu3dNreuK5kkluB/P3hx6Tp\nQ/kD2UX+9jf1MWQXle+svHTlFM00FhTOJOkA4Ldk35TXpmlfqK2ExRXNdDrw1dy0N6bXxyosVzdG\nnSkidkTEYRExtzUAvwM2pfHz6y/uqBTaT5JmS1qUmzwzvf6z4rKVVfTYW5te39A2bXp67Zyp6Vvp\nmh7I7hffAbwjjZ8IPEO6Xxz4BtmdZPu2rXM9cHX6eyJwB/33O5lCmdrWHaQ/b2EulAmYCtwNrExv\nntawoeksXWRaCGwGDm479n5G9o1yWtN5uj320vw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ZAr3ym/ucsDd0mt6PSk2cqa3rJFleG2cuBdh3zErjPIkzXbQ4QwvvcP/9n6pGdpqKrOkpMo21+yX5HN52op3hPqf99rsxXnafa+GMr4/nT+z79fhSCddfFY51ianqIvYFDneJyJHJ0otIUxGJHAXQvphq/ObsqyVL6fwo4zkX/r+JiCQLCCrD9fcZ97kR8EKy8kZ+T7kdS8PDj68QkTOTbUREGhRTixQ+N2ckSVMilSZocD2BM1shwDMiMk5EThaR5iLS0P0QnyYiz+JMixr5Kw1V/ZJ9F5VzcYYZXSDOPOcN3Q/sABH5K07P6kfLaT/C43qPF2cO9p4isr84c9s/BbxACXp2l4Nwr9z+7hCzHHHmOc9wL5BhZXo/qoBBwDoReVFEhohz/4BGItJGRE7D+bUQ/mWbrNq6OGuBj0TkWhFpLc59KH6PcyI3wamOjRrto6rr2VfzcJeI3CUinUWksYj0x5kv5WK8/RyFh8D2LOYiXiaqOpd9F9LLxBkSeYT7uT1IRB5l30V6HvDPEq6/Khzr0roap1q6Ns7Q6cfcY9fYvSYdLCIXishbOM1jkcMPLwdWi3OPiMER19F2InIuzvkhOJ0F30mxPGU558LXrdrA3e51KNO9bkV+l3l+/XXntXnO/fd8YJo491xp4e7vQSJyhYhMxZmoKdKtwA84NSXjxbnvx7HudaORiBwoImeLyMs415a4waCIZOPMYAz75nRIy86lMnvWpeybfWpASWaPIuLeEymmbwC8H7G9ZI9r4uT3AfdRdD72eI+3S7Iv7vqLnRESJ/qel2S73+G80anMIFceM0K2IP49QIpsryzvB9GzIrZKUp6E+5PqvpJkdkMSz06Xyv1EQsB9pTjGsfee2JBg/cnuPdGVfdN0x3u8gdPrPO75VdxnNdkxS3Efm+NUpSrQP0m6hJ/lEpS1vO89Ud7HuthjUIKyJryvQ4L0B5P8vi+Rn/WuEflSuVdNAXBVRZxzOAHKVwnyfBaRrkzXX6JnhLwoxXO8yPUN50v/2RT2N969J1riTD1dXF4FTk1QvkHu8j0kmA20NI/KVtOAqm5T1TNwZl17DafqcBfOh3MTzi+Ce4EeqvqPOPlDqjoC50R5GucDsg3n4rwNZ9zs8zgTQZXLjJDq3Jb0WJzgZSnONKzbcG7IcztOlVFaOqWUsnwbcHosv4FTQ5BwKGxZ349K7k3gdJzPyWycqD0fZ173ZTj3OzjS/TyVxXKcexs8i3P89uK8///BuWA9Hy+TOtXLPd1yrMc55r/gzKB5oapeiHNR8IQ6M1r+1/33onLe1h5VPQunf8j7OPeOKcD5op+G0zxxuFum0qy/Uh/rslDVxThNN5fh3ORoA87nfA9uLRjOMMpW7nEIewJnivYXcL6EN+Aclx049/B5Duiuqi+WoDilPufU+SY82S3XEjdPvP2tFNdfVQ2q6p/d7Y3GOfd344yuWIozGVm4xiY273qca/RZbro1OO9XPs6cG5/j1Eh0VNUPExQhfE6+p4lnAy0xcSMSY4wpMRE5GfgYZ+RSM03fbIfGmFJy+4b8glPrcpyqTknXuitdTYMxpkr5BOdOeg3xdkSQMWafK3AChlnpDBjAahqMMWXkdhacitNrvbMmuIGSMab8uR0gV+D0izhKVWenc/1W02CMKRNVnYbTt6EdpZzkxxiTNn/ECRjeSXfAAFbTYIwxxpgUWU2DMcYYY1JiQYMxxhhjUmJBgzHGGGNSYkGDMcYYY1JiQYMxxhhjUmJBgzHGGGNSYkGDMcYYY1JiQYMxxhhjUmJBgzHGGGNSYkGDMcYYY1JiQYMxxhhjUmJBgzHGGGNSYkGDMcYYY1JiQYMxxhhjUmJBgzHGGGNSYkGDMcYYY1JiQYMxxhhjUmJBgzHGGGNSYkGDMcYYY1JiQYMxxhhjUmJBgzHGGGNSYkGDMcYYY1JiQYMxxhhjUmJBgzHGGGNSYkGDMcYYY1JiQYMxxhhjUmJBgzHGGGNSYkGDMcYYY1JiQYMxxhhjUmJBgzHGGGNSkuF1AWqyxo0ba9u2bb0uhjHGVCnz5s37VVUP8LocNZEFDR5q27Ytc+fO9boYxhhTpYjIaq/LUFNZ84QxxhhjUmJBgzHGGGNSYkGDMcYYY1JiQYMxxhhjUmJBgzHGGGNSYqMnqpCho77g27XbyA+GSr2Outl+Ft47KI2lMsYYU1NY0FCFbNi6B0XLtI4de4O0ve2DEuWxQMMYYwxY0FAl/cE/icH+rwiqjwB+QvgI4COInyA+gvjYo1nspBa7qMVOrcUusp3/tRY7qMUWrcdm6rFV65HHfoAk3F5xgYYAvds24p1hR6d/Z40xxlQaFjRUQbnyC0f4vk/b+grUzxbqsVnrsUXrsZGG/Kz785PmuI/9+Vlz+JX6aJxuMArMWbUlbmBhtRTGGFN9WNBQBY0OnsQnwd74JESGW7/gJ0QGIfwEySBEtuRTm73UYQ+1ZY/zzF7qyB7qsYuGsoMc8mgkedSVPTRhK01ka9Lt5qufn3R/VmtTVmkz99n5e602IZ/MInni1VJYzYQxxlRNFjRUQWu1KWtpShm7NxTKJp+G7CBH8siR7TRlC81lM83lN5rJZprLZprJZvaXPHLlF3L5hWNZELWOkAob2J9loVYs09YsDbViqbZmhbZgL1lRaePVTFggYYwxlZ8FDVVIi4a12JS3l7RFC669ZLGRHDZqTtJVZ5NPK9lErmykrWykrfxMW/mZXNlIK9lEK/mVVv5fOY7/FeYJqI9V2oyl2ooloVy+0/Z8F2rPVupFrTteIGFNG8YYU7mIanq/gEzqevfureV5w6pD7v6YHXuD5bb+SJkEaCMb6STr6Sxr6exbS2dZS1v5Gb8U/YytCR3Ad9qeBaH2fKftWRhqRx61k27DaiOMMQAiMk9Ve3tdjpqo2gcNItIZGAT0AXoDB+J8/wxV1XGlWN9o4JIkSZaqapdU1lXeQUNppDvQyCafDrKBzrKWQ3yr6O5bwSGyiv0kPypdSIWl2pqvQ52ZG+rM16EubCQn6bqtJsKYmsmCBu/UhKDhKWB4nEVlDRpmAcvjJPlJVW9PZV2VMWgoztBRXzB31ZYyNZD4CdJR1tPd9yPd5Ue6+X7kYFlNlkQHK2tCBzBHnSDiy9DBrNJmJBsaakGEMTWDBQ3eqQlBw5U4tQtzgXnAy0B/yh40XKaqo8tStqoYNCRTllqKbPLpISvo41tKH99SevmWUU92R6VZp42ZEezGrNAhzAp1ZQv1E67PAghjqi8LGrxT7YOGWCIyFQsaKkxpayZ8hOgia+jjW8rhviUc7VtMI9lRuDykwiLNZVaoG9ND3ZgT6kJBgn691hfCmOrFggbvWNBQ8vyjsaChTEoTSAghusoq+vkW0s+3gD6+ZWRLQeHy7bof00PdmRzsyZTQoUVGZ0SyWghjqjYLGrxjQUPJ84/GCRrGAr8BdYGNwEzgU1VN+W5SNTVoiKekTRvZ5NPHt5R+vgUM8H1LF9/awmVBFeZrJyYHe/JZqCfLtSXx+kJYDYQxVZMFDd6xoKHk+UeTePTEYuA8VV2QYHkUCxoSK2ltRCv5heN933C8bz5H+hZHdapcEWrOB6Ej+DB4JN9rayyAMKZqs6DBOxY0lDz/DUAQmAysBuoDPYEHgB7AL0BPVV2fIP9VwFUAbdq06bV69epS7EXNU5KaiDrs5hjfAk7wz+c433xyIvpCrAg156PQ4XwYPILFmosFEMZUPRY0eMeChvStNwuYBhwJPK+q1xWXx2oaSi/VIMJPkCN9ixns+4qT/XPYX/IKl60MNWVi6CgmBPuyQlvGzW/9H4ypfCxo8I4FDeld9xnAf4CVqtq+uPQWNKRHSQKII3xLCgOIxrK9cNn/Qu15L3gM/w0exeY4Qzmt9sGYysOCBu9Y0JDedR8ILAXyVTW7uPQWNKTf0FFf8O3abeQHk/dH9RPkcN/3nOmbxan+rwrnhChQP9NC3XkveAyfhXoWudkWQJbfR4/WDSyAMMYjFjR4x4KG9K77KOALYLOq7l9cegsayl8qtRDZ5HOibx5D/DPp7/uWDHECju26H/8J9uWt4HEs0rZx81rzhTEVz4IG71jQkN51PwncAExS1WK/SSxoqDipjsbYn22c7v+SIf6Z9PD9WPj6d6F2vBU8jveDR7Ejzo21rPnCmIpjQYN3LGiIn+YhYAjwXuR9JETkUKAV8JGqBiNezwCuBx4DfMAgVZ1UXFksaPBGqk0YB8pazvd/zhD/TBrKTgB2ajYTg0fxVnAg32hHYkdfWPBgTPmzoME71T5oEJGewN8jXjoYqAf8AGwOv6iqR0bkGY0zF8MYVb004vUzgffcfMuAde66ugEtgBBwu6o+mkrZLGjwXio1ENnkM8j3NednTOFI35LC1xeHchkdPIn/BPvG7ftgAYQx5cOCBu/UhKBhADCluHSqWviTMUnQ0A7njpmHA7nA/oDiBA8zcIZazku1bBY0VC6p9H9oJz9xrn8KZ/unF46+2KJ1eTs4kNcCJ7CeA4rkseDBmPSyoME71T5oqMwsaKicUq19GOybzSUZnxT2fQiq8GmoN2OCJ/Fl6GCs6cKY8mFBg3csaPCQBQ2VX/EBhHKYLOeSjEkM9n1Fpjt99feh1rwUGMz7oaOL3H3TggdjysaCBu9Y0OAhCxqqluKaLw5gCxdmTOZC/2QOkG0A/KQ5vBo4mTeDx5MXZ9SFDdk0puQsaPCOBQ0esqChaiqu9iGTAL/zz+KP/g/o7FsHOHM+/Ct4PK8GBrGRnCJ5LHgwJnUWNHjHggYPWdBQtRU3dFMIMcD3LVdnTCwcdZGvft4P9eUfgdPj3u/CggdjimdBg3csaPCQBQ3VR3G1D91lBVdlTOQU39f4RQmp8EHoCJ4NDGGZti6S3oIHYxKzoME7FjR4yIKG6qe44KGNbORq/0SG+qeS5Xaa/DjYh2cDQ+JOVW33uTCmKAsavGNBg4csaKi+igsemvEbV2dM5AL/52RLAQCfBQ/j2cAQvtWORdJbzYMx+1jQ4B0LGjxkQUP1V1y/hwPYwlUZH3CR/zP2k3wApgR78ERgKAvj3F3dggdjLGjwkgUNHrKgoWZJNmRzf7ZxZcaH/MH/CXVkLwAfBg/nb4GzWa6tiqS34MHUZBY0eMeCBg9Z0FAzJQseGrGdqzMmcql/ErWkgKAKE0L9eCrwe9Zq06i0NkmUqaksaPCOBQ0esqChZksWPDRhC9dlTOB8/+dkSpAC9fN2cADPBobYPA+mxrOgwTsWNHjIggYDyYOHVvILN2S8yxDfDPyi7NFMXgmewt8DZ7AjZoZJq3kwNYUFDd6xoMFDFjSYSMlGXHSQ9fxfxjuc6v8agF+1Pk8FzuKt4EACMfe2sFoHU91Z0OAdCxo8ZEGDiSdZzcOhspw7M1+nj28ZACtCzXk4cD6fhnoRe1dNCx5MdWVBg3csaPCQBQ0mmcTBg3Kybw63ZbxJO99GAL4KdeGBggv5TjtEpbQmC1MdWdDgHQsaPGRBg0lFouAhkwAX+CczPGM8ObIDgAnBo3mk4Hx+Yv+otDazpKlOLGjwjs/rAhhjklt47yD6tG1Elj/6dC0ggzHBkxmw90lGBU5nr2Zwpv8LJmffxLX+CWSTX5g2PxhizqotHHL3xxVdfGNMNWI1DR6ymgZTGolqHlrJJm7PeIPBbmfJ1aEmjAxczORQT6y/g6lOrKbBOxY0eMiCBlNayUZaHO1byD0ZYzjQtx6AqcEe3Bv4Ayu1eVQ66+9gqioLGrxjQYOHLGgwZZWo1iGDABf7P+UvGeOpL7vIVz+vBE/l2cCZ7GS/qLRW62CqGgsavGNBg4csaDDpkih42J9t3JzxNuf4p+ETZaM2ZGTBH/ggdASRTRZW62CqEgsavGNBg4csaDDplOyOmt1lBSMzR3OobwXgNFncFbiMddokKp0FD6YqsKDBOxY0eMiCBlMeEvV3EEKc55/CbRlv0kB2sVuzeCbwe14KnmqzSpoqxYIG71jQ4CELGkx5StRk0Zht3JX5Gmf6vwBgaagVdxRcwTztHJXOah1MZWVBg3csaPCQBQ2mIiQKHvr5FnBfxiuFs0r+KzCQRwLns426Uems1sFUNhY0eMcmdzKmmgtPDiXSIlfaAAAgAElEQVQxr88MdWNQ/iM8HRhCvvq5IGMKk7Nv4lTfbIho3NixN0i72z5g6KgvKrTcxpjKx2oaPGQ1DaaiJap16CDreSDzFY70LQHgo2Af/lpwGZtoGJXOpqM2lYHVNHjHggYPWdBgvBIveBBCnO+fwu0Z/6Ke7Gar1uHegj/wXqgfNqOkqUwsaPCONU8YUwPFa7JQfPwreDwn732EqcEeNJSdPJn1D17JfIzm/BaVf8feoN3HwpgayGoaPGQ1DaYyiN9koZzlm8FfM8fSQHaRp/vxYOAC3gweh00KZbxmNQ3esZoGY2q4+B0lhfGhYzlh72N8EuxFPdnNQ5kv80bmg7RkU2EqBbt7pjE1iNU0eMhqGkxlk6jW4TTfbO7NHM3+ksd23Y97Cy5hfOgYrNbBeMFqGrxjNQ3GmELhWocsf+SlQZgYOoqT9j7KpGBv6stunsgaxajMp8hhe2GqcK2DDc00pvqymgYPWU2DqcziT0etnO2fzt0ZY6knu9mk9bmt4I9MDvWKSmW1DqY8WU2Ddyxo8JAFDaYqiNdk0ZJNPJ75Akf5FwPwVmAA9wUutttumwphQYN3rHnCGJPUwnsHUTfbH/Xaeg7ggoI7uK/gQvZqJudlTOWjrNvoI99HpbOhmcZULxY0GGOKlWheh5eDgzkt/wEWhtrSxreJt7Pu48aMf+NnX82ETUNtTPVhzRMesuYJUxXFa67IJMD1Ge9yrf8/+ESZF+rE8ILrWKcHRKWz5gqTDtY84R2raTDGlEi8ERYFZPBE4BwuKLiTnzSHXr4f+DDrdk7zfRmV15orjKnarKbBQ1bTYKq6eLUODcnjkcyXONnvfLb/HejPPYFL2EWtqHRW62BKy2oavGM1DcaYUovX12Er9bi64C/cVXAZezSTczKm8d+sO+kqK6PyWq2DMVWP1TR4yGoaTHUSr9bhQFnLM5nP0cW3lnz180jgfF4OnoLNJGnKwmoavGM1DcaYtIg3NHOZtuZ3+fcxNnAiWRJkRObrvJj5N+qzozCN3b/CmKrDggZjTNrEa67YSxZ/DVzGVfl/YbvW5iT/PCZm3Uk3+TEqrzVXGFP5VfugQUQ6i8hwEXldRL4XkZCIqIicXcb1XiAiM0Rkm4jsEJG5InKtiFT7Y2pMMu8MO5qVDw8uUuvwSagPg/Mf4LtQO9r4NjEu6x4u8n8KERNV25wOxlRuNeEL7hrgKeBCoDPE3AG4FETkeeANoDcwA/gUOBB4DhgnIv4k2Y2pEeLVOqzVppydfw9jAieSLQHuz3yVZzOfpQ67C9PYja+MqbxqQtCwEHgMOBfoCEwry8pE5CzgT8DPQHdVPU1VhwCdgCXAEOC6MpXYmGoiXq1DPpncHbiM6/L/zA6txen+2byfdRddZE1UXuvnYEzlU+2DBlX9p6reoqr/VtUVaVjl7e7zrar6Q8R2NuLUagDcZs0UxuwTr5PkxNBRnJF/P0tCreng+4kJWSMY6p8alcaaK4ypXOyLrQREpBXQC8gH3oldrqrTgPVAM+DIii2dMZVbvOaKH7UFQ/JH8lZgALWkgMcyX+SBjJfJoqAwjTVXGFN5WNBQMoe5z4tUdXeCNHNi0hpjXPGaK/aQzW2Bq7i54Cr2aiYXZkzmraz7aMrmqLzWXGGM9yxoKJl27vPqJGnCDbPtkqQxpkaL11zxTnAAZ+XfzTptTE/fciZm32m32jamkvE0aBCR/UXkbBF5QET+KSLjROQl9/+zRGR/L8sXR133eWeSNOFZa+qVc1mMqdLi3fhqobbnjL33MyvYlQNkG//KeoBL/R8TOyzTAgdjvJFR0RsUkQxgKM4IhKNwhkDGGwapgIrIF8DfgXGqGqiwgsYXLmep594WkauAqwDatGmTjjIZU2WFp46OnIJ6M/X5Q8Ft3KJvcXXGB9yTOZZuvh+5s+AK9pAN7OsgadNPG1OxKrSmQUQuBlYCrwN9gU3Af4AHgZtwvkxvAh4C3neX98OZE+FHEbmoIssbR577XDdJmvCyvHgLVfVFVe2tqr0POOCAtBbOmKoqtrkiiJ+HAhdyXf6f2aXZnOWfyfise2glvxSmsemnjal4FRY0iMhXwGjADzwBdFPV5qr6e1W9S1X/5g6P/Juq3qmqQ1S1OdAdeBKnVmSMiMyuqDLHscp9zk2SpnVMWmNMCsLNFZEmho7izPyRrAo1patvNe9n3cWRvsVRaay5wpiKU5E1Da2B64Fcd96ERalkUtWFqnoTzhf1cMDLOv1v3OeuIrJfgjR9YtIaY1L0zrCjiwzLXKatOSP/fj4PHkqO7OC1zIe4wD85Kp/N52BMxajIoKGDqj6vqgXFJy1KVQtU9TmgQ5rLVZIyrAXmA1k4/TKiiEh/oBXObJFfVmzpjKke4g3L3E4driy4iRcCg8mUIA9mvsy9Ga+Swb5uTjafgzHlr8KChiTzGniynmRE5CH35lYPxVkcfu0REekYkacJTodNgIdVNVTe5TSmOovt5xDCx0OBC/m//GHs1QwuyfiU0ZmP0CDiNttggYMx5anaz9MgIj1FZHb4AfR0Fz0Y83qk5jg3t2oeuz5VHQf8A2fWxwUi8l8ReRf4ATgYmIBz4ypjTBnFm89hfOhYzs+/i01an37+RUzIGkEHWR+VxjpIGlM+RLXUowfTUwCR1kB/oAVQK0EyVdX7Srn+AcCU4tKpamEzqoiMBi4BxqjqpQnWewFwLdANp3Pn98ArwD9SrWXo3bu3zp07N5WkxtR4kcMyAVrwKy9lPUFX32q2635cX/BnpoYOjcpTN9vPwnsHVXRRTTkTkXmq2tvrctREngUN7nwNzwFXsm/+g9j5GtR9TVW12t1u2oIGY0omNnDYjz08kTmKU/1fE1ThwcCFvBw8hchLSZbfR4/WDWw+h2rEggbveBk03A/cAQSAD3Gq93ckSq+q91ZQ0SqMBQ3GlFxs4CCEGJ7xLjdkvAvAa4ETuCdwCUGif2f0sYmgqg0LGrzjZdCwGsgB+qrqd54UwmMWNBhTOkNHfcGcVVuiXjvd9wWPZ75AthQwJdiD6wquZyfRI6MtcKgeLGjwjpcdIZsA02pqwGCMKb3wfA6R/hs6mgvy72Cz1mWg/1veyRpJM36LSmMdJI0pGy+DhjXAXg+3b4ypwuJNBDVPOzMkfyQrQs052LeaCdl/pausispnM0gaU3peBg1vAf1FJNl9HIwxJqF4E0Gt1maclX8PX4W60Ey28O+sexnoi56g1QIHY0rHy6DhQWAp8IGIHOhhOYwxVVzsfSu2Uo+L82/nvWBf6she/pn5OBf7P4nKY4GDMSXn6TwNIlIHZ7rlg4DVwDog3hwHqqrHV2TZKoJ1hDQmvYp2kFRuyBhfOLLi5cApPBC4kFDE7yWby6HqsY6Q3vFy9ERj4FOcu1jGzs8Qy+ZpMMakJN7Iit/7pvNw5ktkSZAPg4fzl4I/sZesqDQWPFQdFjR4x8ug4Z/A5ThNFKOA5SSfp2FaBRWtwljQYEz5GDrqC+au2kLk1e1I32JezHyC+rKbr0Jd+GP+/7GdOlH5LHCoGixo8I6XQcNPOE0RB6vqNk8K4TELGowpX7ETQXWRNYzOeoRmsoXvQ625JP9WNpITlccCh8rPggbveNkRsh7wRU0NGIwx5S/2hlffaxt+v/deloda0MW3lnez76ajrIvKYx0kjUnMy6BhCU7gYIwx5SY2cNhAY87Ov5u5oQNpKb8xLuteesnSqDwWOBgTn5dBw/PAABtuaYwpb7GBw1bqcWH+HXwa7EVD2ckbWQ9yoi+6qdACB2OK8ixoUNXRwFPAVBG5QkRaeVUWY0z1F57LITxUay9ZDCu4gX8FjqOWFDAq80ku8E+OymOBgzHRvOwIGSw+VSFV1YxyK4xHrCOkMd6I7iCpDPe/y18yxwPwZMFZPB38PZEjwa1zZOViHSG942XzhJTg4WU5jTHVTHRzhfB08CxuK7iSoAp/yRzP3RljkYh55nbsDXLgnR8xdNQX3hTYmErCy+YJX0keXpXTGFM9xfZzeCt4HH8qGM5ezeCyjEk8nvkCfvZViOYHQ8xZtcUCB1Oj2ZexMabGig0cJoUO5/KCm9mp2Zzln8E/Mp8im/yoPBY4mJrMggZjTI0WGzjMCnXjovw72Kp1OMk/j1cyH6MOu6PyWOBgaioLGowxNV5s4PCNduLc/BH8og3p61/EG1kP0pC8qDwWOJiaqMKCBhF5UEQalHEdDUTkwXSVyRhjwmIDh6XahrPz72ZN6AAO9a3g7az7aEL0jbAscDA1TUXWNNwKrBSRu0WkTUkyikgbEbkH+BG4pTwKZ4wx4bkcwtZoU4bm382yUEs6+9YxLuse2sjGqDwWOJiapCKDhr44d7K8G/hRRD4TkdtFZICINBWRDAARyXT/Hygid4jI5zjBwl+BH4CjK7DMxpga5p1hR0cFDhvJ4Zz8v/K/UHva+DYxLuteOsXcr8ICB1NTVPjkTiJyAXAD0BuI3fheIDsyufs8G3haVd8u/xJWHJvcyZjKa+ioL5izal9zRB1281LmExztX8xvWo+L8u9gieZG5enTthHvDLPfNeXNJnfyToV3hFTVf6nq4cDhwEPAl8BunAChlvu8C5gJjAR6qurR1S1gMMZUbrE1DjvZj8sKbmFKsAf7Sx5vZt1PN/kxKs+cVVts2mlTrXk2jXQsEakNNAC2quru4tJXB1bTYEzlF1vjkEUBz2U+w0n+eWzX/bg0/1bma/R992za6fJlNQ3eqTRDLlV1l6r+VFMCBmNM1RBb45BPJn8qGM7E4BHUl928lvUQR8iSqDx2oytTXVWaoMEYYyqr2MAhQAbDC67j3WA/6sheRmc9Ql/fgqg8FjiY6siCBmOMSUFs4BDEz00Fw3grMID9JJ9XMh9ngO+bqDwWOJjqxoIGY4xJUThwyPI7l84QPm4PXMnYwIlkSwEvZv6Nk3xzovJY4GCqEwsajDGmBN4ZdjTLHjilcPZIxcdfA5fyz8ApZEmQv2c+zWDf7Kg8FjiY6sKCBmOMKYXoaaeF+wMX8XzgDDIkxNOZz1ngYKolCxqMMaaUYgOHxwLn8nRgSGHgcGqcwOHAOz+y2SNNleVZ0CAidb3atjHGpEts4PBk4GyeDZxJhoR4JvM5Bvm+jkqfHwzZtNOmyvKypuF7ETnbw+0bY0xaxAYOTwSG8lzgd2RIiGczn+XkmMAB7H4VpmryMmhoDLwtIh+KSFsPy2GMMWUWGzg8HjiHvwfOIFOCPJf5LCfHjKoACxxM1eNl0NAdmAYMAha5d7TM8LA8xhhTJrGBw6OBcxkVON0NHJ4pMhwT4Nu12yq2kMaUgWdBg6ouU9XjgEuBncB9wLci0t+rMhljTFnFBg4PB85jVOA0MiXI85nPcKIv+n4z+cGQjaowVYbnoydUdSzQGXgV6AJ8LiJjROQAb0tmjDGls/DeQRGzRwoPB87nxcBgN3B4muN986LS23BMU1V4HjQAqOoWVb0S6A8sAS7G6Sj5R29LZowxpRM97bTwYOACXgqcSpYE+UfmUzbltKmSKkXQEKaqM4FDgTuBWsAoEZklIt28LZkxxpRcbODwQOBCXnZnjhyV+RRH+RZFpbfAwVR2lSpocLUCVgNTAQGOBOaJyGMisp+XBTPGmJKKDRzuC1zE64HjqSUF/DPzcXrKsqj0NgGUqcw8DRpEJEtEjhaR/xOR8SKyAVgBvAac4ib7BfgN+D+cjpKHeVRcY4wpldjAYUTgMsYHjym8rfYh8mNU+vxgyEZVmErJyxkhvwC2ATOAR4EhQDNgFTAWuBLorKrNgY7AY0BbYIaIHOlBkY0xptTeGXZ01E2ubim4ionBI6gvu3kt62E6y5qo9DaqwlRGXtY0HAlkAYuAUcD5QCtV7aCql6nqK6r6A4Cq7lTVW3HmdMjCGZ5ZIiJygYjMEJFtIrJDROaKyLUiUqJjICL3iIgmeewpadmMMTVD5HDMIH7+UnAtnwZ70kh28HrWQ7SXDVHprY+DqWy8nEzpd8AMVd2aagZV/VxEJgHHlGRDIvI88CdgDzAZKACOB54DjheRoaoaLMk6gW+B/8V5vaCE60mZqpKXl8f27dvZtWsXwWBJi2yM8do75+WyYetuQur8LzzON7KdWuTzDH42aQMC+KPyTP5yPi0aVkyXLr/fT+3atalfvz716tVDRCpku6Zq8CxoUNX/ljLrRqBeqolF5CycgOFn4Nhw7YWINAWm4DSLXAc8XcJyTFDVe0qYp9RUlV9++YWdO3eSk5NDs2bN8Pv9dkIbUwUdBCxav42gOpGDD6W1/Exd2cNezeBHbU5BzOU5JELXlg3KtVyqSjAYZMeOHfz666/s3r2bJk2a2HXGFKqMoyeK8zfgphKkv919vjUcMACo6kbgGvff20raTFHR8vLy2LlzJ7m5uTRs2JCMjAw7kY2pwrq2bECdLCcwCCGs1qbs0myyJUA7+ZkMomsSg6osWl++nSNFhIyMDBo2bEhubi47d+4kLy+vXLdpqpZK/UUZj6ouVtUnU0krIq2AXkA+8E6cdU0D1uN0wKzUnSu3b99OTk4Ofr+/+MTGmCqhQ5O6hYFDEB8rtRm7NYtaUkA7+Rk/oaj0QVVW/LKjQsrm9/vJyclh+/btFbI9UzVUuaChhMLDMxep6u4EaebEpE1VTxF5REReFJGHRWSIiGSVrpjF27VrF3Xr1i2v1RtjPNKhSV38bq1hOHDYo5nsJ/m0lZ/xoVHpd+YHKixwqFu3Lrt27aqQbZmqoboHDe3c59VJ0oTHObVLkiae04FbgD8CtwLvAivK64ZbwWDQahmMqaa6tmxQGDgE8LNSm5GvGdSRveTKRmIbIisqcPD7/dbh2kSp7kFD+Kf5ziRpwmdeqp0rV+D0kzgUaAAcAByHc5vvVsCHItKj5EUtnvVhMKb6igwcCshgpTYjoD7qyW5ayy9xA4eK6ONgTKTqHjSEP/GaNFUJqOprqvqwqn6rqttV9VdVnaKqA4DxQG3ggYQFErnKnSNi7qZNm9JVLGNMNRAZOOwlk5XanKD6aCg7aSG/FklfkX0cjIHqHzSEu/0m6wwQXpaOLsIj3ecTRSQzXgJVfVFVe6tq7wMOsLt/G2OiRQYOu8lilTYlpML+kkdT2VIkfUX2cTCmugcNq9zn3CRpWsekLYvv3ecsoHEa1meMqYG6tmxQ2DSwk1qs0SaoQlPZSmMp2iRhgYOpKNU9aAjfsL5rkjtk9olJWxb7R/xtZ3AFa9u2LSJS7GPq1KleFzXtRo8ejYhw6aWXel2UKmPVqlWICG3btk3resOfs7Kqnbmv4/N2arNOnZrJFrKZRlK0YtQCB1MRvJxGutyp6loRmQ/0BIbi3AirkDvSoRXObJFfpmGT57jPS1XVZkTxyMknn0yzZs0SLk+2zFQ+U6dOZeDAgfTv379aBnyJdGhSl0efGcWtw6/hjLPP574n/45fQ7SQ32jFrwTxs53aUXl2FdhIB1O+qnXQ4HoIZ2KnR0TkC1VdDiAiTYC/u2keVtXCWVRE5DqcqaW/VtU/RLzeBugHjFfVvRGvC3CRuy2AlCafMuXjtttuY8CAAV4Xo0INGTKEI488kgYNyneaYVOxmtSvBUC44uJXrY+fIE1lK234hZXajJ3UKkyv7qyR5T3dtKm5qn3QoKrjROQfOFNGLxCRz9h3w6r6wAScG1dFagx0xqmBiJQDvAGMEpGlOHM8ZAFd2TfPw3Oq+kJ57IsxiTRo0MAChmqsYe0sRARVZaM2wk+IxrKdtmxkhTZnD/vmlQta4GDKUXXv0wCAqv4JuBCYD/QHTgaW49QmnFWCO1yuBR4D5uFMPX0KcCLOcXwbOF5V/5ze0ntj6Kgv6Pvw50UeQ0d94XXR0kZVOeWUUxARrrrqqiLLQ6EQxx9/PCLCddddV/h6ZFt4IBDg4Ycf5qCDDqJWrVo0bdqUSy65hDVr1hRZX9hvv/3GXXfdRbdu3ahbty516tShZ8+ePPnkkxQUFL1J6qWXXoqIMHr0aBYsWMDQoUMLb1j21FNPAYn7NEydOhURYcCAAezZs4cRI0bQsWNH9ttvP9q3b8/9999fOHnP2rVrueKKK2jZsiW1atWiW7duvP766wn3o6CggFGjRnHMMcfQqFEjatWqRadOnbjxxhuJN5w4sox5eXncfPPNtGvXjuzsbFq2bMk111zD5s2bo/IMGDCAgQMHAjBt2rSovimRtUmrV6/moYceYuDAgbRu3Zrs7GxycnIYOHAg//rXvxLuQ2ktWLCAIUOGkJOTU/j+/fOf/0ya56uvvuLmm2+md+/eNG3alKysLFq0aMHZZ5/N7Nmzi6Rv27Ytl112GQBjxoyhe6uG9GjdiB6tG3HFDSPYpnXwS4jdP8xi1OP384czT+KEXgfRq30TjunegWOPO4mPP7bbapv0qvY1DWGq+i8gpauHe/fKe+K8/hvOLJDV3oate8ipU3RW7A1b93hQmvIhIrz22msceuihvPTSSwwcOJDzzz+/cPnIkSP5/PPPOeyww3jiiSfiruPcc89l4sSJDBgwgB49ejBr1izGjh3Lxx9/zPTp0+ncuXNU+gULFjBo0CA2bNhAq1atGDBgAKFQiK+++oobb7yRDz74gA8//JCsrKLHftasWQwbNoyWLVsyYMAA8vLyqF27dpF08eTn53PiiSeyaNEiBgwYQKdOnZg+fTojRoxg/fr13HTTTfTt25fatWtzzDHHsH79embOnMnFF1+MiHDhhRdGrW/79u0MHjyYmTNn0qBBA3r16kXDhg2ZP38+Tz75JOPHj2fatGlxOxlu27aNvn37sn79eo499lgOOeQQZs6cyahRo/j666+ZPXs2mZnOiOVBgwZRq1YtJk2aRNOmTRk0aFDherp06VL492uvvcaIESPo0KEDXbp0oW/fvqxbt44ZM2YwdepUvvrqK55+uqQ3so1v2rRpnHLKKezevZvOnTtz2GGH8dNPP3H11VezePHihPnuvPNOpk6dSteuXTn88MPJzs5m6dKljB8/ngkTJvDmm28ydOjQwvThYGLWrFl06NCBfv36kbengEBQOezwI1mrB+AnyLMvjeXlNyfQvtOBHHhwV+rUrc/6NauYMeVTTpnyKU888QQ33nhjWvbdGFTVHh49evXqpalavHhxymnT4eiHJutpz8wo8jj6ockVWo6SyM3NVUCnTJlSonwzZsxQv9+v9erV02XLlqmq6ueff64+n0/r1aunP/zwQ1T6lStXKs6EYdqkSRNdtGhR4bK9e/fqRRddpID26dMnKt+uXbu0Xbt2CuiDDz6oBQUFhct+++03PeGEExTQu+++OyrfJZdcUri9O++8U4PBYJF9ePXVVxXQSy65JOr1KVOmFObt16+fbt26tXDZ//73P83MzFSfz6cHHXSQDh8+XAOBQOHy5557TgHt0KFDke2de+65CujZZ5+tmzdvLnw9EAjoLbfcooD2798/bhkBPfXUUzUvL69w2fr167V169YK6Ouvvx53H2LXF+nrr7/WhQsXFnl92bJlheudPXt21LLw+5ibm5twvbF27dqlLVu2VEBvv/12DYVChcumTp2qtWvXLtzHWB999JH+/PPPRV5///33NTMzU3NycnTnzp1Ry+K9r8s35um3a7fot2u36MK1v+mkd17VlbMn6o51i3TB2s2Fy157/1OtW6+eZmRm6tq1a1Pex1gVfe1JBTBXK8E1vCY+akTzhKlZBg4cmHC4ZcOGDYuk79evHyNHjiQvL49zzjmHNWvWcMEFFxAKhXjppZfo2LFjwm2NGDGCgw8+uPD/rKwsnnvuORo0aMCcOXOYNWtW4bLRo0ezcuVKzjnnHG6//XYyMvZV9OXk5DBmzBgyMzN5/vnnca6L0bp06cK9996Lz1fy09bn8/Hiiy9G9Xvo0aMHp556KqFQiF27dvHoo49G3d/k6quvJicnhxUrVkQ1tyxevJi3336b3Nxcxo4dS6NGjQqX+f1+HnroIbp37860adNYsGBBkbLUrVuXl19+OeoGbC1atChsApo8eXKJ969Pnz507dq1yOudOnVixIgRAIwbN67E6401btw41q9fT4cOHbjvvvuihlb279+fYcOGJcw7aNAgmjZtWuT1008/naFDh7J582amTJlSbBli74zZ+sjTaNGqNXVkb9R0090P6815l/yRQEEBo8a8VbIdNSaBGtM8YWqOZEMuE1Xn33777UyfPp1JkybRvXt3tm3bxtVXX825556bdFsXXXRRkdcaNGjAaaedxhtvvMHUqVPp27cvAB9++CFAVBV0pBYtWtCpUycWL17MDz/8wIEHHhi1/He/+12pb1qWm5vLQQcdVOT1cEB03HHHFWkSycjIoF27dmzevJkNGzbQpk0bAD766CMATjvtNPbbr+j0Jz6fj379+vHdd9/x5Zdf0q1bt6jlvXr1ivv+hJsbNmzYUIo9hD179jBp0iTmzJnDpk2b2LvXGeD0008/AbBs2bJSrTfStGnTADjvvPPivhcXX3wxf/vb3xLm//XXX5k4cSILFy5k69atBAIBABYuXFhYxsGDBxdbjg5N6rJo/TaCqhSQwYK8enz/+b9ZsPh7NmzZzbZ8J7Bcs2oFACt/XM6KX3bQoYndKdeUjQUNptopzZDLcP+G9u3bs23bNg4++ODCToaJNGzYMG7NBVDYlr9u3brC13788UcgcdAQadOmTUWChtzcZBObJteqVau4r4d/7Re3fM+efX1Zwvvx/PPP8/zzzyfdbrwOkeHgI1b9+vWLbCtVX375Jeecc07U8Y61ffv2Eq83Vnj97drFvylusomiXnjhBW688cakt5ouSRm7tmzAovXb+OzjD7j7puvYtrXoFNNhO/LyCid/ssDBlIUFDSauFg1rxe302KJhrTipq4cJEyawY4czo966desKq6HLIrL6OjxKYfDgwTRunHyW8f3337/Ia/F+1YimWLoAACAASURBVKequCaNkjR5hPejV69eHHLIIUnTxmsyKE3zSjK7du1iyJAhbNy4kSuuuIJrrrmGjh07Uq9ePXw+H5988gknn3xy3CafdEs0E+TcuXO55ppryMjI4LHHHuP000+nVatW1K5dGxHhjjvu4KGHHipxGRtoHrdddyV79uzm8mtvYOjvTuPoNtnUrbMfG6QJL74+nvtu+wu467XAwZSVBQ0mrneGHe11ESrUwoULGT58OFlZWQwdOpQ33niDc889ly+++CLuSAaArVu3sm3btrjzI6xatQpwmhzCWrduzdKlS7nmmmtSqoKurFq3dm7XMnDgQB577DGPSwPTp09n48aN9OrVK+6wx+XLl6dtWy1btgT2vb+xVq5cGff1cePGoapcf/313HTTTWkr48SJE9mzZzcnn/Y7ht92NwB5kkd9+ZWW+isbVxVtkrHAwZSFdYQ0Nd7OnTs555xz2L17N4888ghjx45l4MCBzJs3j5tvvjlp3jfeeKPIa9u2bWPixIkAUc0kp5xyCgDvvPNO+grvgfB+TJgwobBNvjyFg7ZE2wrP7RAOZmKlc56G/v37A/DWW28V1rhEivd5gORl3LRpE59++mncfKnu+0Ed2xXeGfM3rcdGbUh+fj6fffTfuPlsumlTWhY0mBrv2muvZcmSJZxxxhnccMMN+Hw+3njjDZo0acIzzzzDhAkTEuYdOXIkS5YsKfy/oKCA4cOHs23bNnr16kW/fv0Kl1111VW0bt2aMWPGcPfdd8dt2164cCGvvvpqencwzXr27MmZZ57J8uXLE/Yj+Omnn3jqqafSElSEf90vX7487vrCHSg///xzvv/++8LXQ6EQI0eOjBrBUlZnn302zZs3Z/ny5dxzzz1RzQkzZ87kH//4R9x84TKOHTu2sAkMIC8vj8svv5ytW7fGzRfe98jPWLz1jh8/nsYZewoDh3V763DVXU/y42rnvfERisqn6swaaUxJWfOEqXYefvhhRo8enXD5BRdcwEknnQQ4F/ExY8bQunXrqC/r5s2b89prrzFo0CAuv/xyDjvssCIdEdu0aUOvXr049NBDOe6442jQoAFffvkla9asoXHjxowdG3V/NOrWrcsHH3zAaaedxsiRI3nuuefo3r07zZo1Y+PGjaxcuZJVq1ZxxBFHFM4EWFmNGTOGM844g/fee4+PPvqIHj16kJuby/bt21m7di1LliwhFAoxbNiwqKGlpZGbm8thhx3GN998Q/fu3enVqxfZ2dl07tyZm2++mZ49e3L66afz3//+l0MPPZSBAwcWDnlds2YNt9xyC48++mha9rt27dq8/vrrDB48mPvvv59x48YVTu40ffp0hg8fzpNPFr31zGWXXcZTTz3F/Pnzad++Pf369UNVmT59OllZWVx++eW88sorRfIdeeSRNGvWjPnz59O7d2+6du1KZmYmffv25bLLLuOMM84oPDadOnViwIAB7FU/38z5ih152xl2+cWMeuU16spu/IQIRvxOtOmmTWlYTYOpdiZNmsSYMWMSPsKz9n3//ff86U9/IiMjgzfffJOcnJyo9Zx00knceuutbNmyhfPOO6/IFM8iwr///W9GjBjBjz/+yIQJE9i9ezcXXXQRc+bMiZq/Iaxbt2589913PPjgg3Tq1In58+fz7rvvsmzZMpo1a8aIESN48cUXy+/gpEn9+vWZPHkyY8eO5dhjj2XFihW8++67zJs3j4yMDIYNG8akSZOoVSs9HWffffddzjnnHDZv3sybb77Jyy+/zAcffFC4fNy4cTz88MN07NiRqVOnMnnyZLp27crMmTMLm1PS5bjjjmP27NmcccYZ/Pzzz0yYMIEtW7bw/PPPJxxu2ahRI+bOnctVV11VGDzOnTuX3//+98yfPz9h00p2djYff/wxgwcPZuXKlbz++uu8/PLLhUM/MzIymDZtGrfccgvNmzfnk08+4Zuvv6TXEUfx1odTaNX1cAD8KLmyESG6o2VQ1W6nbUpEKqJHsYmvd+/eOnfu3JTSLlmyJO44e1PxVq1aRbt27cjNzU3YIc4YL634ZQc7852mnEwCdJQNZEqQLVqXtXpAkfR+kf9v786jo6jSxo9/n2wkIQtgAAUiEaIEEQUEBEUWAUFBxWEd+SmruACigiDyw21QkAEGZdhEnYA7iy+jgorMC7jCgIAiggiSBBQR2SRCAunc94+qjkm6k3SS7jTpfj7n9KnTXbdu3cpNdz9ddyvyjsP5+NkjIl8ZY1r6uxzBSO80KKVUgMk/a+Q5wkgzF+IwQnXJpLa4zufg0D4OykMaNCilVADKHzicIYIMUwtjoLacoDquTRLaVKE8oUGDUkoFqIa1YvJGVJwimp+xJg2rK0eI4YxLeuccDkoVRYMGpUopKSkJY4z2Z1CVQpO68fnmcIjjiIknRKC+/Eok51zS6xwOqjgaNCilVIBrUjc+r6nikKnBSVOVUMklSX4hjIJBgs7hoIqjQYNSSgWB/E0VB0xN/jBViJAckuQwIW6GYmrgoNzRoEEppYKEs6kiFyHd1CbbhBEt2SSK62qk2jFSuaNBg1JKBZEmdeMREXIItYdihhAvf7gdivnH2RyOnMr2QynV+UqDBqWUCjLR4aEAZBNeYChmNTdDMbNzcum74IuKLqI6T2nQoJRSQSb/HA6niMobillPfiMa1zsLW9NPaOCgAA0alFIqKOXvGHnUxPGbiSNErDUqIii4mqjDGDanHdfAQWnQoJRSwSr/HA6HzAWcMlGEi4P6cthlOW2Arw/oiIpgp0GDUkoFMWfHSANkmFpkmXCi5CwXyxGkUNqzjlyueOJDfxRTnSc0aFBKqSDn7BjpIIQ0U5scE0KcnOZCOeaSNjPboYFDENOgQQWMpKQkRAQRYdWqVUWmu+KKKxAR1q9fX3GFO488+eSTiAhPPvmkX84/ePBgRITU1FS/nL8oqampiAiDBw+usHP6uy6cnB0jRYSzhJNuapNroKacpKpkuaTPzHZo/4YgpUGDCkgTJ04kN9e1TVapipKWloaIkJSU5O+ieKRhrRia2k0VfxDJzyQAUI1MrpFdLum1Y2Rw0qBBBZzo6Gh27NjB66+/7u+inJdGjRrFrl27GDVqlL+LEvTOx7pwNlUcM7EcMfEIhgUR/yBRDruk1Y6RwUeDBhVwHnjgAQCeeOIJzp496+fSnH8SEhJISUkhISHB30UJeudjXeSfw+EXU4MsIqgumSwKn0U0BZsqtGNk8NGgQQWc3r1707p1a/bv38+CBQs8Pq5jx47F9nUoqi0+/+s7d+6kd+/e1KxZk5iYGNq1a8e6devy0r7//vt06NCB+Ph44uLiuPXWW/nhhx+KLNOBAwcYM2YMjRo1Iioqiri4OK677jpSU1Mxxrikz38Nn3zyCT169CAhIYGQkBBWrlwJlNyOvmvXLkaMGEFycjJRUVFUr16dK6+8knHjxpGenl4g7YoVKxg6dChNmjShWrVqREZGkpyczMiRIzlw4ECR11VaDoeDBQsWcO211xIfH09ERAS1a9emRYsWjB07liNHXNdOSE9P5/7776dBgwZUqVKF6tWr06lTJ954441Snbukvg7r169HROjYsWPea4MHD+aSSy7JK4ezr03h5oqS6mLVqlXcdNNNJCQkEBERQWJiIoMGDWLXLtfmAvizX09aWhoff/wxnTt3Jj4+nujoaNq0acO7777r0TU753AwWHcc9ubWISXkALPC5yOFhmJq/4bgokGDCkjTpk0D4JlnniEzs2IW3dmyZQutW7dmz549dO7cmUaNGvH555/TrVs3Pv30U+bMmcNtt92GMYZu3bpRo0YN3nvvPdq3b8/Ro0dd8lu3bh1NmzblhRdeIDc3l+7du3PNNdfwzTffMGTIEAYNGlRkWZYtW0anTp3IyMiga9eudO7cmfDw8BKvYcmSJTRr1oxFixZhjKFnz5506NCB3NxcZs6cWSAAAujfvz9Lly6latWqdOnSha5du5Kdnc28efNo0aIFe/bsKf0f0o1hw4Zx3333sX37dq655hr69OnDVVddxcmTJ5k1axb79u0rkH7Tpk00a9aM+fPnA3D77bfTsmVLPv/8cwYOHMhdd93lNujylnbt2tG7d28AqlatyqBBg/Ieffr08SiPiRMn0rNnT9asWUOTJk3o06cP8fHxLFmyhBYtWhTb2ffll1+mW7duZGZmcvPNN5OSksKmTZvo1asXy5cv9+j8fy5uFcLd58byu4mme+hmRoeudEmr/RuCR5i/C6C85Ml4f5egbJ70TZtop06duPHGG1mzZg0zZ87kiSee8Ml58ps7dy4zZ87k4YcfznttwoQJTJ8+neHDh/PLL7+wfv16rr/+egCysrK48cYb+fTTT5k3bx6TJ0/OO+7QoUP07t2bzMxMUlNTueuuuxDnssYHDnDrrbfy6quvcsMNN7j9BTxv3jwWLlzIiBEjPC7/5s2bGTZsGMYYXnrpJYYOHZp3TsDtr9s33niDnj17Eh0dnfdaTk4OTz31FFOmTGHMmDF88MEHHpfBnfT0dBYvXkxiYiKbN2+mdu3aBfZv376dOnXq5D3Pysqib9++nDhxggcffJAZM2YQGmq103/77bd07tyZV199leuuu4577rmnXGUryvDhw+nSpQsrVqwgISGh1CNFVq9ezbRp06hatSqrV6+mffv2efv+/ve/M378eAYOHMiePXuoVauWy/HTp09n9erVdO/ePe+1KVOmMHnyZCZOnOhx4NKkbjyHMmC/uYjR50bzSvh0Hg5fzm6TyJrcVgXSbk47zhVPfMi3T3UvIjcVCPROgwpYU6dORUSYOXOm29vX3ta2bdsCAQPAo48+CsCePXsYOXJkXsAAEBkZyUMPPQTg8gt+9uzZHD9+nLFjxzJo0KACX96JiYksWrQIgDlz5rgtS9euXUsVMIB1VyYnJ4dx48YxbNiwAucEaNy4MY0bNy7wWr9+/QoEDABhYWH87W9/o06dOqxZs4ZTp06VqhyF/frrrwC0aNHCJWAAaNasWYEvzmXLlnHgwAHq16/P9OnT8wIGsIbbOpsCZsyYUa5y+dLMmTMBGDNmTIGAAeCRRx7hmmuu4eTJk3n/B4WNHj26QMAAMH78eOLj49m7dy8ZGRkelyUi1Pqa2JB7Fc/lDABgVvh8LhPX5idtqgh8eqchUPjoF3tl1qJFC/r168fbb7/NM888w+zZs316vsIf0gDVq1fnggsu4OjRo273X3rppQD8/PPPBV5fvXo1AH379nV7rquvvpqYmBi2b99OVlYWkZGRBfb/5S9/KVXZHQ4Ha9euBaxfyaWxZ88ePvzwQ/bu3UtmZmbeUNecnBxyc3PZu3cvzZs3L1We+aWkpBAbG8uqVat49tlnGThwIPXr1y8y/YYNGwAYOHCg2yaZIUOGMHLkSPbu3ctPP/1E3bp1y1w2X8jJyeHzzz8HKLIfxZAhQ9i0aRPr169n0qRJLvt79uzp8lpERAQNGjRg27Zt/Pzzz1x88cUeladmbBVaJVVnc9pxXnT05PKQdHqFfsGi8JncenYKJ4kpkN7ZVLHs3ms9yl9VLnqnQQW0KVOmEBYWxoIFC1w68XlbvXr13L4eExNT5H7nvqysgr3Sf/zxRwBatWpVoBOd8xESEpL3Be2uP0RxX6ru/Pbbb/zxxx+EhYWRnJzs0TE5OTmMGDGClJQUxowZw5w5c/jXv/7F4sWLWbx4cd4dgt9//71UZSksNjaWV155haioKCZNmkRSUhL16tWjb9++pKamuvztfvrpJ4C8joiFRUZG5jVnONOeT44ePUp2djYhISFF1mPDhg2BostfVEAQFxcHuP6/lWTZvdcSUyUUECacG8GO3CTqh/zKP8NfIBSHS3odihm4NGhQAS05OZnhw4eTnZ3N448/Xq68SposKiSk+LdTSfvzczisD+L+/fsX6ETn7lGlShWX46Oiojw+V1k9//zzLFq0iIsuuoi33nqLjIwMsrKyMMZgjKFt27YAXulw2KdPHzIyMkhNTWXo0KHExMSwfPlyhgwZQkpKSoGRGs7zFW5eyc+bnSC9PYlY/rIVdQ0llb80/2ue+vap7kSEhpBNBCPOjuWIieP60G+ZGOY6GkWHYgYubZ5QAe/xxx9nyZIlvPbaazzyyCNFpouIiAAocrSFr+9U5JeYmMjevXuZPHkyTZo08fn5EhISiI6O5vTp0+zbty/vl2xxli1bBsDChQvd3g7fu3evV8tYrVq1vEAJYN++fdx9992sW7eOCRMm5A2ldN7Rcd6tKSwrK4tDhw4BeNQ0UdH/FwkJCVSpUoXs7GzS0tLymrDy279/P+BZ+b3pqsR4vj5wkkOOC7jv7IO8EfEMw8M+YFdufVbkFux74ezfoM0UgUXvNKiAd9FFFzFmzBhyc3N57LHHikzn/ADevXu3y77Dhw+zdetWn5WxsJtuugn484vZ10JDQ+nSpQsAL730kkfHHDtmLWaUmJjosu/jjz/2eefThg0b5rXnf/3113mvd+jQAYA333yTnJwcl+MWL16MMYbk5GSPvnSL+7+AP/ufFOYMNtyVoThhYWFcd911gDUE1h3naIz8c0NUhGX3XsueZ24ipkooW0wKj+cMAeDZ8JdpJq5Bog7FDDwaNKigMGHChLx5EZy/0grr3LkzYA2ddP4SBevLcdCgQRU23wNYPeTj4uJ49tlnmTt3rtsvno0bN3o1qJg0aRKhoaHMmDHD7RDB3bt3F/jiTElJAWD+/PkFbtHv27ePe++912vl2rZtG2+//TZnzpxx2ffee+8BBftw9O3bl8TERPbv3++yBsl3332XN/x23LhxHp2/VatWxMbGsnPnTt58880C++bNm1fkvAc1a9YkIiKCw4cPc/z4cY/O5eQchTN79uy8TpFOs2bN4ssvvyQ+Pr7UnVa9xdlU8ZbjBpbkdKWKnGNhxCxq4nqd2r8hsGjQoIJCfHx83vDH06dPu03Tr18/mjdvTlpaGk2aNOGWW26hW7duJCcnc/DgQXr16lVh5U1MTGTlypXExsYyatQoLr74Yrp27cqAAQNo3749devWpW3btqxYscJr52zdujUvvvgiYPXOT05Opn///vTq1YumTZvSuHFjNm7cmJd+4sSJhIeHs3DhQho3bsyAAQO48cYbufzyy0lMTOTaa71zWzo9PZ0BAwaQkJDA9ddfzx133EGfPn1o2LAhzz//PLGxsTz99NN56SMjI1m6dCnVqlVjxowZXHbZZfz1r3+lW7duNG/enMOHD3PnnXd6PCQ1Ojo6rz/MwIEDadeuHX369KFRo0Y8+OCDjB8/3u1x4eHh9OjRg5ycHJo3b87AgQMZPnx43v9hcXr06MGECRPIzMykffv2dOzYkTvuuIOmTZsyduxYIiMjee2119wOQa0oVyVac8M8nXMnm3JTqC0nmBvxAmEUDHC1f0Ng0aBBBY3Ro0cXOcIBrNvJa9eu5b777iMqKoqPPvqI3bt3M2jQIL744gvi4yt2Aq1OnTqxc+dOHnvsMWrVqsXGjRtZuXIlGRkZXHrppUydOpVnnnnGq+ccOnQoW7duZfDgwZw7d46VK1fyySefEBoayiOPPMINN9yQl7Zt27b897//pUePHpw8eZJ///vfHDx4kEmTJvHRRx95NAOlJ9q0acPUqVNp3749Bw8eZOXKlaxdu5bo6GjGjh3Ljh07aNmypcsx27dv595778XhcPDOO++wadMm2rRpw2uvvcbixYuL7ShZ2Lhx43j55Ze58sor2bJlC//5z39o2LAhn332WV5TkjuLFi1i2LBhOBwOli5dyssvv8xbb73l0TmnTZvGe++9R9euXdmxYwfLly/n+PHj3HnnnXz11Vdu+5FUpGX3XkurpOrkEMbIs2M4ZGrQOuR7JoW5LhSn8zcEDvHlVKqqeC1btjRbtmzxKO2uXbtcJtZRSilfK+mz54onPiQz20Fz+YG3I54mQhw8ePZ+Vua2c0nbKqm6VzpGishXxpiWJadU3qZ3GpRSSpWZs3/DNnMpT+VYI1umhr9EY3EdVbI1/YTecajkNGhQSilVLs7+Da87OrM0pwNRcpaF4bOIp2DnYYcxOqKikguKoEFE7hCRT0XkpIhkisgWERkpImW6fhHpLiJrROSYiJwWkW9FZJKIuM6yo5RSAc7ZvwGEyTlD+Cb3Ei4OOcLs8LkuS2mDDsWszAI+aBCRucDrQEvgU+Bj4DLgn8ByEQkt5nB3+Y0HPgBuALYCq4BawBRgvYhEF3O4UkoFJOdU09lEcN/ZBzlmYugU+jUPhr3jNr0OxaycAjpoEJHewP3AL8CVxpiexpjbgUuBXcDtwKhS5NcSmAacBq4zxnQxxvQFGgCfAG0A73ZnV0qpSsLZv+EnavLAudE4jDAm7B06h3zlklaHYlZOAR00ABPt7QRjzA/OF40xh4H77KePlqKZ4lFAgOeMMZvy5ZcJDAFygftFpFq5S66UUpXQVYnxRISG8FluU2bk9AfgH+HzSJJDLml1KGblE7BBg4jUA64GzgIu0+YZYzYAPwEXYt0hKCm/CMA5INtlILIx5kfgSyACuLnMBS+GDo9VSlWksnzmOKeajggNYb7jFj50tCJOzrAgfDbRuK6uqf0bKpeADRqA5vZ2pzHGdf5Zy+ZCaYvTCIgGjhlj9nkhv1IJDQ3NW/lQKaUqgsPhIDS0VN2+8lgjKoRx5+5hb24dUkIO8Fz4i4BrIPLzidIt1a38J5CDhkvsbXFL0GUUSutJfhnFpClNfqUSHR1doWsfKKVUZmYm0dFl69vtHFGRSTT3nHuITBPJLaEbGRKq/Rgqs0AOGmLs7R/FpHF+C8f6Ib9SiYuL49ixY3q3QSlVIRwOB8eOHSMuLq7MeTgDh32mLuPOWYuYPRb2BlfL994qpqpggRw0OCeW91ZHAK/kJyIj7HkitpRm6eDY2FiqVq1Keno6J06cICcnR/s4KKW8yhhDTk4OJ06cID09napVqxIbW77fQM6hmB/mtmZRzs2Ei4O5ES9wATrksjIK83cBfOiUvY0pJo1z36li0ng1P2PMi8CLYK094cF5ARARatWqxalTp/j999/59ddf9a6DUsrrQkNDiY6OJiEhgdjY2FIt7FWUb5/qzmWTPuC5nAE0C9lHq5DvmRM+h7vOTcRB2fpMKP8I5KAhzd7WLyZNYqG0nuR3sZfyKzURIS4urly3C5VSyh+uSozn6wMneeDcA7wb8Ri/UY0IySUnJJw61SL9XTzloUAOGrbZ2yYiElXECIpWhdIWZzdwBqghIg2LGEHRuhT5KaVU0CiwuuXvN3Br7EXc6oW7GKpiBWyfBmPMAaxpniOAvoX3i0gHoB7WbJFfepDfWazpowEGusmvAdAWa16IVWUuuFJKBbq4OqABQ6UUsEGDbaq9fU5Ekp0vikgtYJ79dJoxJjffvlEisltElrjJbxpWR8gJItI63zExwCtYf895xpgTXr4OpZRSyu8COmgwxiwH5mPN+rhDRN4TkXeAH4DLgZVYC1fll4A1kZNL3wVjzGasqaSjgS/slS6XAvuADsAmYJKPLkcppZTyq0Du0wCAMeZ+EfkMGIn1xR6K1T/hFWB+/rsMHuY3XUS+AcZi9YmIBH4EXgBmGGOyvVl+pZRS6nwhOtbff1q2bGm2bNni72IopVSlIiJfGWNa+rscwSigmyeUUkop5T0aNCillFLKIxo0KKWUUsoj2qfBj0TkCMWvwlmcBOA3LxZH+YbWU+Wg9VQ5OOupvjGmpr8LE4w0aKikRGSLdgQ6/2k9VQ5aT5WD1pP/afOEUkoppTyiQYNSSimlPKJBQ+X1or8LoDyi9VQ5aD1VDlpPfqZ9GpRSSinlEb3ToJRSSimPaNCglFJKKY9o0HAeEJE7RORTETkpIpkiskVERopImepHRLrbK3AeE5HTIvKtiEwSkSreLnsw8UY9iUiIiFwrIlPsvA6KyFkROSwiq0Wkly+vIRh4+/1UKO8RImLsR+EVclUp+OBzL1RE7hGRT0TkqIhkicgBe3XjW7xd/mClfRr8TETmAvcDWcB/gHNAZyAW+B+grzHGUYr8xgPPAQ5gPXAca3XPmsBGoLMx5rQXLyEoeKueRCQZa2l2gGPAFqw6aoC1aipAKjDU6Juz1Lz9fiqUd31gBxADCDDXGDPKG+UONj743KsBfAC0Bk4CnwOngESgOfCGMWa4N68haBlj9OGnB9AbMMAh4NJ8r9cGvrP3jSlFfi2BXOAP4Jp8r8cAG+z8/uHv665sD2/WE9AQ60OyOxBaaF8HINPOb4i/r7uyPbz9fiqUtwBr7fpJtfP6p7+vuTI+fPC5F4IVJBhgEVC10P4Y4Ap/X3egPPxegGB+YP3KNMBdbvZ1yPfGCvEwv+X2MY+72dcA6+5DNlDN39demR7erqcSzvX/7fz+4+/rrmwPX9YTcJ99/GjgSQ0azp96Au6xj1mPffdcH757aJ8GPxGResDVwFlgWeH9xpgNwE/AhUAbD/KLAG6yn77uJr8fgS+BCODmMhc8yHi7njywzd7W80JeQcOX9SQilwDTsX7Naj+GcvBRPTmbiJ4zdhShfEeDBv9pbm93GmPOFJFmc6G0xWkERAPHjDH7vJCfsni7nkpyqb095IW8golP6klEBHgFCAOG6ZdSuXm1nkTkQuAKrD4R60SkqYg8KSILReRZEela/iKr/ML8XYAgdom9LW6Vy4xCaT3JL6OYNKXJT1m8XU9FEpFo4AH76Yry5BWEfFVPo4COwKPGmO/LUC5VkLfr6Up7mwZMBiZi9T9xmiginwC9jTG6iqkX6J0G/4mxt38UkybT3sb6IT9lqci/6zysD8rv0OlyS8vr9SQiDYGpwFfAjLIXTeXj7XqqYW8vAR4DXgUaA3HADcAuoD2wtNQlVW5p0OA/zmjYW7c7vZ2fslTI31VEJgODsIaL9TPGZPvyfAHIq/WUf5ZDdgAACAVJREFUr1kiAmv4a5mGaSoX3n4/Ob/DwrA6Dw8yxuw2xpwyxqwDbgTOAJ1EpIOXzhnUNGjwn1P2NqaYNM59p4pJ46v8lMXnf1cReRh4GusX1k3GmJ1lySfIebueHsD6hTrVGPNNeQqmCvDV5x64uTtnjDkIrLKfdvYgP1UC7dPgP2n2tn4xaRILpfUkv4u9lJ+ypNlbb9VTASIyGpiJ9WuopzHmy9LmoQDv19Pt9rarm1+oSc40InIFkGmM6elBnsp3n3sA+4tI43z9Qg/yUyXQoMF/nEPrmohIVBE9iVsVSluc3VhfPDVEpGERIyhalyI/ZfF2PeURkZHAC1iz4t1qDzdTZeOrempbzL469uNkKfILdr743PsDqApcUESaBHubWcR+VQraPOEnxpgDwFasNtO+hffbv27qAb9gza9QUn5nsaZRBRjoJr8GWB+AZ/nzdp0qgbfrKd9x92KN+c8Gehlj1nqlwEHKB++njsYYcfcAnrKTzbVfq+a9KwlsPqinc8D79lOX5gcRCcdqZgJrUilVTho0+NdUe/ucvSYBACJSC6snPcA0Y0xuvn2jRGS3iCxxk980rA5GE0Skdb5jYrA6dYUA84wxJ7x8HYHOq/UkInfbx2UDfzHGfOS7ogcVb7+flG94u56mYk2fP1JEOuc7JhRrHZ6GWBNG/Y93LyM4afOEHxljlovIfKwpaneIyFr+XLglDliJ6wx0CVgTOf3iJr/NIvIo1hvlCxH5X+AE1tSstYBNwCQfXU7A8mY9iUgzYCFWL/L9QD8R6efmtL8ZY8Z59UICnLffT8o3fPC597WIPAg8D6wRkc3AQazJoRpgNR/1LWYyKVUKGjT4mTHmfhH5DBiJ9eUeitVO9wowP3+07WF+00XkG2AsVttgJPAjVtv5DB3KVzZerKdq/DnsLMV+uJMOaNBQSt5+Pynf8MHn3hwR2YH1nmkDtMCaVfVFrBEwaV4sflDTpbGVUkop5RHt06CUUkopj2jQoJRSSimPaNCglFJKKY9o0KCUUkopj2jQoJRSSimPaNCglFJKKY9o0KCUUkopj2jQoJSPiYgpwyPVPraj/Xy9f6+i/ERkgn0t3cuRRwsRyRWRGd4sm1LKMzojpFK+t9jNaxcC3bBW6FvuZv9nPi1RBRORi7CmMP/EGPNhWfMxxmwVkXeAB0RkoTHmB68VUilVIp0RUik/EJGOwDog3RiTVEy6aOBi4LQxJqNiSud9IvIicDfQ2Rjzv+XMqynwDbDCGNPHG+VTSnlGgwal/MDToCEQiMgFWAsI/QwkGy986NiLEjUHGlTmYEqpykb7NCh1HiuqT4OIJNmvp4lIiIg8LCI7ReSMiBwUkVn2XQpEpLqIzLbTZovIDyLycDHnFBEZICJrROQ3+5gMEVkkIklluIyhWAunLXEXMIhINRF51i7/6XzXsF5EJhaR52KsRY7uKUN5lFJlpEGDUpXfG8DTWEttrwGqAg8BK0SkBtaS6P2BzVh9JZKAmSLyWOGMRCQcq4/Fm0A74DvgXay+F8OBrSLSspTl62Vv17o5XzTwOTARa/njtVhLI+8FLgeeKCJPZ163lbIsSqly0I6QSlVu9YEs4DJjzM8AIpIIbAO6AxuAr4E7jTFZ9v4ewPvAoyIy2xhzOl9+fwP+AnwCDDTGHHTuEJFRwBzgLRFJMcbklFQ4OyhoBZwDvnKTpA9WcLAK6JU/TxEJxVo22Z3vgeNAExGpbYw5XFJZlFLlp3calKr8HnAGDADGmAPAa/bT+sB9zoDB3r8KqyNhLJB318C+K/EAkAn0zR8w2Mf9E+vLvSFwk4dlawKEA/vzlyGf2vZ2beEgxBjjKKrTpN3Msct+2szDsiilykmDBqUqt3OAuy/WvfZ2izHmNzf7nUMV6+R7rRMQBWwwxvxaxPk22Nu2Hpavlr09WsT+/9rbCSLy/0Skmof5Ahyzt7WLTaWU8hptnlCqcvuliGaCTHt70M2+/Psj873WwN72EJGSRjjU9LB88fb2d3c7jTEbRGQ6MA54FTAishur78UKY8xHxeTtzLM0gYZSqhw0aFCqcsst5/78Qu3t98DGEtJu8jDPE/Y2rqgExpgJIrIAq1NjO+A6rDkd7haRNUCPIgIjZ57HPSyLUqqcNGhQSjkdsLc7jDGDvZSns5njguISGWP2A7PtByLSDmsEx41YQzZfdHOYM8+imlKUUl6mfRqUUk5rsfpIdCll34Li7ASygUtEJMrTg4wxnwGp9tOrCu8XEQFS7KfbyllGpZSHNGhQSgFgD1uci9VH4F0RSSmcxp4oariIeNT50BhzBqspIxy42k1+t4tIexEJKfR6FNDFfpruJusUoDqws5hOm0opL9PmCaVUfuOxRlT0A74Vke1Yk0ZFAolAYyDC3no6N8JKoD1WEFB4Ia4OwBjgiIhsA45gdZ68FqgB7AYWusnTGVD828MyKKW8QO80KKXyGGPOGWP6Y3VKfB8rgLgN60s8DGv2yduBfaXINhU4A9xlNysU3vccsAe4AugLtMYaMvoQ0NoYc9JNnoMAB+4DCqWUj+iCVUopn7NHR9yDrnKpVKWmQYNSyudE5EKsuwnbjDFFTQ3taV7LgVuBJsaYH0pKr5TyHm2eUEr5nDHmF2AK0F5Eupc1HxFpgbU2xhwNGJSqeHqnQSmllFIe0TsNSimllPKIBg1KKaWU8ogGDUoppZTyiAYNSimllPKIBg1KKaWU8ogGDUoppZTyyP8BsSvYUxXU/roAAAAASUVORK5CYII=\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "fig = pyplot.figure(figsize=(6,4))\n", - "pyplot.plot(t[:N], num_sol[:,0], linewidth=2, linestyle='--', label='Numerical solution')\n", - "pyplot.plot(t[:N], y[:N], linewidth=2, alpha=0.8, label='Experimental data')\n", - "pyplot.xlabel('Time [s]')\n", - "pyplot.ylabel('$y$ [m]')\n", - "pyplot.title('Free fall tennis ball (no air resistance) \\n')\n", - "pyplot.legend();" + "fig = plt.figure(figsize=(6,4))\n", + "plt.plot(t[:N], y[:N], 's', alpha=0.8, label='Experimental data')\n", + "plt.plot(t[:N], num_sol[:,0], linewidth=2, linestyle='-', label='Numerical solution')\n", + "plt.xlabel('Time (s)')\n", + "plt.ylabel('$y$ (m)')\n", + "plt.title('Free fall tennis ball (no air resistance) \\n')\n", + "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The two lines look very close… but let's plot the difference to get an idea of the error." + "The two lines look very close… but let's plot the difference to get understand the [error](https://github.uconn.edu/rcc02007/CompMech01-Getting-started/blob/master/notebooks/03_Numerical_error.ipynb)." ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 206, "metadata": {}, "outputs": [ { "data": { - "image/png": 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N/59O1As6Va9twP1EHyr/iC3zd6Kd8uQwPy7bbecSY1dZRHQr7hnhYDOinu4tXRfPi7s/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\nTkSuQmCC\n", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "fig = pyplot.figure(figsize=(6,4))\n", - "pyplot.plot(t[:N], y[:N]-num_sol[:,0])\n", - "pyplot.title('Difference between numerical solution and experimental data.\\n')\n", - "pyplot.xlabel('Time [s]')\n", - "pyplot.ylabel('$y$ [m]');" + "fig = plt.figure(figsize=(6,4))\n", + "plt.plot(t[:N], y[:N]-num_sol[:,0])\n", + "plt.title('Difference between numerical solution and experimental data.\\n')\n", + "plt.xlabel('Time [s]')\n", + "plt.ylabel('$y$ [m]');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise\n", + "\n", + "Create a plot of the analytical solution for y-vs-t for an object that accelerates due to gravity, plot the difference between the analytical solution and the experimental data with the plot above. \n", + "\n", + "_Hint: remember the kinematic equations for constant acceleration_ $y(t) = y(0) + \\dot{y}(0)t - \\frac{gt^2}{2}$" ] }, { @@ -625,9 +545,9 @@ "source": [ "## Air resistance\n", "\n", - "In [Lesson 1](http://go.gwu.edu/engcomp3lesson1) of this module, we computed the acceleration of gravity and got a value less than the theoretical $9.8 \\rm{m/s}^2$, even when using high-resolution experimental data. Did you figure out why?\n", + "In [Lesson 1](./01_Catch_Motion.ipynb) of this module, we computed the acceleration of gravity and got a value less than the theoretical $9.8 \\rm{m/s}^2$, even when using high-resolution experimental data. \n", "\n", - "We were missing the effect of air resistance! When an object moves in a fluid, like air, it applies a force on the fluid, and consequently the fluid applies an equal and opposite force on the object (Newton's third law).\n", + "We did not account for air resistance. When an object moves in a fluid, like air, it applies a force on the fluid, and consequently the fluid applies an equal and opposite force on the object (Newton's third law).\n", "\n", "This force is the *drag* of the fuid, and it opposes the direction of travel. The drag force depends on the object's geometry, and its velocity: for a sphere, its magnitude is given by:\n", "\n", @@ -635,34 +555,16 @@ " F_d = \\frac{1}{2} \\pi R^2 \\rho C_d v^2,\n", "\\end{equation}\n", "\n", - "where $R$ is the radius of the sphere, $\\rho$ the density of the fluid, $C_d$ the drag coefficient of a sphere, and $v$ is the velocity." + "where $R$ is the radius of the sphere, $\\rho$ the density of the fluid, $C_d$ the drag coefficient of a sphere, and $v$ is the velocity.\n", + "\n", + "In the first module, we used the constant $c$, where $c= \\frac{1}{2} \\pi R^2 \\rho C_d$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Since we have another force involved, we'll have to rethink the problem formulation. The state variables are still the same (position and velocity):\n", - "\n", - "\\begin{equation}\n", - "\\mathbf{y} = \\begin{bmatrix}\n", - "y \\\\ v\n", - "\\end{bmatrix}.\n", - "\\end{equation}\n", - "\n", - "But we'll adjust the differential equation to add the effect of air resistance. In vector form, we can write it as follows:\n", - "\n", - "\\begin{equation}\n", - "\\dot{\\mathbf{y}} = \\begin{bmatrix}\n", - "v \\\\ a_y\n", - "\\end{bmatrix},\n", - "\\end{equation}\n", - "\n", - "where $a_y$ now includes the acceleration due to the drag force:\n", - "\n", - "\\begin{equation}\n", - " a_y = -g + a_{\\text{drag}} \n", - "\\end{equation}\n", + "We can update our defintion for drag with this _higher fidelity_ description of drag\n", "\n", "With $F_{\\text{drag}} = m a_{\\text{drag}}$:\n", "\n", @@ -693,36 +595,31 @@ }, { "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 207, + "metadata": {}, "outputs": [], "source": [ - "def fall_drag(state):\n", + "def fall_drag(state,C_d=0.47,m=0.0577,R = 0.0661/2):\n", " '''Computes the right-hand side of the differential equation\n", " for the fall of a ball, with drag, in SI units.\n", " \n", " Arguments\n", " ---------- \n", " state : array of two dependent variables [y v]^T\n", - " \n", + " m : mass in kilograms default set to 0.0577 kg\n", + " C_d : drag coefficient for a sphere default set to 0.47 (no units)\n", + " R : radius of ball default in meters is 0.0661/2 m (tennis ball)\n", " Returns\n", " -------\n", " derivs: array of two derivatives [v (-g+a_drag)]^T\n", " '''\n", - " R = 0.0661/2 # radius in meters\n", - " m = 0.0577 # mass in kilograms\n", + " \n", " rho = 1.22 # air density kg/m^3\n", - " C_d = 0.47 # drag coefficient for a sphere\n", - " pi = numpy.pi\n", + " pi = np.pi\n", " \n", - " a_drag = 1/(2*m) * pi * R**2 * rho * C_d * (state[1])**2\n", + " a_drag = -1/(2*m) * pi * R**2 * rho * C_d * (state[1])**2*np.sign(state[1])\n", " \n", - " derivs = numpy.array([state[1], -9.8 + a_drag])\n", + " derivs = np.array([state[1], -9.8 + a_drag])\n", " return derivs" ] }, @@ -735,13 +632,8 @@ }, { "cell_type": "code", - "execution_count": 22, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 208, + "metadata": {}, "outputs": [], "source": [ "y0 = y[0] # initial position\n", @@ -751,28 +643,18 @@ }, { "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 209, + "metadata": {}, "outputs": [], "source": [ "# initialize array\n", - "num_sol_drag = numpy.zeros([N,2])" + "num_sol_drag = np.zeros([N,2])" ] }, { "cell_type": "code", - "execution_count": 24, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 210, + "metadata": {}, "outputs": [], "source": [ "# Set intial conditions\n", @@ -782,13 +664,8 @@ }, { "cell_type": "code", - "execution_count": 25, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 230, + "metadata": {}, "outputs": [], "source": [ "for i in range(N-1):\n", @@ -804,31 +681,33 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 231, "metadata": {}, "outputs": [ { "data": { - "image/png": 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56DpjUUqVYc6ODrw9ZAwvf1WBNbFvk5QQi+Pm+dBuLLh4WB2euk7XTDIiEnwD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\n4qWXXspxexUrVqRmzZr22A8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qGHNwMLx1fzNucnoQz8v+XCGF8VvfICpsl9Wh5YkmGaWU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\n08Au4Na8cykjp1HAT4CGdP5jwIPAc3nnUs57r6D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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "fig = pyplot.figure(figsize=(6,4))\n", - "pyplot.plot(t[:N], num_sol[:,0], linewidth=2, linestyle='--', label='Num-solution no drag')\n", - "pyplot.plot(t[:N], y[:N], linewidth=2, alpha=0.6, label='Experimental data')\n", - "pyplot.plot(t[:N], num_sol_drag[:,0], linewidth=2, linestyle='--', label='Num-solution drag')\n", + "fig = plt.figure(figsize=(6,4))\n", + "plt.plot(t[:N], num_sol[:,0], linewidth=2, linestyle='--', label='Num-solution no drag')\n", + "plt.plot(t[:N], y[:N], linewidth=2, alpha=0.6, label='Experimental data')\n", + "plt.plot(t[:N], num_sol_drag[:,0], linewidth=2, linestyle='--', label='Num-solution drag')\n", "\n", - "pyplot.title('Free fall tennis ball \\n')\n", + "plt.title('Free fall tennis ball \\n')\n", "\n", - "pyplot.xlabel('Time [s]')\n", - "pyplot.ylabel('$y$ [m]')\n", - "pyplot.legend();" + "plt.xlabel('Time [s]')\n", + "plt.ylabel('$y$ [m]')\n", + "plt.legend();" ] }, { @@ -840,37 +719,41 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 232, "metadata": {}, "outputs": [ { "data": { - "image/png": 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rFe+ZbgPa2/+/BKsXtGu7ioEvsD5UPnNb5lOsg/JX9nx3NV13bWI8WbZiPYp7qX2yCVZP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\nzKxULkbMzMysVP8HpqMcurFJrC4AAAAASUVORK5CYII=\n", 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\n", "text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "fig = pyplot.figure(figsize=(6,4))\n", - "pyplot.plot(t[:N], y[:N]-num_sol[:,0], label='No drag')\n", - "pyplot.plot(t[:N], y[:N]-num_sol_drag[:,0], label='With drag')\n", - "pyplot.title('Difference between numerical solution and experimental data.\\n')\n", - "pyplot.xlabel('Time [s]')\n", - "pyplot.ylabel('$y$ [m]')\n", - "pyplot.legend();" + "fig = plt.figure(figsize=(6,4))\n", + "plt.plot(t[:N], y[:N]-num_sol[:,0], label='No drag')\n", + "plt.plot(t[:N], y[:N]-num_sol_drag[:,0], label='With drag')\n", + "plt.title('Difference between numerical solution and experimental data.\\n')\n", + "plt.xlabel('Time [s]')\n", + "plt.ylabel('$y$ [m]')\n", + "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "##### Discuss with your neighbor\n", + "## Discussion\n", + "\n", + "* What do you see in the plot of the difference between the numerical solution and the experimental data?\n", "\n", - "* What do you see in the plot of the difference between the numerical solution and the experimental data?" + "* Is the error plotted above related to truncation error? Is it related to roundoff error?" ] }, { diff --git a/notebooks/01_Catch_Motion.ipynb b/notebooks/01_Catch_Motion.ipynb index 8d8ca10..b3a91be 100644 --- a/notebooks/01_Catch_Motion.ipynb +++ b/notebooks/01_Catch_Motion.ipynb @@ -33,7 +33,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -51,7 +51,7 @@ " " ], "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -86,9 +86,9 @@ "metadata": {}, "outputs": [], "source": [ - "import imageio\n", - "import numpy\n", - "from matplotlib import pyplot" + "import imageio \n", + "import numpy as np\n", + "import matplotlib.pyplot as plt" ] }, { @@ -111,7 +111,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -120,7 +120,7 @@ "imageio.plugins.ffmpeg.FfmpegFormat.Reader" ] }, - "execution_count": 28, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -131,7 +131,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -162,10 +162,9 @@ " - download by calling (in Python): imageio.plugins.ffmpeg.download()\n", "```\n", "\n", - "If you do, we suggest to install `imageio-ffmpeg` package, an ffmpeg wrapper for Python that includes the `ffmpeg` executable. You can install it via `pip` or `conda`:\n", + "If you do, we suggest to install `imageio-ffmpeg` package, an ffmpeg wrapper for Python that includes the `ffmpeg` executable. You can install it via `conda`:\n", "\n", - "- `pip install --upgrade imageio-ffmpeg`\n", - "- `conda install imageio-ffmpeg -c conda-forge`" + " `conda install imageio-ffmpeg -c conda-forge`" ] }, { @@ -183,13 +182,13 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "%matplotlib notebook\n", "\n", - "pyplot.rc('font', family='serif', size='18')" + "plt.rc('font', family='serif', size='18')" ] }, { @@ -201,7 +200,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -210,7 +209,7 @@ "(1080, 1440, 3)" ] }, - "execution_count": 8, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -222,7 +221,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -231,7 +230,7 @@ "imageio.core.util.Array" ] }, - "execution_count": 9, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -244,7 +243,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Naturally, `imageio` plays well with `pyplot`. You can use [`pyplot.imshow()`](https://matplotlib.org/devdocs/api/_as_gen/matplotlib.pyplot.imshow.html) to show the image in a figure. We chose to show frame 1100 after playing around a bit and finding that it gives a good view of the long-exposure image of the falling ball.\n", + "Naturally, `imageio` plays well with `pyplot`. You can use [`plt.imshow()`](https://matplotlib.org/devdocs/api/_as_gen/matplotlib.plt.imshow.html) to show the image in a figure. We chose to show frame 1100 after playing around a bit and finding that it gives a good view of the long-exposure image of the falling ball.\n", "\n", "##### Explore:\n", "\n", @@ -253,7 +252,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -1039,7 +1038,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -1050,7 +1049,7 @@ } ], "source": [ - "pyplot.imshow(image, interpolation='nearest');" + "plt.imshow(image, interpolation='nearest');" ] }, { @@ -1066,7 +1065,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -1078,7 +1077,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -1864,7 +1863,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -1875,8 +1874,8 @@ } ], "source": [ - "fig = pyplot.figure()\n", - "pyplot.imshow(image, interpolation='nearest')\n", + "fig = plt.figure()\n", + "plt.imshow(image, interpolation='nearest')\n", "\n", "coords = []\n", "connectId = fig.canvas.mpl_connect('button_press_event', onclick)" @@ -1886,28 +1885,31 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Notice that in the previous code cell, we created an empty list named `coords`, and inside the `onclick()` function, we are appending to it the $(x,y)$ coordinates of each mouse click on the figure. After executing the cell above, you have a connection to the figure, via the user interface: try clicking with your mouse on the endpoints of the white lines of the metered panel (click on the edge of the panel to get approximately equal $x$ coordinates), then print the contents of the `coords` list below." + "Notice that in the previous code cell, we created an empty list named `coords`, and inside the `onclick()` function, we are appending to it the $(x,y)$ coordinates of each mouse click on the figure. After executing the cell above, you have a connection to the figure, via the user interface: \n", + "\n", + "## Exercise \n", + "Click with your mouse on the endpoints of the white lines of the metered panel (click on the edge of the panel to get approximately equal $x$ coordinates), then print the contents of the `coords` list below." ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[[607.5022321428571, 117.32366071428555],\n", - " [607.5022321428571, 242.97301136363626],\n", - " [610.4243100649351, 365.700284090909],\n", - " [607.5022321428571, 497.1937905844155],\n", - " [610.4243100649351, 616.9989853896103],\n", - " [610.4243100649351, 745.5704139610389],\n", - " [613.3463879870129, 862.4535308441557],\n", - " [613.3463879870129, 982.2587256493506]]" + "[[610.6982548701299, 118.4194399350647],\n", + " [613.6203327922078, 244.0687905844154],\n", + " [613.6203327922078, 372.6402191558441],\n", + " [610.6982548701299, 492.44541396103887],\n", + " [610.6982548701299, 618.0947646103895],\n", + " [619.4644886363636, 746.666193181818],\n", + " [619.4644886363636, 866.4713879870129],\n", + " [619.4644886363636, 983.3545048701299]]" ] }, - "execution_count": 13, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" } @@ -1925,43 +1927,43 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([607.50223214, 607.50223214, 610.42431006, 607.50223214,\n", - " 610.42431006, 610.42431006, 613.34638799, 613.34638799])" + "array([610.69825487, 613.62033279, 613.62033279, 610.69825487,\n", + " 610.69825487, 619.46448864, 619.46448864, 619.46448864])" ] }, - "execution_count": 14, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "numpy.array(coords)[:,0]" + "np.array(coords)[:,0]" ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "2.2810463468175857" + "3.848250153233547" ] }, - "execution_count": 15, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "numpy.array(coords)[:,0].std()" + "np.array(coords)[:,0].std()" ] }, { @@ -1980,23 +1982,23 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([117.32366071, 242.97301136, 365.70028409, 497.19379058,\n", - " 616.99898539, 745.57041396, 862.45353084, 982.25872565])" + "array([118.41943994, 244.06879058, 372.64021916, 492.44541396,\n", + " 618.09476461, 746.66619318, 866.47138799, 983.35450487])" ] }, - "execution_count": 16, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "y_lines = numpy.array(coords)[:,1]\n", + "y_lines = np.array(coords)[:,1]\n", "y_lines" ] }, @@ -2017,16 +2019,16 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "123.56215213358072" + "123.56215213358074" ] }, - "execution_count": 17, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } @@ -2040,7 +2042,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "##### Discuss with your neighbor\n", + "## Discussion \n", "\n", "* Why did we slice the `y_lines` array like that? If you can't explain it, write out the first few terms of the sum above and think!" ] @@ -2062,7 +2064,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 70, "metadata": {}, "outputs": [ { @@ -2848,7 +2850,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -2859,34 +2861,42 @@ } ], "source": [ - "fig = pyplot.figure()\n", - "pyplot.imshow(image, interpolation='nearest')\n", + "fig = plt.figure()\n", + "plt.imshow(image, interpolation='nearest')\n", "\n", "coords = []\n", "connectId = fig.canvas.mpl_connect('button_press_event', onclick)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise\n", + "\n", + "Click on the locations of the _ghost_ ball locations in the image above to populate `coords` with x-y-coordinates for the ball's location. " + ] + }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[[724.385349025974, 61.11931818181802],\n", - " [724.385349025974, 87.41801948051943],\n", - " [724.385349025974, 128.3271103896102],\n", - " [724.385349025974, 180.9245129870128],\n", - " [724.385349025974, 253.9764610389609],\n", - " [721.4632711038961, 344.56087662337654],\n", - " [721.4632711038961, 452.6777597402596],\n", - " [718.5411931818181, 581.2491883116882],\n", - " [721.4632711038961, 718.5868506493506],\n", - " [721.4632711038961, 879.3011363636363]]" + "[[724.6592938311688, 88.65077110389598],\n", + " [730.5034496753246, 120.79362824675309],\n", + " [724.6592938311688, 188.00142045454527],\n", + " [724.6592938311688, 258.1312905844154],\n", + " [724.6592938311688, 351.637784090909],\n", + " [721.7372159090909, 456.8325892857142],\n", + " [724.6592938311688, 579.5598620129869],\n", + " [724.6592938311688, 719.8196022727271],\n", + " [721.7372159090909, 883.4559659090908]]" ] }, - "execution_count": 19, + "execution_count": 71, "metadata": {}, "output_type": "execute_result" } @@ -2908,27 +2918,27 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 72, "metadata": {}, "outputs": [], "source": [ - "y_coords = numpy.array(coords)[:,1]\n", + "y_coords = np.array(coords)[:,1]\n", "delta_y = (y_coords[1:] - y_coords[:-1]) *0.25 / gap_lines.mean()" ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([0.89391892, 1.39054054, 1.78783784, 2.48310811, 3.07905405,\n", - " 3.675 , 4.37027027, 4.66824324, 5.46283784])" + "array([1.0828125, 2.2640625, 2.3625 , 3.15 , 3.54375 , 4.134375 ,\n", + " 4.725 , 5.5125 ])" ] }, - "execution_count": 21, + "execution_count": 73, "metadata": {}, "output_type": "execute_result" } @@ -2940,17 +2950,17 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([ 8.34324324, 6.67459459, 11.68054054, 10.01189189, 10.01189189,\n", - " 11.68054054, 5.00594595, 13.34918919])" + "array([19.845 , 1.65375, 13.23 , 6.615 , 9.9225 , 9.9225 ,\n", + " 13.23 ])" ] }, - "execution_count": 22, + "execution_count": 74, "metadata": {}, "output_type": "execute_result" } @@ -2962,16 +2972,16 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "9.77351351351352" + "9.095624999999998" ] }, - "execution_count": 23, + "execution_count": 79, "metadata": {}, "output_type": "execute_result" } @@ -2984,7 +2994,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Yikes! That's some wide variation on the acceleration estimates. Our average measurement for the acceleration of gravity is not great, but it's not far off… In case you don't remember, the actual value is $9.8\\rm{m/s}^2$." + "Yikes! That's some wide variation on the acceleration estimates. Our average measurement for the acceleration of gravity is not great, but it's not far off. The actual value we are hoping to find is $9.81\\rm{m/s}^2$." ] }, { @@ -2998,7 +3008,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -3016,7 +3026,7 @@ " " ], "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3038,7 +3048,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 20, "metadata": {}, "outputs": [ { @@ -3076,7 +3086,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 21, "metadata": {}, "outputs": [], "source": [ @@ -3094,16 +3104,16 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "('Projectile_Motion.mp4', )" + "('Projectile_Motion.mp4', )" ] }, - "execution_count": 27, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -3116,7 +3126,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 23, "metadata": {}, "outputs": [], "source": [ @@ -3125,27 +3135,7 @@ }, { "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "3531" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(reader)" - ] - }, - { - "cell_type": "code", - "execution_count": 30, + "execution_count": 24, "metadata": {}, "outputs": [ { @@ -3154,7 +3144,7 @@ "(720, 1280, 3)" ] }, - "execution_count": 30, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" } @@ -3166,7 +3156,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 25, "metadata": {}, "outputs": [ { @@ -3952,7 +3942,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -3963,35 +3953,46 @@ } ], "source": [ - "fig = pyplot.figure()\n", - "pyplot.imshow(image, interpolation='nearest')\n", + "fig = plt.figure()\n", + "plt.imshow(image, interpolation='nearest')\n", "\n", "coords = []\n", "connectId = fig.canvas.mpl_connect('button_press_event', onclick)" ] }, { - "cell_type": "code", - "execution_count": 32, + "cell_type": "markdown", "metadata": {}, + "source": [ + "## Exercise \n", + "\n", + "Grab the coordinates of the 0, 10, 20, 30, 40, ..., 100-cm vertical positions so we can create a vertical conversion from pixels to centimeters with `gap_lines2`. " + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "scrolled": true + }, "outputs": [ { "data": { "text/plain": [ - "[[723.8145161290322, 117.54032258064524],\n", - " [723.8145161290322, 169.1532258064516],\n", - " [723.8145161290322, 223.3467741935484],\n", - " [723.8145161290322, 277.5403225806451],\n", - " [723.8145161290322, 329.1532258064516],\n", - " [723.8145161290322, 385.92741935483866],\n", - " [723.8145161290322, 437.5403225806451],\n", - " [723.8145161290322, 489.1532258064516],\n", - " [723.8145161290322, 540.766129032258],\n", - " [723.8145161290322, 594.9596774193548],\n", - " [723.8145161290322, 651.7338709677418]]" + "[[298.25, 115.48387096774195],\n", + " [298.25, 169.67741935483878],\n", + " [295.6693548387097, 221.29032258064512],\n", + " [298.25, 275.48387096774195],\n", + " [298.25, 329.67741935483866],\n", + " [298.25, 383.8709677419355],\n", + " [295.6693548387097, 432.9032258064516],\n", + " [298.25, 489.67741935483866],\n", + " [295.6693548387097, 543.8709677419354],\n", + " [298.25, 598.0645161290322],\n", + " [295.6693548387097, 647.0967741935483]]" ] }, - "execution_count": 32, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } @@ -4002,39 +4003,39 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([117.54032258, 169.15322581, 223.34677419, 277.54032258,\n", - " 329.15322581, 385.92741935, 437.54032258, 489.15322581,\n", - " 540.76612903, 594.95967742, 651.73387097])" + "array([115.48387097, 169.67741935, 221.29032258, 275.48387097,\n", + " 329.67741935, 383.87096774, 432.90322581, 489.67741935,\n", + " 543.87096774, 598.06451613, 647.09677419])" ] }, - "execution_count": 33, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "y_lines2 = numpy.array(coords)[:,1]\n", + "y_lines2 = np.array(coords)[:,1]\n", "y_lines2" ] }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "53.41935483870966" + "53.16129032258063" ] }, - "execution_count": 34, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -4066,7 +4067,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 29, "metadata": {}, "outputs": [ { @@ -4852,7 +4853,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -4864,7 +4865,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "7d91a6c017334f98835351d139242191", + "model_id": "f109ae4a8d8c4b7f80b2aebec982ca5f", "version_major": 2, "version_minor": 0 }, @@ -4885,10 +4886,10 @@ "\n", "def catchclick(frame):\n", " image = reader.get_data(frame)\n", - " pyplot.imshow(image, interpolation='nearest');\n", + " plt.imshow(image, interpolation='nearest');\n", "\n", "\n", - "fig = pyplot.figure()\n", + "fig = plt.figure()\n", "\n", "connectId = fig.canvas.mpl_connect('button_press_event',onclick)\n", "\n", @@ -4897,41 +4898,41 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[[298.008064516129, 116.25],\n", - " [321.2338709677419, 118.83064516129036],\n", - " [344.4596774193548, 121.41129032258061],\n", - " [370.2661290322581, 123.99193548387098],\n", - " [393.4919354838709, 129.1532258064516],\n", - " [416.71774193548384, 139.47580645161293],\n", - " [439.94354838709677, 149.79838709677426],\n", - " [463.1693548387097, 160.1209677419355],\n", - " [488.97580645161287, 173.02419354838707],\n", - " [509.62096774193543, 185.92741935483878],\n", - " [532.8467741935483, 198.83064516129036],\n", - " [558.6532258064517, 219.47580645161293],\n", - " [581.8790322580644, 234.95967741935488],\n", - " [607.6854838709678, 255.60483870967744],\n", - " [628.3306451612902, 273.66935483870964],\n", - " [654.1370967741934, 296.89516129032256],\n", - " [674.7822580645161, 320.1209677419355],\n", - " [698.008064516129, 345.92741935483866],\n", - " [723.8145161290322, 376.89516129032256],\n", - " [744.4596774193549, 402.70161290322574],\n", - " [767.6854838709678, 431.0887096774193],\n", - " [790.9112903225807, 462.0564516129032],\n", - " [816.7177419354839, 495.6048387096774],\n", - " [837.3629032258063, 531.733870967742],\n", - " [860.5887096774193, 567.8629032258063],\n", - " [886.3951612903224, 606.5725806451612]]" + "[[298.25, 98.75],\n", + " [324.05645161290323, 98.75],\n", + " [344.7016129032258, 101.33064516129036],\n", + " [370.5080645161291, 106.49193548387098],\n", + " [393.7338709677419, 114.23387096774195],\n", + " [414.37903225806446, 121.97580645161293],\n", + " [442.7661290322581, 134.8790322580645],\n", + " [463.41129032258067, 140.04032258064512],\n", + " [489.21774193548384, 155.52419354838707],\n", + " [515.0241935483871, 168.42741935483878],\n", + " [538.25, 181.33064516129036],\n", + " [558.8951612903227, 196.8145161290323],\n", + " [584.7016129032259, 214.8790322580645],\n", + " [607.9274193548388, 235.52419354838707],\n", + " [628.5725806451612, 256.16935483870964],\n", + " [654.3790322580644, 276.8145161290322],\n", + " [675.0241935483871, 305.20161290322574],\n", + " [700.8306451612902, 325.8467741935484],\n", + " [724.0564516129032, 354.23387096774195],\n", + " [749.8629032258063, 382.6209677419355],\n", + " [773.0887096774193, 411.008064516129],\n", + " [793.733870967742, 449.7177419354838],\n", + " [819.5403225806451, 478.1048387096774],\n", + " [840.1854838709676, 511.65322580645153],\n", + " [865.991935483871, 552.9435483870967],\n", + " [889.2177419354839, 589.0725806451612]]" ] }, - "execution_count": 37, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -4949,17 +4950,17 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 31, "metadata": {}, "outputs": [], "source": [ - "x = numpy.array(coords)[:,0] *0.1 / gap_lines2.mean()\n", - "y = numpy.array(coords)[:,1] *0.1 / gap_lines2.mean()" + "x = np.array(coords)[:,0] *0.1 / gap_lines2.mean()\n", + "y = np.array(coords)[:,1] *0.1 / gap_lines2.mean()" ] }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 32, "metadata": {}, "outputs": [ { @@ -5745,7 +5746,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -5757,8 +5758,8 @@ ], "source": [ "# make a scatter plot of the projectile positions\n", - "fig = pyplot.figure()\n", - "pyplot.scatter(x,-y);" + "fig = plt.figure()\n", + "plt.scatter(x,-y);" ] }, { @@ -5770,23 +5771,23 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 33, "metadata": {}, "outputs": [], "source": [ - "delta_y = (y[1:] - y[:-1])" + "delta_y = (y[1:] - y[0:-1])" ] }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The acceleration in the y direction is: 10.14\n" + "The acceleration in the y direction is: 10.19\n" ] } ], @@ -5798,14 +5799,14 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The acceleration in the x direction is: 0.72\n" + "The acceleration in the x direction is: -0.73\n" ] } ], @@ -5820,7 +5821,30 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "##### Discuss\n", + "## Saving our hard work\n", + "\n", + "We have put a lot of effort into processing these images so far. Let's save our variables `time`, `x`, and `y` so we can load it back later. \n", + "\n", + "Use the command `np.savez(file_name, array1,array2,...)` to save our arrays for use later.\n", + "\n", + "The x-y-coordinates occur at 1/60 s, 2/60s, ... len(y)/60s = `np.arange(0,len(y))/60`" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [], + "source": [ + "t = np.arange(0,len(y))/60\n", + "np.savez('../data/projectile_coords.npz',t=t,x=x,y=-y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Discussion\n", "\n", "* What did you get for the $x$ and $y$ accelerations? What did your neighbor get?\n", "* Do the results make sense to you? Why or why not?" @@ -5855,27 +5879,17 @@ "\n", "Suppose we had some high-resolution experimental data of a falling ball. Might we be able to compute the acceleration of gravity, and get a value closer to the actual acceleration of $9.8\\rm{m/s}^2$?\n", "\n", - "You're in luck! Physics professor Anders Malthe-Sørenssen of Norway has some high-resolution data on the website to accompany his book [3]. We contacted him by email to ask for permission to use the data set of a falling tennis ball, and he graciously agreed. _Thank you!_ His data was recorded with a motion detector on the ball, measuring the $y$ coordinate at tiny time intervals of $\\Delta t = 0.001\\rm{s}$. Pretty fancy.\n", - "\n", - "We have the data in our repository for this course, but you may have to download it first, if you got this Jupyter notebook by itself. If so, add a code cell below, and execute:\n", - "\n", - "```Python\n", - "filename = 'fallingtennisball02.txt'\n", - "url = 'http://go.gwu.edu/engcomp3data1'\n", - "urlretrieve(url, filename)\n", - "```\n", - "\n", - "You already imported `urlretrieve` above to get the video. Remember to then comment the assignment of the `filename` variable below. " + "You're in luck! Physics professor Anders Malthe-Sørenssen of Norway has some high-resolution data on the website to accompany his book [3]. We contacted him by email to ask for permission to use the data set of a falling tennis ball, and he graciously agreed. _Thank you!_ His data was recorded with a motion detector on the ball, measuring the $y$ coordinate at tiny time intervals of $\\Delta t = 0.001\\rm{s}$. Pretty fancy." ] }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 130, "metadata": {}, "outputs": [], "source": [ "filename = '../data/fallingtennisball02.txt'\n", - "t, y = numpy.loadtxt(filename, usecols=[0,1], unpack=True)" + "t, y = np.loadtxt(filename, usecols=[0,1], unpack=True)" ] }, { @@ -5887,7 +5901,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 131, "metadata": {}, "outputs": [ { @@ -6673,7 +6687,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -6684,8 +6698,8 @@ } ], "source": [ - "fig = pyplot.figure(figsize=(6,4))\n", - "pyplot.plot(t,y);" + "fig = plt.figure(figsize=(6,4))\n", + "plt.plot(t,y);" ] }, { @@ -6697,7 +6711,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 132, "metadata": {}, "outputs": [ { @@ -6708,18 +6722,18 @@ " 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057])" ] }, - "execution_count": 45, + "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "numpy.where( y < 0 )[0]" + "np.where( y < 0 )[0]" ] }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 133, "metadata": {}, "outputs": [], "source": [ @@ -6728,7 +6742,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 134, "metadata": {}, "outputs": [ { @@ -6737,7 +6751,7 @@ "0.001000000000000002" ] }, - "execution_count": 47, + "execution_count": 134, "metadata": {}, "output_type": "execute_result" } @@ -6749,7 +6763,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 135, "metadata": {}, "outputs": [ { @@ -6775,7 +6789,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 136, "metadata": {}, "outputs": [ { @@ -7561,7 +7575,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -7572,15 +7586,15 @@ } ], "source": [ - "fig = pyplot.figure(figsize=(6,4))\n", - "pyplot.plot(ay);" + "fig = plt.figure(figsize=(6,4))\n", + "plt.plot(ay);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "##### Discuss with your neighbor\n", + "## Discussion\n", "\n", "* What do you see in the plot of acceleration computed from the high-resolution data?\n", "* Can you explain it? What do you think is causing this?" @@ -7598,6 +7612,7 @@ "* Observed acceleration of falling bodies is less than $9.8\\rm{m/s}^2$.\n", "* Capture mouse clicks on several video frames using widgets!\n", "* Projectile motion is like falling under gravity, plus a horizontal velocity.\n", + "* Save our hard work as a numpy .npz file __Check the Problems for loading it back into your session__\n", "* Compute numerical derivatives using differences via array slicing.\n", "* Real data shows free-fall acceleration decreases in magnitude from $9.8\\rm{m/s}^2$." ] @@ -7615,179 +7630,62 @@ "3. _Elementary Mechanics Using Python_ (2015), Anders Malthe-Sorenssen, Undergraduate Lecture Notes in Physics, Springer. Data at http://folk.uio.no/malthe/mechbook/" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problems\n", + "\n", + "1. Instead of using $\\frac{\\Delta v}{\\Delta t}$, we can use the [numpy polyfit](https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html) to determine the acceleration of the ball. \n", + "\n", + " a. Use your coordinates from the saved .npz file you used above to load your projectile motion data\n", + " \n", + " ```python\n", + " npz_coords = np.load('projectile_coords.npz')\n", + " t = npz_coords['t']\n", + " x = npz_coords['x']\n", + " y = npz_coords['y']```\n", + " \n", + " b. Calculate $v_x$ and $v_y$ using a finite difference again, then do a first-order polyfit to $v_x-$ and $v_y-$ vs $t$. What is the acceleration now?\n", + " \n", + " c. Now, use a second-order polynomial fit for x- and y- vs t. What is acceleration now?\n", + " \n", + " d. Plot the polyfit lines for velocity and position (2 figures) with the finite difference velocity data points and positions. Which lines look like better e.g. which line fits the data?" + ] + }, { "cell_type": "code", - "execution_count": 50, + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "execution_count": 50, - "metadata": {}, - "output_type": "execute_result" - } - ], "source": [ - "# Execute this cell to load the notebook's style sheet, then ignore it\n", - "from IPython.core.display import HTML\n", - "css_file = '../style/custom.css'\n", - "HTML(open(css_file, \"r\").read())" + "2. Not only can we measure acceleration of objects that we track, we can look at other physical constants like [coefficient of restitution](https://en.wikipedia.org/wiki/Coefficient_of_restitution), $e$ . \n", + "\n", + " During a collision with the ground, the coefficient of restitution is\n", + " \n", + " $e = -\\frac{v_{y}'}{v_{y}}$ . \n", + " \n", + " Where $v_y'$ is y-velocity perpendicular to the ground after impact and $v_y$ is the y-velocity after impact. \n", + " \n", + " a. Calculate $v_y$ and plot as a function of time from the data `'../data/fallingtennisball02.txt'`\n", + " \n", + " b. Find the locations when $v_y$ changes rapidly i.e. the impact locations. Get the maximum and minimum velocities closest to the impact location. _Hint: this can be a little tricky. Try slicing the data to include one collision at a time before using the `np.min` and `np.max` commands._\n", + " \n", + " c. Calculate the $e$ for each of the three collisions\n", + " " ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/notebooks/02_Step_Future.ipynb b/notebooks/02_Step_Future.ipynb index c0c067e..a103501 100644 --- a/notebooks/02_Step_Future.ipynb +++ b/notebooks/02_Step_Future.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "###### Content under Creative Commons Attribution license CC-BY 4.0, code under BSD 3-Clause License © 2017 L.A. Barba, N.C. Clementi" + "###### Content modified under Creative Commons Attribution license CC-BY 4.0, code under BSD 3-Clause License © 2020 Ryan C. Cooper" ] }, { @@ -13,26 +13,14 @@ "source": [ "# Step to the future\n", "\n", - "Welcome to Lesson 2 of the course module \"Tour the dynamics of change and motion,\" in _Engineering Computations_. The previous lesson, [Catch things in motion](http://go.gwu.edu/engcomp3lesson1), showed you how to compute velocity and acceleration of a moving body whose positions were known. \n", + "Welcome to Lesson 2 of the course module \"Initial Value Problems (IVPs),\" in _Computational Mechanics_ The previous lesson, [Catch things in motion](http://go.gwu.edu/engcomp3lesson1), showed you how to compute velocity and acceleration of a moving body whose positions were known. \n", "\n", - "Time history of position can be captured on a long-exposure photograph (using a strobe light), or on video. But digitizing the positions from images can be a bit tedious, and error-prone. Luckily, we found online a data set from a motion-capture experiment of a falling ball, with high resolution [1]. You computed acceleration and found that it was not only smaller than the theoretical value of $9.8 \\rm{m/s}^2$, but it _decreased_ over time. The effect is due to air resistance and is what leads to objects reaching a _terminal velocity_ in freefall.\n", - "\n", - "In general, not only is [motion capture](https://en.wikipedia.org/wiki/Motion_capture) (a.k.a., _mo-cap_) expensive, but it's inappropriate for many physical scenarios. Take a roller-coaster ride, for example: during design of the ride, it's more likely that the engineers will use an _accelerometer_. It really is the acceleration that makes a roller-coaster ride exciting, and they only rarely go faster than highway speeds (say, 60 mph) [2].\n", - "How would an engineer analyze data captured with an accelerometer?" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## A roller-coaster ride\n", - "\n", - "Prof. Anders Malthe-Sorenssen has a file with accelerometer data for a roller-coaster ride called \"The Rocket\" (we don't know if it's real or made up!). He has kindly given permission to use his data. So let's load it and have a look. We'll first need our favorite numerical Python libraries, of course." + "Time history of position can be captured on a long-exposure photograph (using a strobe light), or on video. But digitizing the positions from images can be a bit tedious, and error-prone. Luckily, we found online a data set from a motion-capture experiment of a falling ball, with high resolution [1]. You computed acceleration and found that it was smaller than the theoretical value of $9.8 \\rm{m/s}^2$ and _decreased_ over time. The effect is due to air resistance and is what leads to objects reaching a _terminal velocity_ in freefall." ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -42,92 +30,13 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 147, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", - "\n", - "plt.rc('font', family='sans', size='18')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If you don't have the data file in the location we assume below, you can get it by adding a code cell and executing this code in it, then commenting or deleting the `filename` assignment before the call to `numpy.loadtxt()`.\n", - "\n", - "```Python\n", - "from urllib.request import urlretrieve\n", - "URL = 'http://go.gwu.edu/engcomp3data2?accessType=DOWNLOAD'\n", - "urlretrieve(URL, 'therocket.txt')\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "filename = '../data/therocket.txt'\n", - "t, a = np.loadtxt(filename, usecols=[0,1], unpack=True)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We'll take a peek at the data by printing the first five pairs of $(t, a)$ values, then plot the whole set below. Time is given in units of seconds, while acceleration is in $\\rm{m/s}^2$." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.0 0.2731644\n", - "0.1 1.4411079\n", - "0.2 2.6693138\n", - "0.3 4.2383806\n", - "0.4 5.6499504\n" - ] - } - ], - "source": [ - "for i in range(0,5): print(t[i],a[i])" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot the acceleration over time\n", - "fig = plt.figure(figsize=(8, 3))\n", - "\n", - "plt.plot(t, a, color='#004065', linestyle='-', linewidth=1) \n", - "plt.title('Acceleration of roller-coster ride data, from [1]. \\n')\n", - "plt.xlabel('Time [s]')\n", - "plt.ylabel('[m/s$^2$]');" + "plt.rcParams.update({'font.size': 22})\n", + "plt.rcParams['lines.linewidth'] = 3" ] }, { @@ -136,7 +45,7 @@ "source": [ "### Set things up to compute velocity and position\n", "\n", - "Our challenge now is to find the motion description—the position $x(t)$—from the acceleration data. In the [previous lesson](http://go.gwu.edu/engcomp3lesson1), we did the opposite: with position data, get the velocity and acceleration, using _numerical derivatives_:\n", + "Our challenge now is to find the motion description—the position $x(t)$—from a function of acceleration. In the [previous lesson](http://go.gwu.edu/engcomp3lesson1), we did the opposite: with position data, get the velocity and acceleration, using _numerical derivatives_:\n", "\n", "\\begin{equation}\n", "v(t_i) = \\frac{dx}{dt} \\approx \\frac{x(t_i+\\Delta t)-x(t_i)}{\\Delta t}\n", @@ -146,81 +55,76 @@ "a(t_i) = \\frac{dv}{dt} \\approx \\frac{v(t_i+\\Delta t)-v(t_i)}{\\Delta t}\n", "\\end{equation}\n", "\n", - "Since this time we're dealing with horizontal acceleration, we swapped the position variable from $y$ to $x$ in the equation for velocity, above. \n", + "Almost every problem that deals with Newton's second law is a second-order differential equation. The acceleration is a function of position, velocity, and sometimes time _if there is a forcing function f(t)_. \n", "\n", - "The key to our problem is realizing that if we have the initial velocity, we can use the acceleration data to find the velocity after a short interval of time. And if we have the initial position, we can use the known velocity to find the new position after a short interval of time. Let's rearrange the equation for acceleration above, by solving for the velocity at $t_i + \\Delta t$:\n", + "The key to solving a second order differential equation is realizing that if we have the initial velocity, we can use the acceleration to find the velocity after a short interval of time. And if we have the initial position, we can use the known velocity to find the new position after a short interval of time. Let's rearrange the equation for acceleration above, by solving for the velocity at $t_i + \\Delta t$:\n", "\n", "\\begin{equation}\n", " v(t_i+\\Delta t) \\approx v(t_i) + a(t_i) \\Delta t\n", "\\end{equation}\n", "\n", - "We need to know the velocity and acceleration at some initial time, $t_0$, and then we can compute the velocity $v(t_i + \\Delta t)$. For the roller-coaster ride, it's natural to assume that the initial velocity is zero, and the initial position is zero with respect to a convenient reference system. We're actually ready to solve this!\n", + "Consider our first computational mechanics model of a freefalling object that is dropped.\n", "\n", - "Let's save the time increment for our data set in a variable named `dt`, and compute the number of time increments in the data. Then, we'll initialize new arrays of velocity and position to all-zero values, with the intention of updating these to the computed values." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0.1" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "#time increment\n", - "dt = t[1]-t[0]\n", - "dt" + " \n", + "\n", + "An object falling is subject to the force of \n", + "\n", + "- gravity ($F_g$=mg) and \n", + "- drag ($F_d=cv^2$)\n", + "\n", + "Acceleration of the object:\n", + "\n", + "$\\sum F=ma=F_g-F_d=cv^2 - mg = m\\frac{dv}{dt}$\n", + "\n", + "so,\n", + "\n", + "$a=\\frac{c}{m}v(t_{i})^2-g$\n", + "\n", + "then, our acceleration is defined from Newton's second law and position is defined through its definition, $v=\\frac{dx}{dt}$. \n", + "\n", + "_Note: the direction of positive acceleration was changed to up, so that a positive $x$ is altitude, we will still have the same speed vs time function from [Module_01-03_Numerical_error](https://github.uconn.edu/rcc02007/CompMech01-Getting-started/blob/master/notebooks/03_Numerical_error.ipynb)_" ] }, { - "cell_type": "code", - "execution_count": 8, + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "151" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], "source": [ - "#number of time increments\n", - "N = len(t)\n", - "N" + "### Step through time\n", + "\n", + "In the code cell below, we define acceleration as a function of velocity and add two parameters `c` and `m` to define drag coefficient and mass of the object. " ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 163, "metadata": {}, "outputs": [], "source": [ - "#initialize v and x arrays to zero\n", - "v = numpy.zeros(N)\n", - "x = numpy.zeros(N)" + "def a_freefall(v,c=0.25,m=60):\n", + " '''Calculate the acceleration of an object given its \n", + " drag coefficient and mass\n", + " \n", + " Arguments:\n", + " ---------\n", + " v: current velocity (m/s)\n", + " c: drag coefficient set to a default value of c=0.25 kg/m\n", + " m: mass of object set to a defualt value of m=60 kg\n", + " \n", + " returns:\n", + " ---------\n", + " a: acceleration of freefalling object under the force of gravity and drag\n", + " '''\n", + " a=-c/m*v**2*np.sign(v)-9.81\n", + " return a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Step through time\n", + "Now we use a `for` statement to step through the sequence of acceleration values, each time computing the velocity and position at the subsequent time instant. We first have to __initialize__ our variables `x` and `v`. We can use initial conditions to set `x[0]` and `v[0]`. The rest of the values we will overwrite based upon our stepping solution.\n", "\n", - "In the code cell below, we use a `for` statement to step through the sequence of acceleration values, each time computing the velocity and position at the subsequent time instant. We are applying the equation for $v(t_i + \\Delta t)$ above, and a similar equation for position:\n", + "We are applying the equation for $v(t_i + \\Delta t)$ above, and a similar equation for position:\n", "\n", "\\begin{equation}\n", " x(t_i+\\Delta t) \\approx x(t_i) + v(t_i) \\Delta t\n", @@ -229,32 +133,62 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 164, "metadata": {}, "outputs": [], "source": [ - "for i in range(N-1):\n", - " v[i+1] = v[i] + a[i]*dt\n", - " x[i+1] = x[i] + v[i]*dt" + "N = 100 # define number of time steps\n", + "t=np.linspace(0,12,N) # set values for time (our independent variable)\n", + "dt=t[1]-t[0]\n", + "x=np.zeros(len(t)) # initialize x\n", + "v=np.zeros(len(t)) # initialize v\n", + "\n", + "x[0] = 440 # define initial altitude of the object\n", + "v[0] = 0\n", + "\n", + "for i in range(1,N):\n", + " dvdt = a_freefall(v[i-1])\n", + " v[i] = v[i-1] + dvdt*dt\n", + " x[i] = x[i-1] + v[i-1]*dt" + ] + }, + { + "cell_type": "code", + "execution_count": 165, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-9.393333333333334" + ] + }, + "execution_count": 165, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a_freefall(-10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "And there you have it. You have computed the velocity and position over time from the acceleration data. We can now make plots of the computed variables. Note that we use the Matplotlib [`subplot()`](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplot.html?highlight=matplotlib%20pyplot%20subplot#matplotlib.pyplot.subplot) function to get the two plots in one figure. The argument to `subplot()` is a set of three digits, corresponding to the number of rows, number of columns, and plot number in a matrix of sub-plots. " + "And there you have it. You have computed the velocity __and position__ over time from Newton's second law. We can now make plots of the computed variables. Note that we use the Matplotlib [`subplot()`](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplot.html?highlight=matplotlib%20pyplot%20subplot#matplotlib.pyplot.subplot) function to get the two plots in one figure. The argument to `subplot()` is a set of three digits, corresponding to the number of rows, number of columns, and plot number in a matrix of sub-plots. " ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 166, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" + "
" ] }, "metadata": { @@ -265,17 +199,26 @@ ], "source": [ "# plot velocity and position over time\n", - "fig = pyplot.figure(figsize=(10,6))\n", + "fig = plt.figure(figsize=(8,6))\n", "\n", - "pyplot.subplot(211)\n", - "pyplot.plot(t, v, color='#0096d6', linestyle='-', linewidth=1) \n", - "pyplot.title('Velocity and position of roller-coster ride (data from [1]). \\n')\n", - "pyplot.ylabel('$v$ [m/s] ')\n", + "plt.subplot(211)\n", + "plt.plot(t, v, color='#0096d6', linestyle='-', linewidth=1) \n", + "plt.title('Velocity and position of \\nfreefalling object m=60-kg and c=0.25 kg/s. \\n')\n", + "plt.ylabel('$v$ (m/s) ')\n", "\n", - "pyplot.subplot(212)\n", - "pyplot.plot(t, x, color='#008367', linestyle='-', linewidth=1) \n", - "pyplot.xlabel('Time [s]')\n", - "pyplot.ylabel('$x$ [m]');" + "plt.subplot(212)\n", + "plt.plot(t, x, color='#008367', linestyle='-', linewidth=1) \n", + "plt.xlabel('Time (s)')\n", + "plt.ylabel('$x$ (m)');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise\n", + "\n", + "The initial height is 440 m, the height of the tip of the [Empire State Building](https://en.wikipedia.org/wiki/Empire_State_Building). How long would it take for the object to reach the ground from this height? How accurate is your estimation e.g. what is the error bar for your solution?" ] }, { @@ -284,7 +227,9 @@ "source": [ "## Euler's method\n", "\n", - "The method we used above to compute the velocity and position from acceleration data is known as _Euler's method_. The eminent Swiss mathematician Leonhard Euler presented it in his book _\"Institutionum calculi integralis,\"_ published around 1770 [3].\n", + "We first used Euler's method in [Module_01: 03_Numerical_error](https://github.uconn.edu/rcc02007/CompMech01-Getting-started/blob/master/notebooks/03_Numerical_error.ipynb). Here we will look at it with more depth. \n", + "\n", + "The eminent Swiss mathematician Leonhard Euler presented it in his book _\"Institutionum calculi integralis,\"_ published around 1770 [3].\n", "\n", "You can understand why it works by writing out a Taylor expansion for $x(t)$:\n", "\n", @@ -294,7 +239,11 @@ "\n", "With $v=dx/dt$, you can see that the first two terms on the right-hand side correspond to what we used in the code above. That means that Euler's method makes an approximation by throwing away the terms $\\frac{d^2 x}{dt^2}\\frac{\\Delta t^2}{2} + \\frac{d^3 x}{dt^3}\\frac{\\Delta t^3}{3!}+\\cdots$. So the error made in _one step_ of Euler's method is proportional to $\\Delta t^2$. Since we take $N=T/\\Delta t$ steps (for a final time instant $T$), we conclude that the error overall is proportional to $\\Delta t$. \n", "\n", - "#### **Euler's method is a first-order method** because the error in the approximation goes with the first power of the time increment $\\Delta t$." + "#### **Euler's method is a first-order method** because the error in the approximation goes is proportional to the first power of the time increment $\\Delta t$.\n", + "\n", + "i.e.\n", + "\n", + "error $\\propto$ $\\Delta t$" ] }, { @@ -309,14 +258,14 @@ "Consider the differential equation corresponding to an object in free fall:\n", "\n", "\\begin{equation}\n", - "\\ddot{y}=-g,\n", + "\\ddot{y}=\\frac{c}{m}v^2-g,\n", "\\end{equation}\n", "\n", "where the dot above a variable represents the time derivative, and $g$ is the acceleration of gravity. Introducing the velocity as intermediary variable, we can write:\n", "\n", "\\begin{eqnarray}\n", "\\dot{y} &=& v \\nonumber\\\\\n", - "\\dot{v} &=& -g\n", + "\\dot{v} &=& \\frac{c}{m}v^2-g\n", "\\end{eqnarray}\n", "\n", "The above is a system of two ordinary differential equations, with time as the independent variable. For its numerical solution, we need two initial conditions, and Euler's method:\n", @@ -338,7 +287,7 @@ "\n", "\\begin{equation}\n", "\\dot{\\mathbf{y}} = \\begin{bmatrix}\n", - "v \\\\ -g\n", + "v \\\\ \\frac{c}{m}v^2-g\n", "\\end{bmatrix}.\n", "\\end{equation}\n", "\n", @@ -349,35 +298,37 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Study the code below: the function `freefall()` computes the right-hands side of the equation, and the function `eulerstep()` takes the state and applies Euler's method to update it one time increment." + "Study the code below: the function `freefall()` computes the right-hand side of the equation, and the function `eulerstep()` takes the state and applies Euler's method to update it one time increment." ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 197, "metadata": {}, "outputs": [], "source": [ - "def freefall(state):\n", + "def freefall(state,c=0,m=60):\n", " '''Computes the right-hand side of the freefall differential \n", " equation, in SI units.\n", " \n", " Arguments\n", " ---------- \n", " state : array of two dependent variables [y v]^T\n", + " c : drag coefficient for object; default set to 0 kg/m (so no drag considered)\n", + " m : mass of falling object; default set to 60 kg\n", " \n", " Returns\n", " -------\n", - " derivs: array of two derivatives [v -g]^T\n", + " derivs: array of two derivatives [v, c/m*v**2-g]\n", " '''\n", " \n", - " derivs = np.array([state[1], -9.8])\n", + " derivs = np.array([state[1], -c/m*state[1]**2*np.sign(state[1])-9.81])\n", " return derivs" ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 198, "metadata": {}, "outputs": [], "source": [ @@ -406,20 +357,29 @@ "source": [ "## Numerical solution vs. experiment\n", "\n", - "Here's an idea! Let's use the `freefall()` and `eulerstep()` functions to obtain a numerical solution with the same initial conditions as the falling-ball experiment from [Lesson 1](./01_Catch_Motion.ipynb), and compare with the experimental data. \n", + "Use the `freefall()` and `eulerstep()` functions to obtain a numerical solution with the same initial conditions as the falling-ball experiment from [Lesson 1](./01_Catch_Motion.ipynb), and compare with the experimental data. \n", + "\n", + "In [Lesson 1](./01_Catch_Motion.ipynb), we had considered only the acceleration due to gravity. So before we get into the specifics of the effects on drag, leave c=0 so that we have a constant acceleration problem, \n", + "\n", + "$\\ddot{y} = -g$\n", "\n", + "and our vector form is \n", "\n", - "You already imported `urlretrieve` above. Remember to then comment the assignment of the `filename` variable below. We'll load it from our local copy." + "\\begin{equation}\n", + "\\dot{\\mathbf{y}} = \\begin{bmatrix}\n", + "v \\\\ -g\n", + "\\end{bmatrix}.\n", + "\\end{equation}\n" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 310, "metadata": {}, "outputs": [], "source": [ "filename = '../data/fallingtennisball02.txt'\n", - "t, y = numpy.loadtxt(filename, usecols=[0,1], unpack=True)" + "t, y = np.loadtxt(filename, usecols=[0,1], unpack=True)" ] }, { @@ -431,7 +391,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 311, "metadata": {}, "outputs": [], "source": [ @@ -441,7 +401,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 312, "metadata": {}, "outputs": [], "source": [ @@ -459,28 +419,40 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 314, "metadata": {}, "outputs": [], "source": [ "#initialize array\n", - "num_sol = numpy.zeros([N,2])" + "num_sol = np.zeros([N,2])" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 315, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1.6 , -0.00981])" + ] + }, + "execution_count": 315, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "#Set intial conditions\n", "num_sol[0,0] = y0\n", - "num_sol[0,1] = v0" + "num_sol[0,1] = v0\n", + "eulerstep(num_sol[0],freefall,dt)" ] }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 316, "metadata": {}, "outputs": [], "source": [ @@ -497,12 +469,12 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 317, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -514,44 +486,57 @@ } ], "source": [ - "fig = pyplot.figure(figsize=(6,4))\n", - "pyplot.plot(t[:N], y[:N], 's', alpha=0.8, label='Experimental data')\n", - "pyplot.plot(t[:N], num_sol[:,0], linewidth=2, linestyle='--', label='Numerical solution')\n", - "pyplot.xlabel('Time [s]')\n", - "pyplot.ylabel('$y$ [m]')\n", - "pyplot.title('Free fall tennis ball (no air resistance) \\n')\n", - "pyplot.legend();" + "fig = plt.figure(figsize=(6,4))\n", + "plt.plot(t[:N], y[:N], 's', alpha=0.8, label='Experimental data')\n", + "plt.plot(t[:N], num_sol[:,0], linewidth=2, linestyle='-', label='Numerical solution')\n", + "plt.xlabel('Time (s)')\n", + "plt.ylabel('$y$ (m)')\n", + "plt.title('Free fall tennis ball (no air resistance) \\n')\n", + "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The two lines look very close… but let's plot the difference to get an idea of the error." + "The two lines look very close… but let's plot the difference to get understand the [error](https://github.uconn.edu/rcc02007/CompMech01-Getting-started/blob/master/notebooks/03_Numerical_error.ipynb)." ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 318, "metadata": {}, "outputs": [ { "data": { - "image/png": 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NMrNPdVCVRETa7cVlG/nXiyv47FHjGdK3MulwpIfY6cO0JzCzycBtwKHuvsDM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\nTkSuQmCC\n", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "fig = pyplot.figure(figsize=(6,4))\n", - "pyplot.plot(t[:N], y[:N]-num_sol[:,0])\n", - "pyplot.title('Difference between numerical solution and experimental data.\\n')\n", - "pyplot.xlabel('Time [s]')\n", - "pyplot.ylabel('$y$ [m]');" + "fig = plt.figure(figsize=(6,4))\n", + "plt.plot(t[:N], y[:N]-num_sol[:,0])\n", + "plt.title('Difference between numerical solution and experimental data.\\n')\n", + "plt.xlabel('Time [s]')\n", + "plt.ylabel('$y$ [m]');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise\n", + "\n", + "Create a plot of the analytical solution for y-vs-t for an object that accelerates due to gravity, plot the difference between the analytical solution and the experimental data with the plot above. \n", + "\n", + "_Hint: remember the kinematic equations for constant acceleration_ $y(t) = y(0) + \\dot{y}(0)t - \\frac{gt^2}{2}$" ] }, { @@ -560,9 +545,9 @@ "source": [ "## Air resistance\n", "\n", - "In [Lesson 1](./01_Catch_Motion.ipynb) of this module, we computed the acceleration of gravity and got a value less than the theoretical $9.8 \\rm{m/s}^2$, even when using high-resolution experimental data. Did you figure out why?\n", + "In [Lesson 1](./01_Catch_Motion.ipynb) of this module, we computed the acceleration of gravity and got a value less than the theoretical $9.8 \\rm{m/s}^2$, even when using high-resolution experimental data. \n", "\n", - "We were missing the effect of air resistance! When an object moves in a fluid, like air, it applies a force on the fluid, and consequently the fluid applies an equal and opposite force on the object (Newton's third law).\n", + "We did not account for air resistance. When an object moves in a fluid, like air, it applies a force on the fluid, and consequently the fluid applies an equal and opposite force on the object (Newton's third law).\n", "\n", "This force is the *drag* of the fuid, and it opposes the direction of travel. The drag force depends on the object's geometry, and its velocity: for a sphere, its magnitude is given by:\n", "\n", @@ -570,34 +555,16 @@ " F_d = \\frac{1}{2} \\pi R^2 \\rho C_d v^2,\n", "\\end{equation}\n", "\n", - "where $R$ is the radius of the sphere, $\\rho$ the density of the fluid, $C_d$ the drag coefficient of a sphere, and $v$ is the velocity." + "where $R$ is the radius of the sphere, $\\rho$ the density of the fluid, $C_d$ the drag coefficient of a sphere, and $v$ is the velocity.\n", + "\n", + "In the first module, we used the constant $c$, where $c= \\frac{1}{2} \\pi R^2 \\rho C_d$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Since we have another force involved, we'll have to rethink the problem formulation. The state variables are still the same (position and velocity):\n", - "\n", - "\\begin{equation}\n", - "\\mathbf{y} = \\begin{bmatrix}\n", - "y \\\\ v\n", - "\\end{bmatrix}.\n", - "\\end{equation}\n", - "\n", - "But we'll adjust the differential equation to add the effect of air resistance. In vector form, we can write it as follows:\n", - "\n", - "\\begin{equation}\n", - "\\dot{\\mathbf{y}} = \\begin{bmatrix}\n", - "v \\\\ a_y\n", - "\\end{bmatrix},\n", - "\\end{equation}\n", - "\n", - "where $a_y$ now includes the acceleration due to the drag force:\n", - "\n", - "\\begin{equation}\n", - " a_y = -g + a_{\\text{drag}} \n", - "\\end{equation}\n", + "We can update our defintion for drag with this _higher fidelity_ description of drag\n", "\n", "With $F_{\\text{drag}} = m a_{\\text{drag}}$:\n", "\n", @@ -628,36 +595,31 @@ }, { "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 319, + "metadata": {}, "outputs": [], "source": [ - "def fall_drag(state):\n", + "def fall_drag(state,C_d=0.47,m=0.0577,R = 0.0661/2):\n", " '''Computes the right-hand side of the differential equation\n", " for the fall of a ball, with drag, in SI units.\n", " \n", " Arguments\n", " ---------- \n", " state : array of two dependent variables [y v]^T\n", - " \n", + " m : mass in kilograms default set to 0.0577 kg\n", + " C_d : drag coefficient for a sphere default set to 0.47 (no units)\n", + " R : radius of ball default in meters is 0.0661/2 m (tennis ball)\n", " Returns\n", " -------\n", " derivs: array of two derivatives [v (-g+a_drag)]^T\n", " '''\n", - " R = 0.0661/2 # radius in meters\n", - " m = 0.0577 # mass in kilograms\n", + " \n", " rho = 1.22 # air density kg/m^3\n", - " C_d = 0.47 # drag coefficient for a sphere\n", - " pi = numpy.pi\n", + " pi = np.pi\n", " \n", - " a_drag = 1/(2*m) * pi * R**2 * rho * C_d * (state[1])**2\n", + " a_drag = -1/(2*m) * pi * R**2 * rho * C_d * (state[1])**2*np.sign(state[1])\n", " \n", - " derivs = numpy.array([state[1], -9.8 + a_drag])\n", + " derivs = np.array([state[1], -9.8 + a_drag])\n", " return derivs" ] }, @@ -670,13 +632,8 @@ }, { "cell_type": "code", - "execution_count": 22, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 320, + "metadata": {}, "outputs": [], "source": [ "y0 = y[0] # initial position\n", @@ -686,28 +643,18 @@ }, { "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 321, + "metadata": {}, "outputs": [], "source": [ "# initialize array\n", - "num_sol_drag = numpy.zeros([N,2])" + "num_sol_drag = np.zeros([N,2])" ] }, { "cell_type": "code", - "execution_count": 24, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 322, + "metadata": {}, "outputs": [], "source": [ "# Set intial conditions\n", @@ -717,13 +664,8 @@ }, { "cell_type": "code", - "execution_count": 25, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "execution_count": 323, + "metadata": {}, "outputs": [], "source": [ "for i in range(N-1):\n", @@ -739,31 +681,33 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 324, "metadata": {}, "outputs": [ { "data": { - "image/png": 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56DpjUUqVYc6ODrw9ZAwvf1WBNbFvk5QQi+Pm+dBuLLh4WB2euk7XTDIiEnwD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\n4qWXXspxexUrVqRmzZr22A8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qGHNwMLx1fzNucnoQz8v+XCGF8VvfICpsl9Wh5YkmGaWU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\n08Au4Na8cykjp1HAT4CGdP5jwIPAc3nnUs57r6D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razdAKVXt1MZTi3OA+ZXQ7nfAASfz/6yEdbktL29f+nUaTL9Og3Pm2bIy+fXgj/xw8FuaNYmA+COQcJxtcpSzHhn8nvAH72/9AJ/vPWgi9Wkd2JGRHcYyuGOk3iaglKo01TmR7QSWAtuAn4BXgcgKaPc/IrK8AtqpdSxWD7q16Uu3Nn3/mpmVwT0/f8Z3B9ezN3EPR8xJEj0yOchxDqYcx2vzDgaf2ABhbYjxqc9Jz1B6t7wYo4lNKVVBqm0iE5H/5P5ZP/iqKasnw3teyfCeVwL2o7af92/h691fsOvcrwwLrGfvaBK7hVWn9rPCI5bAaG9aWFvQs2F/ovpMpXFwfRdvhFLKnVXbRKbck8XqQY92A+jRboB9hgicPwqn95Jw7lV8M4+R6JHGb+zht5N7eH3NqzTJDOOSuv14YORC8A507QYopdxObUxkg40xXYAA4CTwLfCViNhcG1YNZQwEN4PgZixuNZT701P5cvvHbDj4P3Yl/06s53mOep4mJG49fJkEIc25ULc1a8+nMr7HGLw9vVy9BUqpaq42JrIZTub9boyZIiI7qjyaWsbTy4dRfSYzqs9kAGL/3M+qH1ZykS3RPoT1uUOsP7SZh22/8+TvD9HW0oqhra5kyiWT8PHUYbaUUgVV2+73+RljorF39ihr9/v/A7KAr4HDQBDQHXgY6AqcArqLyLFClp8NzAYIDw/vcfjw4TJshSpSRiqc3strm9/ijbPrOeuZllPkk2WljaUVQy+6khn9rsaqo44o5XZq3X1k+ZU3kRXRrhewAegDLBORucUtUxvuI3M1W1YmX2//lLW73+e39N2c9rSPnByS6Ul0xDgsTbpBk57YAhroSCNKuYnaeB9ZlRCRdGPMEuAjYKSr41F2FqsHw3pdybBeVyK2LNb//Bkf71pNE0sClpQzcOB/HNn5MVMSfqazT1em9ppFZO7bApRStUatT2QOexyvTVwahXLKWKxc1mMMl/UYAzYbnP0Djv3EB9vfIdEjje8zf+D7zT8QtjGQS0IGcsOAm2jdoIWrw1ZKVRE9J2NX1/F6waVRqOJZLBDWCrpGcfM1/+Xe8P+jR2YLfLIsnPZM5NMLnzFh3VjGvTaC9NMH7N3/lVI1mh6R2U12vP7o0ihUqXh6+RA1+AaiBt9A/PlTvLnhFTac/Jr9nnH4ZibgtfnfENiYzKa92eFVn27hHV0dslKqEtSoROa41jUe+FBE7s41/2KgKbBORLJyzfcA5jkmgH9VYbiqAgXXqc8tY+/hFu5h/+EdnI/5FlKPQuJxvtr8EnfadhGeWZ9h4eOYfeks/Lx9XR2yUqqCVNtEZozpDjyfa1YHx+sjxpjbs2eKSJ9cdRoBbR2vuTUHPgTOGmP2AUeBQKAz0BiwAXeJyBcVuQ3KNVpHdIaIzpCVCSd38NvXT+NhMxzxOMWrx1/m7ZWv0cu3N3MH3U77Rq1dHa5Sqpyqbfd7Y8wgYH1x9UQkZxDGXI9qeUNErs01vwX2kfR7AxHYr4kJ9oS2CXu3+59KGpt2v3c/Mcf28drG5/juwhZOeaUAYAR6mva8NmEZBNRzcYRK1Xy1/j6y6kQTmfuyZWbw3sblfHjwPXZ7nmBsRkMeatgB6rXnfOOeUK8ddXwDXB2mUjWSJrJqRBNZzfDL3s3UPf0rzeIPgC2DJ0/t5x1znEt8L+G2offQsl64q0NUqkbRRFaNaCKrYdKT4Mhmpn3zML96nwbAKobOlvbcPOBO+rTs4eIAlaoZNJFVI5rIaiaxZfHehuWsOrCSvZ5x4Lj62iqrGX/vdSvDOg91bYBKubnKSmR6Q7RSDsZiJWrwDaye9TX/7vwYPTKaY7UZDlhjOfHT87DtNYg/4uowlVL56BFZGegRWe2x68B2Vnz/LIuD6+DlOEJ74PwZwhr35abIG/HQUfiVKjE9tViNaCKrhVLi4dAGYvZ8wbiEb8kyQkimP+PCo7jlsrl4Wj1dHaFS1Z6eWlTKlXyDocOV1LnsAa70HkydDE/OeSTx+vHXGLy8P4+ue5y09LTi21FKVTg9IisDPSJTCYlnefazR/gycT3nPNMBCMz04f0hz9EoojcYU0wLStU+ekSmVDUSFBjKvVFP8NnV33CN32jC0r2JyPKk0Y63YfNzcPYP9EuiUlVDj8jKQI/IVH7JyYmc3vMF4ad+goxkNiTE8UBqDNPbzua6/jMxeoSmlB6RKVWd+fkFEt59Ilx2H7QezmtJRzntkci/Dj7J8NcjeW/bKj1CU6qSaCJTqiJ5+UG7USyd8C6jLP3wy7RywnqOxbseZMzrw4jes9HVESpV42giU6oS1K/biEenv8T7o9YwjB74ZFk4bD3JLVtu5tk1d0FGqqtDVKrG0ESmVCVq2rA5T81czpuXvc0lGW3ws1mZkHkOvlkMMd8hWVnFN6KUKpJ29igD7eyhyurY4V9oErsezsWQZstiwumf6dNwOHdevhAvD29Xh6dUpdLOHkrVAE0iLob+/wc9ruPthPMc9kjg3dOrGfrGpaz4/g3tEKJUGWgiU6qqGQONL+aaqP9wfeAkQjO8OOeRzNL9TzBu+Qi2H97u6giVciuayJRyES8vbxZcdT9rJn3JSNMP7ywLf1iOc936mdy9ej7YbK4OUSm3oIlMKRcLqVOXx2a8xKsDltM1LRwb0DzhEGx8HE7vd3V4SlV72tmjDLSzh6osYrPxybfvMTJtLx6pZwF4LjWTDp0ncFm7y1wcnVLlU1mdPfRhSkpVI8ZiYeylUyArAw6uZ/+O93n1wmYyt26k10+deWzsM9QLrOfqMJWqVvTUolLVkdUT2gzHq+9d9Mpsi0Xgx8wdjFo1nGXrn9HejUrloolMqWosonFLXv7bKh5q8xBN0wJJsWby4pH/MHb5MH6L/cXV4SlVLWgiU8oNjOl3JR/M+IarPIbjm2UlxnKSf35+MxzZAnp0pmo5TWRKuQlfHx/+ec2TvDJwBV1Tm3FfQGv49R34/t+knTvs6vCUchnttVgG2mtRuZwIHNsOuz7AlppI1Klt+Po25skrl1EvsIGro1PKKR2iSin1F2OgaQ8YfA+b/SI44HGBn7P2MnrVFbzx3Suujk6pKqWJTCl35uVH/2G3sbjdEpqkBpJszeCJA88yZcVYjp074urolKoSmsiUqgFG9x3FqmlfMYKBeNkMu+QQ49aM5cXoZ10dmlKVThOZUjVEoL8/S2c+z+Ndn6Z5agiplixi938Cv72nD/JUNZp29igD7eyhqruU1FSe+eifzPNJxs8C+AQT02IQERcNwhjj6vBULaWdPZRSJebr48PCqCX4DV4IweGcTDjJ1RsXMGnFSI6di3V1eEpVKE1kStVkQY2g/wK+9G5FJsJejjJ+zVhWfK89G1XNoYlMqZrOYmH66Nt5vNsyIlKDSbFksnT/s8x4awJnk067Ojqlyk0TmVK1xOBuA3hn+pcMtw3E02b4OWsfo969nE9/+cDVoSlVLprIlKpFAv18efK651nUZgmNUwO4YE2HHatg///0idTKbWmvxTLQXouqJoiLj+fjrx7nBp8k+4yQFpxoO5KG9dq4NjBVY2mvRaVUhaoXHMwNkx6BS24C7yC+itnKFWsn8tjn92ETPTpT7kMTmVK1Xf32EHkXa1KyyLQIb51cw6Q3r+DPeO2mr9yDJjKlFHgH8PR17zDJayK+WVb2yXHGfTiWNdvfdnVkShVLE5lSCgBPDyv3X72Ih7s+R7OUOiRbMrlvxxLmr76etEwd4kpVX5rIlFJ5DOsxgBVXr6NfancsAlsTthO36RlIPe/q0JRyShOZUqqAsDqBvDh7OTeF/R93e3am6YXjsOFx5NQeV4emVAHa/b4MtPu9qlVS4uGXlXB6Hw/F7eW4f12eGv8KPl5+ro5MuZla1/3eGNPWGDPfGPOWMWaPMcZmjBFjzMRytjvVGLPJGHPeGHPBGLPNGHOzMabavhdKuZRvMFwyh9/r9uADc5xNqb8xZuUw9p741dWRKQVU40QGzAGeBq4B2gLlfvaEMWYZsBLoCWwCvgLaAM8Bq40x1vKuQ6kayWKhfd/p3NjgDkLSvThhSWDquhms3PyCqyNTqlonsp3AUiAKaAVsKE9jxpgJwN+BE0AXERktIuOB1sBuYDwwt1wRK1WDGWO4ceR0noxcyUVJ9Um32Hh03/PcsmoGqenJrg5P1WLVNpGJyH9E5E4ReU9EDlZAk3c7Xu8Skf251nMS+9EfwEI9xahU0Xq1acfyGZ8yML0/VpshOvlnbnv3akhLdHVoqpaqFR/axpimQA8gHViVv1xENgDHgIZAn6qNTin3Exzgw7JZL3BD3QU0TfXnDu96sHEpnItxdWiqFqoViQzo5njdJSIphdT5MV9dpVQRjDHcMvY6Vk/5lOaNO0HqebK+fZY31j+KzZbl6vBULVJbElkLx+vhIuocyVdXKVUC/nXqQt+50HwgD53ayRNHVnLN22M5n3zG1aGpWsKjuArGmG8qaF0iIkMqqK3SCnC8JhVR54LjNbCSY1Gq5rF6QOeJZP62H5+0/7KTI4x99wqWDfs3nZpe4uroVA1XbCIDBlXQulx553V21/0yx2CMmQ3MBggPD6+ImJSqcRZfczdt1l/M6/sXEeedwoz//Y3b281hap85xS+sVBmVJJEBfA48Vo71LASGl2P58sruThVQRJ3sMqddr0TkZeBlsI/sUXGhKVWzTB98BZ3C27P4ixvZ73+cJXuf5+c/f+KRsc/jafVydXiqBippIjvh6NlXJsaYa8u6bAWJcbxGFFGnWb66Sqky6nZRc16Zvoa7V85nq89m9sbtQH56A7rPAA9vV4enapiSdPb4lb86QpRVLPBbOdsoj58drx2NMb6F1OmVr65SqhzqBvry/N9eZFrA33k+rDdeJ3fCd89A8llXh6ZqmGITmYh0E5EHyrMSEblfRFzWrV1EYoHtgBcwKX+5MSYSaIp91I/NVRudUjWXh9XCHRPn0HTYveBfj8z4o1z/7gQ+/XmFq0NTNUiN6n5vjFniGGB4iZPi7HmPGWNa5VqmPvC848dHRcRW2XEqVesENoABt/Ls+SR+tJzm7l+XsvSLu9Cnb6iKUG0TmTGmuzFmS/YEdHcUPZJvfm6NsA8w3Ch/eyKyGngB++gdO4wxnxhjPgD2Ax2ANdgHD1ZKVQYvP6JGP8PFF7oiwIoTn3HjexNJSS/qrhililfSzh4FGGOaAZFAY8CnkGoiIovLuIogwNkNKK3L2B4i8ndjzLfAzdhjtwJ7gNeAF/RoTKnK1SQ0gJf+tpx/vPkgm8xHbE7dx8R3RvCfMctpFHqRq8NTbqrUD9Y0xnhgP3KZxV/3Z+V/xIo45omI1LhHo+iDNZUqHxHhqY/e4cO4JznvlU6gzZPlQ1+gTTO9ebomq6wHa5bliOwB7DcGZwKfYT81d6GoBZRSKjdjDLeNm8pFW1vzwvb/I8CaRbNf3wOvQGjQwdXhKTdTlkQ2HftQT/1FxJVd6pVSbm7cJb1o2WA1DWLfxzd+P/zwMikdxuLTcjDGlPtZuqqWKEtnj/rABk1iSqmK0KV5IxoMuBlaDyfNlsWM9fcw//2pZGSkuTo05SbKksiOAPobppSqOMZAu1G8Ze3AQWsS65N2cs27ozmfdMrVkSk3UJZE9l8g0hhT1LiFSilVajOvuJER3jfjn+nB7qwTTFg1liNxO10dlqrmypLIHgH2Ap8aY9pUcDxKqVrMw2rh4atnM6PJo9RN8+GkSWLy2un8cOBzV4emqrFSd/YQkTRjzHDsQzntMsYcBo4Czu7BcuUzyJRSbsgYw99HXE6zbY1Y9sNcjvmfY/a3d/JKWiq9Oo5zdXiqGip1IjPGhAFfAR2x3yvW0jE5o+PPKKXKZEzPLjSu+x4PrZ2Ft/dZuh5YD/5h0HyAq0NT1UxZut8/CnTFfnrxReAAeh+ZUqoS9GjRkGeu/i9BR7/AK3Yj7FjFhQsn8G0/Dqu1zAMTqRqmLL8Jo4A/gT4icr6C41FKqTzCwwIgbAKENiXpl7eYtnUp9Xe9ybPj38bHy9/V4alqoCydPQKB7zWJKaWqVPglvGntyVGTyubUP5j+3ljOXzjp6qhUNVCWRLYbezJTSqkqNWvEdIZ6L8A/w4M9WacI0gV5AAAgAElEQVSY/P44/jyzz9VhKRcrSyJbBgzSrvdKqarmYbWwZOpMrqr/MCFpPhznApM/mcreY/o83Nqs1IlMRJYDTwPRxpgbjDFNKzwqpZQqhDGGO8eO5Pq2z9MgOZB4k8a0r+Zw8Mi3rg5NuUhZut9n5frxZce8wqqLiNT6rkUiQmJiIgkJCSQnJ5OVlVX8QkqpIl1SP4AuwS+SmHYWC0LaaQu7E34Dq6erQ6u1PDw8qFOnDqGhoXh4VN1Hf1nWVJohqWv98NUiwqlTp0hKSiI0NJSGDRtitVp1ZG+lKkhyWgbemeexZiQDBptvCBZvHUGvqokI6enpnDlzhtjYWCIiIrBYynL1qvTKcmrRUpqpMoJ2J4mJiSQlJREREUFwcDAeHh6axJSqQH7enlj96oJ3EFli42BiLCcTjlLahwar8jHG4O3tTaNGjfDw8ODcuXNVtu5an2gqW0JCAqGhoVitNe5B2UpVH8aAbzAnbB6kY+N0+nn+PH9Yk5kLGGMIDg4mKSmpytapiaySJScnExCgpzmUqgr1gxvhkxUEwLnMJI7GH0LE2TCwqjL5+fmRkpJSZevTRFbJsrKy9GhMqSriabUQEdYEX1sIBkjISuHwuYPYbNrBqipZLBZstqr7AlFsIjPG3OoY7b7MjDHDjTG3lqcNd6bXxJSqOh5WCxFhjfCzhWGAJFs6MecOYrNlujq0WqOqP/NKckT2BDClnOu5GlhazjaUUqpErBZDeFh9/KmPRQwWmw2TdAb0yKxG0lOLSqkayWIxhNcNo65XE8K9AjFZaZAUp8msBirpfWQTjTGDyrGesHIsq5RSZWKMoX6dOmDzhwtxZGamcezcQRoFNcPL09fV4akKUtIjsgCgeTkm7banCtW8eXOMMRhj+PTTTwut16lTJ4wxREdHV11wbigmJgZjDM2bN6+ydUZHR2OMYdCgQVW2zlKxeCD+9YjNTOOCZHDo/CHS0pNdHZVTrth/7q4kR2QtKj0KpRzuvvturrjiiiobEUCVTPPmzTl8+DCHDh1y3w9YixVfr8akp8WSabFxKCGG5kHh+Hjp92x3V2wiE5HDVRGIUn5+fuzYsYOVK1cyffp0V4ejSqF3797s3r0bPz8/V4dSKGMMDesEYBIiiE89QqYli0MJR2ge2Axfb30ylTvTr72q2pg3bx4AixYtIj093cXRqNLw8/OjXbt2hIeHuzqUYjUI8iPUNxwPmxUbQkxiLMlp+pxgd6aJTFUbEyZMoHfv3hw6dIgXX3yxxMsNGjSoyGtn1157LcYYli9fXuj8Xbt2MWHCBOrVq0dAQAADBgxg/fr1OXXXrl1LZGQkderUISgoiLFjx7J///6ybCZffvklo0aNon79+nh6ehIaGkq7du24/vrr2b59e4H6SUlJPPzww3Tt2pWAgAD8/f25+OKLeeSRR0hOLvl1npJce8m+Vplt+fLlGGM4fNh+YqZFixY5dYwxxMTEAMVfI9u1axczZsygWbNmeHt7ExYWxsiRI1m3bp3T+rn3zYEDB5g6dSoNGjTA29ubdu3a8dhjj5X6htvcbZ4/eZx/3LyIyPaRdG1yMV06deOxJQ8V2mZGRgbPPfccl1xyCUFBQfj6+tK+fXsWLlzI2bNnSxVHtk2bNjFs2DCCgoIIDAykf//+fPjhh4XWz73/MjMzeeKJJ+jatSv+/v4EBwfn1Nu6dSt33HEHPXv2pEGDBnh5edG4cWMmTpzIli1bCm0/IyODxx57jPbt2+Pj40PDhg2ZMWMGR44c4YEHHsAYwwMPPFCmba10IqJTKacePXpISf3+++8lrltbRURECCA//vijfPPNNwJI/fr1JTExMU+9jh07CiDr16/PMz8yMtLp/GwzZ84UQF5//XWn82+++Wbx8/OTTp06SVRUlHTv3l0A8fT0lI0bN8qzzz4rFotFBg4cKJMmTcqJt2HDhnL69OlSbevrr78ugFgsFunbt69MmTJFRo8eLV27dhVjjCxZsiRP/bi4OOncubMAEhISIuPGjZPx48dLcHCwANK1a1c5c+ZMnmUOHTokgERERJRofm6A2D8W7DZt2iQzZ84Uf39/AWTChAkyc+bMnCkuLk5ERNavXy+AREZGFmjzo48+Em9vbwGkY8eOcvXVV8vAgQPFYrEIIPfee2+BZbL3zfz58yUoKEhatmwpUVFRMmjQIPHw8BBA5s6dW8y7XXyb4ydMlL79+vzV5t9vKrBcSkqKDBo0SADx8/OTUaNGyaRJk6Rhw4Y57+fBgwdLFcs777yTs/3dunWTq6++Wnr37i2ALFiwoMj9Fx4eLmPHjhUvLy8ZOnSoTJkyRfr165dTb8iQIWK1WqVLly4yevRomTBhgnTq1EkAsVqt8t577xWIJzMzU0aMGCGA+Pr6yhVXXCGTJ0+WJk2aSFhYmFx77bUCyKJFi0q8jc4++4BtUgmfyS5PCu44VXQii7hrbaHTyi2Hc+qt3HK4yLq5jXp2Y6H1Fr7/a06932Lji2zzt9j4nLoL3/+1wHoqQu5EJiIyfPhwAeSBBx7IU6+yEhkgTz75ZJ6yO++8UwBp06aNBAUFycaNG3PKUlJSZODAgQLIgw8+WKptbdGihQDy3XffFSiLjY2VXbt25Zk3adIkAWTgwIFy7ty5nPlnz56Vfv36CSBTpkzJs0xFJrJs2fvo0KFDTpcrLJH9+eefEhQU5PQ9Xr9+vfj5+Qkgn3/+eZ6y3Ptm0aJFkpWVlVO2YcMGsVgsYrFY5MiRI4VuS36FtWmz2WTDFx/ntLl73295lrvjjjsEkHbt2snRo0dz5icnJ8tVV10lgPTp06fEcRw7dkwCAgIEkBdeeCFP2X//+9+cBFfY/stOZvv373fa/rp16+TEiRMF5n/88cfi6ekpoaGhkpSUlKfsX//6V846//jjj5z5qampMmXKlDzvW0lVZSLTU4uq2lmyZAnGGJ588kni4uIqfX19+/bl1lvzjqC2cOFCAPbt28fNN9/MwIEDc8p8fHxYsGABQJ7TjyVx8uRJgoOD6devX4Gypk2b0qFDh5yfDx8+zOrVq7FYLLz88st5Th+FhITwyiuvYLFYeO+994iNjS1VHFXllVdeISEhgX79+hV4jwcNGsTcuXMBeOKJJ5wu36tXLxYtWpSnF+ull17K5Zdfjs1mK/X776xNYwyXDhvN8KGXYbPZ+ODLT0hIPg1ASkoKL7zwAgDPPvssTZo0yWnH19eXl156CX9/f7Zs2cJ3331XovW/+uqrXLhwgcjISG666aY8ZVFRUYwbN67YNpYsWUKrVq2clo0YMYIGDRoUmD9mzBgmTZrE2bNnC7xvzz77LAAPPfQQLVr81VHd29ub5557Dn9//2JjcqVa//Tm6iDm0VElqjf1knCmXlKyi+lrbxlYfCWgc9M6JV7/kqu6sOSqLiWqWx7du3dn8uTJvPvuuzz88MM8/fTTlbq+ESNGFJgXEhJC3bp1OXPmjNPy1q1bA3D8+PFSrat3795ER0czY8YMFixYwMUXX1zouHSbNm1CROjbty/t2rUrUN6hQwd69+7Nli1b2LhxI9dcc02pYqkKGzZsAOzXp5y5/vrrefzxx/n222+dDrA9cuRIp+9Pu3btWLduXanf/0LbNIaL2naEL/9H3Ik4YpNP0gz4bfseLly4QOPGjRk2bFiBtsLCwhgzZgz//e9/iY6Opn///sWuP/s9mTZtmtPy6dOn88EHHxTZxvjx44ssP336NGvXrmXnzp3Ex8eTmWkfZ3Lnzp2A/QvaqFH2v/vY2FgOHTqE1WolKiqqQFt169Zl2LBhrFmzpugNc6FSJzJjTICIXKiMYJTK9tBDD/H+++/z4osvsmDBAiIiIiptXU2bNnU6PyAggDNnzjgtz340T2pqas6806dPc/vttxeoO2DAAGbNmgXA888/z6hRo3jzzTd58803qVOnDr1792bYsGFMnz6dhg0b5ix37NgxgDzfkPO76KKL2LJlS07d6qa4bWjRogUWi4XU1FTOnDlD/fr185QX1gsyKMj+qJbc739JFdZmWKj9iDczxT6EVWzySfb/sbvI+MG+D4AS74OjR48W2WZx9+nVr18fX9/CRyV56aWXuPXWW4vsCJSQkJDz/+y4GzVqhKenp9P6lfn3VxHKcmpxjzFmYoVHolQurVq1YtasWaSlpXH//feXq63iercVd/N1SW/OvnDhAm+88UaB6dtvv82p0759e/bu3csnn3zCggULaNu2LevXr+fOO+/koosu4vPPP8+pa7+kUPRI4tl1KkJlPHajJNtQlMq4Mb64Nv296+CZ5Q3A6bR4oOr2QUkUlcS2bdvGnDlzyMjIYOnSpezZYz+itNlsiAh333034Dzmoraxug9QUJbowoB3jTGfGWOaV2w4Sv3l/vvvx8/Pj7feeivnlIgzXl5egD2ROJPddbyyNW/e3OmF6Pzd/j09PRk9ejRPPfUUW7du5dSpU8yfP5/k5GRuuOGGnHrZR4J//PFHoes8dOgQQJ5rN4VxxftU3DbExMRgs9nw8fEhNDS0wtdfFj6eVhoEhuOZ5U3DRvYj5D/+OFho/dLsg9z1sm9dyK+w+SWxevVqRIR58+Zx++2307ZtW/z9/XOS1IEDBwos07hxY8B+mjwjI6PCY6oKZUlkXYANwAhglzHmH8YYvdamKlyjRo2YP38+NpuNf/zjH4XWy/5g2LNnT4GykydPOr03qzoJCQlh6dKlWCwWjh8/ntPBZeDAgRhj2LJlC/v27Suw3O7du9m6dSsWi4VLL7202PXUq1cPLy8vzpw547QTzWeffVbostlJMPtaS0lFRkYCsGLFCqflr7/+OmA//erhUX0+Rur4eVE/MJyunbrh7+/H8eN/8vXnBccBPXPmDJ988glAiceZzH5PVq5c6bS8sPklkX1PW7NmzQqUxcXF8dVXXxWYHx4eTkREBFlZWaxatcppm86Wq05KnchEZJ+IXAZcCyQBi4FfjTGRFRybUtx1112EhobyySef5HzzzW/IkCEALFu2jD///DNn/tmzZ5k5c2ahRyBVLTk5maeeesppEvn000+x2WwEBQXl9E6MiIhgwoQJ2Gw2brzxRs6f/2v0ifj4eG688UZsNhuTJ092+sGVn6enZ07vy/vvvz/P6aVvv/22yFO42V8Wdu/eXbKNdfjb3/5GYGAg3377bU7PuGwbN27k3//+NwC33XZbqdqtCsF+XrRs2JabZl0PwPwFt3L88F9HZqmpqcyZM4cLFy7Qp0+fEnX0ALjhhhvw9/dn/fr1vPLKK3nKVq9eXWxHj6JkdwpasWJFnt/7xMRErr/+euLj450ud8sttwBwzz335DkyT09PZ968edXmb6gwZT7xKSIrgLbA60A74BtjzBvGmHoVFZxSderUyekKX9jF68mTJ9OtWzdiYmLo2LEjY8aM4fLLL6dVq1YcPXq0RN2Zq0J6ejq33XYbjRo1olu3bkyePJkpU6bQq1evnF5ojz32WJ4L7i+88AKdOnUiOjqali1bMmHCBCZMmEDLli3ZtGkTXbt2ZdmyZSWO4cEHH8TLy4sXX3yRjh07MmnSJHr37k1kZCR///vfC10uO75rrrmGiRMnMmvWLGbNmsWZM2eKXF/Dhg1588038fb2Zv78+XTp0oWpU6cyaNAgBg8eTFJSEvfee6/TnqHVQYCPJw8teZxBlw5g1559tO7QmZGjRhAVFUXLli1ZtWoV4eHhpTqKatKkCS+++CIWi4XZs2fTo0cPpk6dSt++fZk0aRLz588vc7zXXXcdzZo1Y/v27bRs2ZKrrrqK8ePH07x5c7Zt28b111/vdLn58+czfPhwYmJiaN++PaNHjyYqKirnuu2MGTOAv47Mq5tyXcETkXMiMguIBHYD07F3BvlbRQSnFNi/LRbWsxDsf1z/+9//mDNnDr6+vnzxxRfs2bOHmTNn8v3331OnTp0qjLZwAQEBvPDCC0ycOJGUlBS++OILPv74Y+Lj45k6dSpbtmwpcF9RWFgYmzdvZvHixTRp0oR169axbt06mjVrxsMPP8x3331XqmtL/fr14+uvv2bIkCHExsbmnE5csWIFixcvLnS5uXPn5sSwdu1aXn31VV599VUSExOLXeeVV17Jtm3bmDZtGmfOnGH16tXs2LGD4cOH8+mnnxa53urAx9eXL776mgceWUTLthexYcMmPvroI4KCgrjzzjtzkkZpTJs2LWc/7Nu3L+f05KpVq3LGHC2LkJAQtm3bxuzZswkICODTTz9l27ZtXHXVVWzfvr3QI3cPDw8++eQTHnnkEcLDw/nqq6+Ijo7m0ksvZdu2bTlfrsLCquejJU1F9bhxXCe7A7gX8AG2ADeJyI4KWUE10rNnT9m2bVuJ6u7evZv27dtXckRKqcp2LimduAtHyLCmYYBwvwYE+FXPD/aKlJmZSadOndi7dy/btm2jR48eJVrO2WefMeYnEelZ0TFWZJ/KpsBhIBowQB/gJ2PMUmOMPopVKeXWQvy9CPNvhmeWNwIcST5JUkrZBgyujn755ZcCvRaTk5OZN28ee/fupVOnTiVOYlWtTN2EjDFeQE+gL9DP8Zo9Jkr2zQinHK+3AVcaY6JE5OdyxKqUUi4VGuCNjWacSTpCpjWdw0l/EoHB3zfE1aGV29y5c9m1axddu3alUaNGxMXF8euvv3L69GmCg4ML3EZSnZRlZI/vgW5A9lW/7MR1CNgIbAI2ich+Y4w/cD+wANhkjBkqIoU/R0Appaq5sABvRJpxLjmWDGs68clx+Hv4gqePq0Mrl9mzZ/P222+zY8cOtm7dCti78U+ePJk77rijWj8ZvCxHZH2wj4S8C3vS2og9cRUY9ExEkoC7jDFfAJ9j76pfcMCyIhhjpgJzsN+/ZgX2YO8p+YKIlHgoAmPMA8CiIqqkiYh7/yYqpapEvUAfsmxNyUg/SWOrBZJPg3898PB2dWhlNmPGjJzeie6mLInsSuyJy/kNCU6IyDeOZFaykWwdjDHLgL8DqcDXQAYwBHgOGGKMmSQiWaVpE/gV+MXJfOe3tCullBMNgnyACEzKWUhPIvPCKbL8gvH2CnR1aLVOqROZiHxSxnWdBEq8h40xE7AnsRPApSKy3zG/AbAeGA/MBZ4pZRxrROSBUi6jlFJ55IxN6BtKhi2LQymnsSUk0iIoHG+vANcGV8tU5UiQTwEFhwYv3N2O17uykxiAiJzEfqoRYKExpnqPZqmUqtmM4ZwtEBELWQgxCUdIS09ydVS1SpUlARH5XUT+VZK6xpimQA8gHSgw+JeIbACOAQ2xX7NTSimXqRfog6+1CR42K5kIMQmHychIcXVYtUZ1PZrp5njdJSKF/Tb8mK9uSXU3xjxmjHnZGPOoMWa843YCpZQqE2MMTUMD8LbkTmYxZGaW/nlpqvSqz3DTeWU/ca6o50ocyVe3pMY4ptyOGmOmOY70lFKq1CzGEB4aQMyZRogcJx0bMedjaBHcEqtVvytXpup6RJZ9pbSoE83ZwzGXtAPJQezX3S4G6gD1gMuwP5KmKfCZMaZr6UNVSik7i8UQUTcQq60hFjF42QyWpDNgK23nalUa1fWILPsm6wp79KqIvOlk9npgvTFmNTABeBgY7TQgY2YDs6HwR6UrpZTVYqFFWB3iEj1oaEnE2DIg6TQE1APtm1Ypquu7mj2kdlF9WLPLih9+u3gPOl6HGWM8nVUQkZdFpKeI9KxXT59Uo5QqnIfVQqPgQExAfbB4kJGZysnzhxFbicdwUKVQXRNZjOM1oog62c8jiCmiTkllP1rYC6j5w1krpaqGxYMsvzBiMpM5nZnMnwkxVNQTR9Rfqmsiyx5cuGMRI+f3yle3POrm+n/1fhRqDdS8eXOMMcVO0dHRrg61wi1fvhxjDNdee62rQ3EbMTExGGMqfOy/7N+zipYuVrIy7U/9PpeZwsmEw6DJrEJVy2tkIhJrjNkOdAcmAStylxtjIrF30DgBbK6AVU52vO4VkYo4VanK4PLLL6dhw4aFlhdVpqqf6OhoBg8eTGRkZI38ElKU5cuXc9111zFz5kyWL19O09B6HD1rI8sznjMZSVgTj1IvsClUQuKsjaplInNYgv1m6MeMMd+LyAEAY0x94HlHnUdzDxxsjJmLfdiqH0RkRq754cAA4H0RScs13wDTHOsCKNEN26pyLFy4kEGDBrk6jCo1fvx4+vTpU22eYq0qR4C3B42D63M83kaWZwKn0hOwXjhOaGATV4dWI1TbRCYiq40xL2AfjmqHMeZ//DVocBCwBvvgwbmFAW2xH6nlFgqsBF40xuzFfg+aF9CRv+5De05EXqqMbVGqMHXq1NEkVksE+XqSZWvAyQQbWZ4X+DMtHh+rN3614CnTla26XiMDQET+DlwDbAcigcuBA9iPuiaUYuT7WGAp8BP2Ya2uwP44GQvwLjBERG6p2OhVZRERrrjiCowxzJ49u0C5zWZjyJAhGGOYO3duzvzc11YyMzN59NFHad++PT4+PjRo0ICZM2dy5MiRAu1lO3PmDPfeey+dO3cmICAAf39/unfvzr/+9a8CT9YFuPbaazHGsHz5cnbs2MGkSZNo2LAhVquVp59+Gij8Gll0dDTGGAYNGkRqair33XcfrVq1wtfXl5YtW/LQQw+RlWX/9Y+NjeWGG26gSZMm+Pj40LlzZ956661CtyMjI4MXX3yRgQMHEhISgo+PD61bt+bWW28lLi6uQP3cMSYmJnLHHXfQokULvL29adKkCXPmzOHs2bxPSh40aBCDBw8GYMOGDXmudeY+6j58+DBLlixh8ODBNGvWDG9vb0JDQxk8eDBvv/12odtQVjt27GD8+PGEhobm7L///Oc/RS6zdetW7rjjDnr27EmDBg3w8vKicePGTJw4kS1bCj5esXnz5lx33XUAvPHGG3m2fcHNswkNaIBHph8ndsew5IHF9Ovbh8aNG+Pl5UW9evUYOXIkn3/+eYVve40mIjqVcurRo4eU1O+//17iurVVRESEALJ+/foSLxMXFydNmjQRQN5+++08ZYsWLRJAunXrJqmpqTnzDx06JIBERETIVVddJV5eXjJ8+HCJioqSpk2bCiD169eXPXv2FFjfb7/9Jo0bNxZAmjZtKqNGjZIrrrhCQkNDBZAhQ4ZIWlpanmVmzpwpgMyaNUu8vb2lZcuWEhUVJSNHjpSXXnpJRERef/11AWTmzJl5ll2/fr0A0rdvXxkwYICEhITI+PHjZcSIEeLn5yeA3HTTTXLgwAFp0KCBtGjRQqKiomTAgAGC/f5Leeuttwpsx/nz53Pq1KlTRy677DK56qqrpHnz5gJIeHi4HDp0KM8y2TGOGzdOOnfuLKGhoTJu3DgZPXq0BAcHCyDdu3eX9PT0nGWWLFkil19+uQDSoEEDmTlzZs60ZMmSnHqLFy8WQC666CIZOnSoREVFSf/+/cVqtQog8+bNK7ANufdjaURHR4uvr68A0rZtW5kyZYpERkaKxWKRBQsW5Lxv+Q0ZMkSsVqt06dJFRo8eLRMmTJBOnToJIFarVd5777089W+77Tbp379/znbl3vZXXnlFbDabnEtKk+uvnS6AtG/bSkZcPkwmT54sPXv2zInjySefLNX2VTfOPvuAbVIJn8kuTwruOFVoIvt4nntOFagsiUxEZNOmTWK1WiUwMFD27dsnIiLffPONWCwWCQwMlP379+epn/0BmJ2wdu3alVOWlpYm06ZNE0B69eqVZ7nk5GRp0aKFAPLII49IRkZGTtmZM2dk6NChAsiiRYvyLJedyAC55557JCsrq8A2FJfIABkwYIDEx8fnlP3yyy/i6ekpFotF2rdvL/Pnz5fMzMyc8ueeey7nQzS/qKgoAWTixIly9uzZnPmZmZly5513CiCRkZFOYwRk5MiRkpiYmFN27NgxadasmdPEmb0N+dvL7YcffpCdO3cWmL9v376cdrds2ZKnrCyJLDk5OeeLz9133y02my2nLDo6OufLgbNEtm7dOjlx4kSB+R9//LF4enpKaGioJCUl5SkrbL/mFh0dLYd2/yrpZ2Pk0Ok9kpZmf1+3bNkiQUFB4unpKbGxsSXexuqmKhNZtT61qGqXwYMHF9r1Pjg4uED9AQMG8OCDD5KYmMjkyZM5cuQIU6dOxWaz8corr9CqVatC13XffffRoUOHnJ+9vLx47rnnqFOnDj/++CPfffddTtny5cs5dOgQkydP5u6778bD469Ly6Ghobzxxht4enqybNky+7fDfNq1a8c///lPLJbS/7lZLBZefvnlPNfRunbtysiRI7HZbCQnJ/P4449jtVpzym+88UZCQ0M5ePBgnlOlv//+O++++y4RERGsWLGCkJCQnDKr1cqSJUvo0qULGzZsYMeOHQViCQgI4NVXXyUg4K9xCho3bpxz+vbrr78u9fb16tWLjh07FpjfunVr7rvvPgBWr15d6nbzW716NceOHeOiiy5i8eLFebrZR0ZGctNNNxW67IgRI2jQoEGB+WPGjGHSpEmcPXuW9evXlzqmyMhImrbuxJHMdJIkk8OJsWRmpHLJJZcwd+5cMjIy+Oijj0rdbm1UbTt71BpjSvtc0JqrqO73fn5+TufffffdbNy4kS+++IIuXbpw/vx5brzxRqKioopc17Rp0wrMq1OnDqNHj2blypVER0fTv39/AD777DMAJk2a5LStxo0b07p1a37//Xf2799PmzZt8pRfeeWVeRJNaURERNC+ffsC87OT9GWXXYaXV94BaT08PGjRogVnz57l+PHjOUOqrVu3DoDRo0fj61vw9kyLxcKAAQP47bff2Lx5M507d85T3qNHD6f7p127dgAcP368DFsIqampfPHFF/z444/ExcWRlmbvWPznn38CsG/fvjK1m9uGDfbxwKdMmeJ0X0yfPp2nnnqq0OVPnz7N2rVr2blzJ/Hx8WRmZgKwc+fOnBhHjRpV6rguXEjk47TF/HoAACAASURBVA828fuuzcTHx2PLyCTAK5ADBw7mtKuKp4lMVRtl6X5vjOHNN9+kZcuWnD9/ng4dOuR0pChMcHCw0yM8IOcm26NHj+bM++OPP4DCE1lucXFxBRJZRERRA9QUrWnTpk7nZx8VFVeemvrXY0Syt2PZsmUsW7asyPU66/RR2BijQUFBBdZVUps3b2by5Ml53u/8EhISSt1uftntt2jh/GEZRd1c/dJLL3HrrbeSnJxcaJ2yxPjRRx9x/fXXF+goU952ayNNZMrtrVmzhgsX7AOyHD16NOcUUnnkPvWU3Ttw1KhRhIUV3VW6bt26BeY5O/opqeJOR5bmdGX2dvTo0YNOnToVWdfZ6b6ynBotSnJyMuPHj+fkyZPccMMNzJkzh1atWhEYGIjFYuHLL7/k8ssvd3q6tqIVNqLHtm3bmDNnDh4eHixdupQxY8bQtGlT/Pz8MMbwj3/8gyVLlpQ6xqNHj3L11VeTkpLCwoULmTApCgKD8Qm6gLEa1r75IQtvva9Ktr0m0ESm3NrOnTuZP38+Xl5eTJo0iZUrVxIVFcX3339f4JRbtvj4eM6fP+/0/q2YmBjAfrowW7Nmzdi7dy9z5swp0+mj6qJZM/vwpIMHD2bp0qUujgY2btzIyZMn6dGjh9Mu8AcOHKiwdTVpYr/xOHv/5nfo0CGn81evXo2IMG/ePG6//fYKi3Ht2rWkpKQwYcIEliyxj8eQlJbJ4TP/396dx0dV3Y0f/3wnK9lIQgigYNjEaCi7gCyGpeDCopalvnChUuoCVlwqpcUCRbHgU5eHVvHRX2XTPj4Un1oBUauyGBAKIgo0+IiyJBgDBBLIQrY5vz/uzJhlJpmEmWQGvu/X677ua+4999xz70nmzD33LHkQcoqvHE/Pyjva2EMFraKiIiZPnkxJSQlLlixh1apVDB8+nM8++4zHH3+8zmPfeOONWtsKCgpYv349QLUqzptuugmAv/3tb75LfDNwXsfbb7/tesfjT84fEp7O5axScxawNfmyH1l6ejoAb775puvJtCp3fw9QdxpPnjzJP//5T7fHNebaoyNCaZ+QSNm5KD5a96G1saJUx2X0ghZkKmjNnDmTzMxMxo8fz8MPP4zNZuONN94gOTmZpUuX8vbbb3s8duHChWRmZro+l5eXM2vWLAoKCujbty9Dhgxx7bv33nvp0KEDK1euZP78+W7flezfv5/ly5f79gJ9rE+fPtx6660cOnTI43upnJwcXnjhBZ8UdM6noEOHDrmNz9lI5OOPP+bgwYOu7Xa7nYULF1ZrOXqhJk6cSLt27Th06BALFiyoVmWXkZHBsmXL3B7nTOOqVatc1dcA586dY9q0aeTn57s9znntVf/G3MX71ltvkZub69oeGWL4z6cWcexolrXBXoEp1fdk9dGqRRUwFi9ezIoVKzzunzJlCqNHjwasL5aVK1fSoUOHagVIu3btWL16NTfeeCPTpk2jd+/etRpbXHHFFfTt25devXoxYsQIWrZsyaeffsqxY8dISkpi1apqY1QTExPDhg0bGDt2LAsXLuTPf/4zPXr0oG3btuTm5nL48GGOHDnCgAEDXCM6BKqVK1cyfvx4/v73v7Nx40Z69uxJSkoKZ8+eJSsri8zMTOx2O/fff3+1bgaNkZKSQu/evfn888/p0aMHffv2JSIigquuuorHH3+cPn36MG7cONatW0evXr0YPny4q/vDsWPHmD17Ns8884xPrjsqKorXX3+dMWPG8NRTT7F27Vp69+5NTk4OW7duZdasWTz/fO2hVu+55x5eeOEF9uzZQ+fOnRkyZAjGGLZu3Up4eDjTpk3jtddeq3XcwIEDadu2LXv27KFfv36kpaURFhbG4MGDueeeexg/frzr3lx55ZUMGzaMyMhItm3bRkFBAQ899BBLly7FjuHbou9oay8nWoey8swfndMu9kVH9vAtZ4fo+pbnn3/eGGNMZmamiY6ONqGhoSYjI8NtnHPmzDGAGThwoGvEiaodacvLy82TTz5punXrZiIiIkzr1q3NnXfeWWtUi6ry8/PN008/bQYMGGDi4uJMeHi4ufzyy83AgQPN7373O/PFF19UC+/sEL18+XKPcdbXIdpTZ2Ln6CU1O2E7paene+xkXlFRYVatWmVGjx5tkpKSTGhoqGndurXp2bOnmTFjhnn//fe9SqM3aT18+LCZPHmyadOmjWu0jqrhSktLzeLFi01aWpqJjIw0SUlJZty4cWbHjh0e423syB7GWJ3Jx48fb+Lj402LFi1Mz549zbJly4wxxmOH6NzcXHPvvfeaTp06mfDwcNO+fXszffp0891339WZD3v37jVjxowxiYmJxmaz1bqHZ8+eNbNnz3b9DbZt29bcfvvt5uDBg657fttPJ5j9J/ebf588YM6fL2jw9TanpuwQLUbrXxusX79+Zvfu3V6FzczMdNsPSDW9I0eO0KlTJ1JSUjy+9FcqUNjthm9PFVJBDpW2csJE6BTXkbAw930qA4277z4R+cwY08/X59J3ZEopFYBsNqFjq2jE3oYQewjlxnDs7DEqK8uaO2kBRwsypZQKUKEhNjq2isFekYzNCOdNJdkFRzB2byf+uDRoQaaUUgEsIiyElFZx2MtbIwiF9nLOnjuuzfKr0FaL6pLRsWNHHSlBBaXoiFAuj2/J8fxK4sPOEWeA4tMQlQgeRiW5lGhBppRSQSA+KpywkCSiQhKQopNQXoQ5H4K0cD9u6KVEqxaVUipIREeEIqERENWK88bON0U5FBWfau5kNTstyJRSKsiUSwRZ5YZS7BwrPkHpJT76hxZkSikVZGw2MCaJEHsYdgzHCo9TUV7S3MlqNlqQKaVUkAmx2ejYKsrRLN9GmbGTdfYY9sry5k5as9CCTCmlglB4aAgprWKoLLP6mBWbCnLOHsXY7c2dtCanBZlSSgUpq1l+LJXlrRAgv7KUosKcS66PmRZkSikVxBKiw0mKjoPyeFqZcGLslXC+oLmT1aS0H5lSSgW5NnGRRIUnExtaAUWnoPQsxhaKRMQ0d9KahD6RKaVUkBMR4lqEIWEtoEUCJXY7RwqzKS8rrP/gi4AWZKrZdezYERFBRNiwYYPHcN27d0dE2Lx5c9MlLggdOXIEEaFjx45Nds7NmzcjIgwbNqzJzulrP/vZzxCROid3DQalthZkVZZRbCo5di6byorS5k6S32lBpgLKb37zG+yXYKurQOf8saHzuAW+SmMoK0vCZmycN5UcP3v0oh8tXwsyFTCioqLYt28fb7zxRnMnRTVQ//79yczMZNWqVc2dlEteVHgo7RNiqCxLQhDO2cvJPXv0om7JqAWZChgPPfQQAPPnz6esTCcPDCZRUVGkpqZyxRVXNHdSFNYAw61jYzFliQDkVZRw5iKe+kULMhUwJkyYQP/+/Tl8+DAvv/yy18cNGzaszndnnt59VN1+4MABJkyYQOvWrYmJiWHIkCFs2rTJFXb9+vWkp6fTsmVL4uLiGD9+PF9//XVjLpMPPviAMWPGkJycTFhYGImJiaSmpjJt2jT27NlTK3xRURGLFi2iZ8+exMTEEB0dTa9evXj66acpLi72+rzevDtzvqt0WrFiBSLC0aNHAejUqZMrTNWqxvrekR04cIC7776bDh06EBERQVJSEjfffDMbN250G75q3hw6dIgpU6bQpk0bIiIiSE1NZcmSJY2qgi4qKmLu3Ll06dKFiIgIOnTowIwZM8jLy/N4TNW07Nu3j0mTJtG2bVtCQkJ44YUXADh37hyvvPIKt956K127diUqKoqYmBh69+7NokWLKCnxPHzU3r17ueWWW0hMTCQ6Opq+ffvy2muvAbXzoyGSYyOIiYhFyuMAyCkroOz8mUbFFei0+b0KKIsXL2bEiBEsWrSIadOmERPj/+bDu3fvZubMmXTu3JmRI0fy9ddfs23bNm644QY++ugj9u7dy8MPP8zgwYO54YYb+Ne//sW6devYtWsX+/fvp1WrVl6fa8WKFdxzzz3YbDYGDBhASkoKhYWFZGVlsWLFCrp160afPn1c4U+dOsWIESPYt28fCQkJjBo1ChFh06ZNzJ07lzVr1vDxxx+TmJjoj1tD165dmTp1KmvXrqWoqIgJEyZUyxNv8uedd95h8uTJlJaWkpaWxtChQ8nOzub9999n48aNPPHEEzz55JNuj927dy+zZs0iKSmJ4cOHk5ubS0ZGBnPmzCE7O5s//elPXl9LUVERw4cPZ9euXcTFxXHTTTcREhLCm2++yQcffEBaWlqdx2/bto3777+fyy+/nGHDhnHu3DmioqIA+OKLL7jvvvtITk7mqquuol+/fuTl5bFz506eeOIJ3nnnHbZs2UJkZGS1OD/++GPGjBnD+fPnSU1NpVevXnz//ffce++9ZGZmen1t7ogI7ROi+OakncqKcpJC7YSXFkJoCwhrcUFxBxxjjC4NXPr27Wu89e9//7veMN1XdPe4rPlqjSvcmq/W1Bm2qknvTPIYbv62+a5w+0/trzPO/af2u8LO3za/1nl8ISUlxQBm165dxhhjRo8ebQCzYMGCauHS0tIMYDZt2lRte3p6utvtTlOnTjWAWb58udvtgHn22Wer7Zs9e7YBTLdu3UxcXJzZunWra19JSYkZOnSoAczChQsbdK2dOnUygNm2bVutfVlZWebAgQPVtk2aNMkAZujQoebMmTOu7adPnzaDBg0ygLn99turHXP48GEDmJSUFK+2V+W8HzU58+jw4cNuj9u0aZMBTHp6erXtOTk5Ji4uzu093rRpk4mKijKAee+996rtq5o38+fPN5WVla59W7ZsMTabzdhsNnPs2DGP11LTo48+agDzox/9yOTm5rq2nzlzxnUv6/s7mTt3brW0OGVlZZmPPvqo1r4zZ86YG2+80QBm8eLF1fYVFRWZdu3aGcDMmzfP2O12175t27aZmJgYj/nREKXlFSavsNSYknxjzhw1Jj/LmIqyC4rTG+6++4Ddxg/fyVq1qALOH/7wB0SEZ599lpMnT/r9fNdddx2PPvpotW1z5swB4P/+7/+YOXMmQ4cOde2LjIzkkUceAahW/eiN3Nxc4uPjGTRoUK197du355prrnF9Pnr0KGvXrsVms/HKK68QH//DBIoJCQm8+uqr2Gw21qxZQ1ZWVoPS0VReffVVzp49y6BBg2rd42HDhvHggw8C8Mc//tHt8ddeey3z58/HZvvhq+r666/nhhtuwG63e33/S0pKeOWVVwBYunQpycnJrn3x8fEsW7as3iq81NRUfv/731dLi1P79u0ZMWJErX3x8fEsXboUgLVr11bbt3btWnJycujWrRvz58+vdv5BgwYxY8YMr66tPuGhISRGh0NEHIRFUWJ3jsl48bRk1KrFALBv6j6vwk3qNolJ3SZ5FXbNuDVehUtrleb1+RcMWsCCQQu8Cnsh+vTpw+TJk/mf//kfFi1a5HoP4S833nhjrW0JCQm0atWKvLw8t/uvvPJKAL777rsGnat///5s3ryZu+++m0ceeYRevXp5/AL95JNPMMZw3XXXkZqaWmv/NddcQ//+/dmxYwdbt27ljjvuaFBamsKWLVsA6z2TO9OmTeOZZ54hIyODyspKQkJCqu2/+eab3d6f1NRUNm7c6PX9/+yzzygsLHRVC9bUo0cPevTowRdffOExjltuuaVW+qoyxrBt2za2bt1KdnY2JSUlricGsH4UVeW8Nz/96U/dFo5TpkzhmWee8ebyvCNCcWgcR0tOYMcQcvYYyS07QiPfwQUSLchUQHrqqad46623ePnll3nkkUdISUnx27nat2/vdntMTAx5eXlu9zvfDZ0/f9617dSpU/zqV7+qFXbIkCFMnz4dgJdeeokxY8awevVqVq9eTcuWLenfvz+jRo3irrvuom3btq7jjh8/DlgNLDzp0qULO3bscIUNNPVdQ6dOnbDZbJw/f568vLxqT0qAx1aQcXFWA4aq978u2dnZdaYDrL5ydRVkdf0N5ubm8pOf/ITt27d7DHP2bPXJL533xlO8/vibP1Ncib0sAcJPc7KimMjCHOJiL/P5eZqaVi2qgNS1a1emT59OaWkp8+bNu6C46mvd5u7XcEP2OxUWFrJy5cpaS0ZGhivM1VdfzVdffcW6det45JFHuOqqq9i0aROzZ8+mS5cuvPfee66wzl/ydVV5OcP4gj86ontzDXXx9t43hRYtPDeQmD59Otu3b2fw4MH885//5MSJE5SVlWGMobS07pE1PN0bf1x7u/hIIkJjkQrrh1h26RnOl5z2+XmaWuD8lShVw7x584iKiuL1119n//79HsOFh4cDVkHijrPpuL917NjR7Yvoms3+w8LCGDt2LM899xw7d+7kxIkTzJo1i+LiYn7+85+7wjmfBL/99luP5zx8+DAAl19+eb3pa477VN81HDlyBLvdTmRkpN9aXsIP96eukUkaO2pJUVER7777LiEhIaxfv54f//jHtG7dmrCwMAAOHTrk9rjLLrOehDzdd3+MomITIaVVFGISsFVGYIBjxd9TUVbk83M1JS3IVMBq164ds2bNwm6389vf/tZjOOeX1MGDB2vty83Ndds3K5AkJCTwH//xH9hsNr777jtXA5ehQ4ciIuzYsaPW+xWAzMxMdu7cic1m4/rrr6/3PK1btyY8PJy8vDy3jWjeffddj8c6C8GKigpvLwuA9PR0AI8jfixfvhywql9DQ/33pqNv375ER0eTnZ3N1q1ba+3fv38/X375ZaPiLigowG63ExsbW61BjpOnkWqcebZmzRq3T8P//d//3aj01CcsxEZKqygqKpKw2UMoN4asc1mYIJ5dWgsyFdB+/etfk5iYyLp161xPHzWNHDkSgBdffJGcnBzX9tOnTzN16lSPTyBNrbi4mOeee85tIbJhwwbsdjtxcXGuL8OUlBQmTJiA3W7nvvvuo6Dghzmm8vPzue+++7Db7UyePJkOHTrUe/6wsDBX68t58+ZVq5bMyMioswrX+WOhoX2bfvGLXxAbG0tGRoar9Z7T1q1bXf3AHnvssQbF21BRUVGu95SzZs2qlgcFBQXMmDGj0dW0bdq0ISEhgfz8fP76179W2/fee+/x3HPPuT1u0qRJtGnThoMHD7Jo0aJq59+5cycvvvhio9LjjajwUNrHR1FR3hqbsRFPGFKcByY4xznVgkwFtJYtW7qawnsaxWLy5Mn07t2bI0eOkJaWxrhx47jhhhvo2rUr2dnZ3HrrrU2ZZI/Kysp47LHHaNeuHb1792by5MncfvvtXHvttdx2220ALFmyxFUlBbBs2TK6d+/O5s2b6dy5MxMmTGDChAl07tyZTz75hJ49ezboC2/hwoWEh4fz8ssvk5aWxqRJk+jfvz/p6el1Nvd2pu+OO+5g4sSJTJ8+nenTp9c5IgZA27ZtWb16NREREcyaNYsePXowZcoUhg0bxvDhwykqKuKJJ55w2zLU15566in69OnD3r176dq1K7fddhsTJ06kc+fOHD9+nPHjxzcq3pCQEObOnQtY92fQoEFMmTKFAQMGcNNNN9XqduAUHR3tujfz5s0jLS2NKVOmMGLECAYPHuwqeKv+PfhSQnQ4rWOiaBfVkYSwKKgsg+K8oBzGSgsyFfB++ctfemxZCFa114cffsgDDzxAixYteP/99zl48CBTp05l+/bttGzZsglT61lMTAzLli1j4sSJlJSU8P777/POO++Qn5/PlClT2LFjB/fff3+1Y5KSkvj000958sknufzyy9m4cSMbN26kQ4cOLFq0iG3btjXo3dKgQYP46KOPGDlyJFlZWa7qxFWrVnkcXQPgwQcfdKVh/fr1/OUvf+Evf/kL586dq/ect9xyC7t37+bOO+8kLy+PtWvXsm/fPkaPHs2GDRvqPK8vxcTEsGXLFubMmUNiYiLvvvsuO3bsYOLEiezcuZOEhIRGx/3YY4+xdu1aBg4cyIEDB1i/fj0hISG8/vrrLFq0yONxo0aNYvv27YwbN46cnBzefvttzpw5w4svvujqq5iUlNTodNWnbcsWxEe3gOgkEBslZYUUF/u/76aviS9bPV0q+vXrZ3bv3u1V2MzMTK6++mo/p0gpdbFZvXo1d999N2PHjmXdunV+P19B4WmOn88hBKFzbAfCImIvKD53330i8pkxpt8FReyGPpEppVQzOXHihNtWizt27ODxxx8HPHcm96UKu53ssyGIPZQKDFmFx7EH0YSc2iFaKaWayZdffsmoUaPo3r07nTp1Ijw8nG+//ZbPP/8cgLvuuosJEyb4PR2hNhtt4yI5XtCasPDvKaGS789mcVl8J7B5Hs0kUAT8E5mITBGRT0SkQEQKRWS3iMwUkUalXURuFJEPROS0iBSLyH4RmSsiEb5Ou1JK1SU1NZUHHngAu91ORkYG//jHPzh69CgjRoxg1apVrFy5ssnSkhgdTmKLSCrKrXdyZ+ylnA6SOcwC+olMRF4EZgDngY+AcmAk8GdgpIhMMsZ4PfKliMwGlgCVwGbgDJAOPAWMFZGRxhjvJ3hSSqkL0L59e1566aXmTgZgjTByWXwLSk5VUlbeEsIK+L78HJHFJ4mKTq4/gmYUsE9kIjIBqxD7HuhhjBlrjLkNuBLIBG4DHmxAfP2AxUAxMNgY82NjzCSgM7AVGAh4bl6klFIXOZtNSEmMRkwctkprSK7KskIoC+zf9wFbkAG/cax/bYxxTcVrjMkFHnB8nNOAKsY5gABLjDE7q8RXCNwD2IEZIlK7a75SSl0iwkNtXJHYAntlKy4LSyZWQqHkNATwyB8BWZCJSHugL1AG/K3mfmPMFuA40BbrSaq++MKBmxwfa40XY4z5FvgUCAdubnTCPdAuDkqpYBITGcZVbWOJj0uCsCgwdsoKc8HLOcya+jsvIAsyoLdjfcAYU+IhzK4aYetyFRAFnDbGfOOD+LwWEhJCZeXFM4GdUurSEGqzWXOVRSVyyl7JofICznjZ+MNutzfpzAWBWpA5Jw2qazjuYzXCehPfsTrCNCQ+r0VFRQXMWH9KKdVQBSUVnCgNwwA55eco8WLkj+Li4jqnvfG1QC3IYhzruuYWcJYO3nQ/93V8XouLi+P06dP6VKaUCkoRYSHY7bHYKltggMLSAqijs7Qxhvz8fKKjo5ssjYFakDlnmvNVResFxyci9zr6sO12N3q5J7GxsURHR3P06FHy8/OpqKjQd2ZKqaARGRZC+4QWlJcnEl4eS2x4MoSE1wrnnEQ0JyeHioqKCxq7sqECtR+ZcyTSmDrCOPfVP2qpD+IzxrwCvALWWItenBOw+mYkJydz7tw5zp49y4kTJ/TpTCkVdIpKysk9X8GZFvnERrofkT80NJSWLVuSnJzcpO/IArUgO+JYp9QRxjkB05E6wtSM7wofxdcgIkJcXBxxcXG+jloppZpEeaWdHd/m0f/K1s2dlFoCtWrxc8c6TUQ8vTG8tkbYuhwESoBEEeniIUz/BsSnlFKXlLAQG0MDsBCDAC3IjDFZwB6sfl2Tau4XkXSgPdaoH596EV8ZsNHx8Q438XUGrsPqt7ah0QlXSinV5AKyIHP4g2O9RES6OjeKSDLgHJxssTE/zM0tIg+KyEERWeUmvsVYjT1+LSL9qxwTA7yGdS9eMsbk+/g6lFJK+VHAFmTGmLXAMqzRO/aJyDoR+V/ga+Aa4G2swYOrSsLq/FzrXZgxZhfWMFVRwHbHCPhrgG+wBg7eCcz10+UopZTyk0Bt7AGAMWaGiGQAM7EKmxCs912vAcuqPo15Gd8zIvIl8BjWO7ZI4FtgKfBHY0zwzCSnlFIKANE+TQ3Xr18/s3v37uZOhlJKBRUR+cwY08/X8QZs1aJSSinlDS3IlFJKBTUtyJRSSgU1fUfWCCJykrpH5q9PEnDKR8lR/qP5FPg0j4KDM59SjDE+71WtBVkzEJHd/njhqXxL8ynwaR4FB3/nk1YtKqWUCmpakCmllApqWpA1j1eaOwHKK5pPgU/zKDj4NZ/0HZlSSqmgpk9kSimlgpoWZEoppYKaFmQXSESmiMgnIlIgIoUisltEZopIo+6tiNzoGJn/tIgUi8h+EZkrIhG+Tvulwhd5JCI2ERkkIk854soWkTIRyRWRd0XkVn9ew6XA1/9LNeK+V0SMY6k5a4ZqAD9854WIyH0islVE8kTkvIhkOWY8GedVJMYYXRq5AC9izXFWAqwH/g6cdWz7XyCkgfHNdhxbAXwI/A044dj2KRDV3NccbIuv8gjo6jjGAHnA+8CbwL+qbF+O472zLs2TTx7iTnHEZXfE9+fmvt5gXfzwnZeINYWWAfKxJjZ+E9gGFAP/z6t4mvvGBOsCTHDc/Bzgyirb2wD/duyb1YD4+jn+0YqAAVW2xwBbHPE939zXHUyLL/MI6AJ8BNxY858Va4qhQkd89zT3dQfb4uv/pRpxi+NHYSGwQguywMknrBrBbY7jXgWia+yPAbp7FVdz35xgXYDdjgy4282+9CoZbvMyvrWOY+a52dcZqARKgfjmvvZgWXydR/Wc6wlHfB8193UH2+LPfAIecBz/S2CBFmSBk0/AfY5jNnOBNRn6jqwRRKQ90Bcow6r+q8YYswU4jjW79UAv4gsHbnJ8fMNNfN9iVS2GAzc3OuGXEF/nkRc+d6zb+yCuS4Y/80lEOgHPYP3q1/diF8BP+fSgY73EOEq2xtKCrHF6O9YHjDElHsLsqhG2LlcBUcBpY8w3PohP+T6P6nOlY53jg7guJX7JJxERrJnkQ4GfX+gXpfJtPolIW6A7UA5sEpEficgCEfkvEXlaREY1JHGhDQmsXDo51nWNgH+sRlhv4jtWR5iGxKd8n0ceiUgU8JDj41sXEtclyF/59CAwDJhjjPmqEelS1fk6n3o41keA3wG/wXqf6fQbEdkKTDDG1Du7gT6RNU6MY11UR5hCxzq2GeJTTXtPX8L65/03OmRSQ/k8n0SkC/AHK1CmWgAAB0dJREFU4DPgj41PmqrC1/mU6Fh3An4LrAauBuKAEUAmcD2wxpvEaUHWOM5fDr6qrvB1fKqJ7qmI/A6YChQAk40xpf4830XIp/lUpUoxHJhmjKn0RbzK5/9PzrInFKuB1FRjzEFjzDljzCZgNFYT/+Eiku5tZKphzjnWMXWEce47V0cYf8WnmuCeisijwEKsX6I3GWMONCaeS5yv8+khrF/yfzDGfHkhCVPV+Os7D9zUYhhjsrH6lAGMrC8yfUfWOEcc65Q6wnSoEdab+K7wUXzK93lUjYj8EngW61fjWGPMpw2NQwG+z6fbHOtRbn7Jd3SGEZHuQKExZqwXcSr/fecBHPYQxrm9bX2RaUHWOM6m1mki0sJDK55ra4Sty0GsL8REEenioeVi/wbEp3yfRy4iMhNYCpwHxjuaHqvG8Vc+XVfHvsscS0ED4rvU+eM7rwiIBlp5CJPkWBd62O+iVYuNYIzJAvZg1cNPqrnf8UuwPfA9Vv+v+uIrAzY6Pt7hJr7OWP+YZfzwuK3q4Os8qnLc/Vh9kkqBW40xH/okwZcoP/wvDTPGiLsF+L0j2IuObfG+u5KLmx/yqRxriCtwU3UoImFYVcRgdcSuN0JdGtfLfSI/9GTvWmV7MnAAN8O1YDUJPgischPftfwwRFX/KttjsHq+6xBVzZ9Hv3Dk0Xng5ua+votl8XU+1XGeBejIHgGTT0BPrBGLioGRVbaHAM854ssGWtSXNq1abCRjzFoRWYY1BM4+EfkQq3PfSKwmpG9TezSBJKzOz9+7iW+XiMwBlgDbReRjrEE007H+UHYCc/10ORclX+aRiPQC/gur9dZhYLKITHZz2lPGmF/59EIucr7+X1L+4YfvvC9E5GHgP4EPRGQXVsHVG2tYvgJgkvHcAdtFC7ILYIyZISIZwEysAicE69fHa8AyY4y9gfE9IyJfAo9hPaFFAt9ivY/5o9Gm3Q3mwzyK54cmyKmOxZ2jgBZkDeTr/yXlH374zvuTiOzD+p8ZCPTBeuJ7Bavl6RFv4hHHo5xSSikVlLSxh1JKqaCmBZlSSqmgpgWZUkqpoKYFmVJKqaCmBZlSSqmgpgWZUkqpoKYFmVJKqaCmBZlSdRAR04hlhePYYY7Pm5v3KhpHRH7m5tr6XWCc+e7ulVIXQkf2UKpuK91sawvcgDUu5lo3+zP8mqKm9w0/XFO9087X469AFNAVGHyBcSkFaEGmVJ2MMT+ruU1EhmEVZKfc7a/iX1jTtxf7I21NKKOe6/SaMWYGWE97aEGmfEQLMqX8xBhTjDUOnVLKj/QdmVJ+4ukdmYh0dGw/IiI2EXlURA6ISImIZIvIcyIS5QibICIvOMKWisjXIvJoHecUEbldRD4QkVOOY46JyKsi0tEP1xgpInNEZI+IFDrOlyMin4rIUyIS6etzKlWTPpEp1bz+CozFmnPuENZkgo8AV4vIHcAOIBbrHVWiY/+zIhJpjHm6akSOyQjfBH6CNeP4biAX6A5MByaIyGhjTP0TFXpBRGxYE72OwJpyY4tj3QZr6o65WNN66FQryq+0IFOq+aRgTdLZzRjzHYCIdMCaKv5GrILhC+AuY8x5x/4xWDPrzhGRFxzVl05PYhViW4E7jDHZzh0i8iDwJ+BNEUk1xlT4IP1DsAqxPcD1xpiiKucTYBBw1gfnUapOWrWoVPN6yFmIgWtK+dcdH1OAB5yFmGP/BuBLrKc0V1N4EUkEHgIKsSYjdBVijuP+jPX01AW4yUdpb+NYf1K1EHOczxhjttUoaJXyCy3IlGo+5cDHbrYfcqx3G2PcNXf/2rG+rMq24UALYIsx5oSH821xrK9raEI92IM1Vf3PRWSGiLSp7wCl/EELMqWaz/ceqvgKHetsN/uq7q/akKKzYz3GU0dt4BlHmNYXlmyLMeYbrPd54cCLwPci8o2IrBaRiSIS4ovzKFUffUemVPOpb1r4hkwb7yw0vsJqIFKXnQ2It06Oqer/BtyK9c5sCHCnY9krIunGGH1PpvxKCzKlLg5ZjvU+X3Ve9pYx5nvgZceCiPQEVgO9gDnAb5syPerSo1WLSl0cPsR65/ZjEYlvzoQYY74A/tPxsWdzpkVdGrQgU+oiYIzJxXpPFQ+8IyKpNcM4OldP91WjDBEZISI3i0hoje0hwM2Oj0d9cS6l6qJVi0pdPGZjtWScDOwXkb3AYaxGIR2wxn0Md6xzfXC+HsDzQIGI7AFysAYEHgC0w+oIvcQH51GqTlqQKXWRMMaUAz8VkTeAaUB/rMLmHFYh81fgH1ij2fvCOqwnwOuxRrMfhNWi8hjW+7JlxpiTPjqXUh6JMaa506CUCkCOEeqXAyt93YDEn3GrS48+kSml6jOkygSYC4wxRxobkYi8xA/zkSnlE1qQKaXq08WxgDUI8JELiGsK0PJCE6RUVVq1qJRSKqhp83ullFJBTQsypZRSQU0LMqWUUkFNCzKllFJBTQsypZRSQU0LMqWUUkHt/wN0rupBORFX8QAAAABJRU5ErkJggg==\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "fig = pyplot.figure(figsize=(6,4))\n", - "pyplot.plot(t[:N], num_sol[:,0], linewidth=2, linestyle='--', label='Num-solution no drag')\n", - "pyplot.plot(t[:N], y[:N], linewidth=2, alpha=0.6, label='Experimental data')\n", - "pyplot.plot(t[:N], num_sol_drag[:,0], linewidth=2, linestyle='--', label='Num-solution drag')\n", + "fig = plt.figure(figsize=(6,4))\n", + "plt.plot(t[:N], num_sol[:,0], linewidth=2, linestyle='--', label='Num-solution no drag')\n", + "plt.plot(t[:N], y[:N], linewidth=2, alpha=0.6, label='Experimental data')\n", + "plt.plot(t[:N], num_sol_drag[:,0], linewidth=2, linestyle='--', label='Num-solution drag')\n", "\n", - "pyplot.title('Free fall tennis ball \\n')\n", + "plt.title('Free fall tennis ball \\n')\n", "\n", - "pyplot.xlabel('Time [s]')\n", - "pyplot.ylabel('$y$ [m]')\n", - "pyplot.legend();" + "plt.xlabel('Time [s]')\n", + "plt.ylabel('$y$ [m]')\n", + "plt.legend();" ] }, { @@ -775,37 +719,41 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 325, "metadata": {}, "outputs": [ { "data": { - "image/png": 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rFe+ZbgPa2/+/BKsXtGu7ioEvsD5UPnNb5lOsg/JX9nx3NV13bWI8WbZiPYp7qX2yCVZP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\nzKxULkbMzMysVP8HpqMcurFJrC4AAAAASUVORK5CYII=\n", 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\n", "text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "fig = pyplot.figure(figsize=(6,4))\n", - "pyplot.plot(t[:N], y[:N]-num_sol[:,0], label='No drag')\n", - "pyplot.plot(t[:N], y[:N]-num_sol_drag[:,0], label='With drag')\n", - "pyplot.title('Difference between numerical solution and experimental data.\\n')\n", - "pyplot.xlabel('Time [s]')\n", - "pyplot.ylabel('$y$ [m]')\n", - "pyplot.legend();" + "fig = plt.figure(figsize=(6,4))\n", + "plt.plot(t[:N], y[:N]-num_sol[:,0], label='No drag')\n", + "plt.plot(t[:N], y[:N]-num_sol_drag[:,0], label='With drag')\n", + "plt.title('Difference between numerical solution and experimental data.\\n')\n", + "plt.xlabel('Time [s]')\n", + "plt.ylabel('$y$ [m]')\n", + "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "##### Discuss with your neighbor\n", + "## Discussion\n", + "\n", + "* What do you see in the plot of the difference between the numerical solution and the experimental data?\n", "\n", - "* What do you see in the plot of the difference between the numerical solution and the experimental data?" + "* Is the error plotted above related to truncation error? Is it related to roundoff error?" ] }, { @@ -836,6 +784,144 @@ "\n", "4. _Computational Physics with Python_, lecture notes by Eric Ayars, California State University, Chico. Available online on the author's website: https://physics.csuchico.edu/ayars/312/handouts/comp-phys-python.pdf" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problems\n", + "\n", + "1. Integrate the `fall_drag` equations for a tennis ball and a [lacrosse ball](https://en.wikipedia.org/wiki/Lacrosse_ball) with the same initial conditions as above. Plot the resulting height vs time. \n", + "\n", + "_Given:_ y(0) = 1.6 m, v(0) = 0 m/s\n", + "\n", + "|ball| diameter | mass|\n", + "|---|---|---|\n", + "|tennis| $6.54$–$6.86 \\rm{cm}$ |$56.0$–$59.4 \\rm{g}$|\n", + "|lacrosse| $6.27$–$6.47 \\rm{cm}$ |$140$–$147 \\rm{g}$|\n", + "\n", + "Is there a difference in the two solutions? At what times do the tennis ball and lacrosse balls reach the ground? Which was first?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Projectile motion with drag](../images/projectile.png)\n", + "\n", + "The figure above shows the forces acting on a projectile object, like the [lacrosse ball](https://en.wikipedia.org/wiki/Lacrosse_ball) from [Flipping Physics](http://www.flippingphysics.com) that we analyzed in [lesson 01_Catch_Motion](./01_Catch_Motion.ipynb). Consider the 2D motion of the [lacrosse ball](https://en.wikipedia.org/wiki/Lacrosse_ball), now the state vector has two extra variables, \n", + "\n", + "\\begin{equation}\n", + "\\mathbf{y} = \\begin{bmatrix}\n", + "x \\\\ v_x \\\\\n", + "y \\\\ v_y \n", + "\\end{bmatrix},\n", + "\\end{equation}\n", + "\n", + "and its derivative is now, \n", + "\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{y}} = \\begin{bmatrix}\n", + "v_x \\\\ -c v_x^2 \\\\\n", + "v_y \\\\ g - cv_y^2 \n", + "\\end{bmatrix}, \n", + "\\end{equation}\n", + "\n", + "where $c= \\frac{1}{2} \\pi R^2 \\rho C_d$. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2. Create a `projectile_drag` function that returns the derivative of $\\mathbf{y}$, given $\\mathbf{y}$ e.g. \n", + "\n", + " $\\mathbf{\\dot{y}} = projectile\\_drag(\\mathbf{y})$\n", + " \n", + " Below is the start of a function definition, be sure to update the help file. \n", + " \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 241, + "metadata": {}, + "outputs": [], + "source": [ + "def projectile_drag(state,C_d=0.47,m=0.143,R = 0.0661/2):\n", + " '''Computes the right-hand side of the differential equation\n", + " for the fall of a projectile lacrosee ball, with drag, in SI units.\n", + " \n", + " Arguments\n", + " ---------- \n", + " state : array of two dependent variables [y v]^T\n", + " m : mass in kilograms default set to 0.143 kg (mass of lax ball source wiki)\n", + " C_d : drag coefficient for a sphere default set to 0.47 (no units)\n", + " R : radius of ball default in meters is 0.0661/2 m (tennis ball)\n", + " Returns\n", + " -------\n", + " derivs: array of four derivatives [?? ?? ?? ??]\n", + " '''\n", + " \n", + " rho = 1.22 # air density kg/m^3\n", + " pi = np.pi\n", + "\n", + " return derivs" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "3. Integrate your `projectile_drag` function using the Euler integration method. Use initial conditions from the saved data in lesson [01_Catch_Motion](01_Catch_Motion.ipynb), there is a numpy `npz` file in the data folder if you want to check your results from lesson 1. The initial conditions in the provided npz file are\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{y}(0) = \\begin{bmatrix}\n", + "x(0) \\\\ v_x(0) \\\\\n", + "y(0) \\\\ v_y(0) \n", + "\\end{bmatrix}\n", + "= \\begin{bmatrix}\n", + " 0.5610~m \\\\ 2.6938~m/s \\\\\n", + "-0.1858~m \\\\ -0.0759~m/s \n", + "\\end{bmatrix},\n", + "\\end{equation}\n", + "\n", + "Compare your converged numerical integration to the data points in [projectile_coords.npz](../data/projectile_coords.npz). Is there a noticeable effect of drag on the lacrosse ball?" + ] + }, + { + "cell_type": "code", + "execution_count": 326, + "metadata": {}, + "outputs": [], + "source": [ + "npz = np.load('../data/projectile_coords.npz')\n", + "t3=npz['t']\n", + "x3=npz['x']\n", + "y3=npz['y']" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/notebooks/03_Get_Oscillations.ipynb b/notebooks/03_Get_Oscillations.ipynb index 85e4e98..7b32bd6 100644 --- a/notebooks/03_Get_Oscillations.ipynb +++ b/notebooks/03_Get_Oscillations.ipynb @@ -21,7 +21,7 @@ "* form the state vector and the vectorized form of a second-order dynamical system;\n", "* improve the simple free-fall model by adding air resistance.\n", "\n", - "You also learned that Euler's method is a _first-order_ method: a Taylor series expansion shows that stepping in time with Euler makes an error—called the _truncation error_—proportional to the time increment, $\\Delta t$.\n", + "You also learned that Euler's method is a _first-order_ method: a Taylor series expansion shows that stepping in time with Euler makes an error—called the _truncation error_ —proportional to the time increment, $\\Delta t$.\n", "\n", "In this lesson, you'll work with oscillating systems. Euler's method doesn't do very well with oscillating systems, but we'll show you a clever way to fix this. (The modified method is _still_ first order, however. We will also confirm the **order of convergence** by computing the error using different values of $\\Delta t$.\n", "\n", @@ -31,12 +31,7 @@ { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "metadata": {}, "outputs": [], "source": [ "import numpy\n", @@ -48,12 +43,7 @@ { "cell_type": "code", "execution_count": 2, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "metadata": {}, "outputs": [], "source": [ "def eulerstep(state, rhs, dt):\n", @@ -82,13 +72,14 @@ "A prototypical mechanical system is a mass $m$ attached to a spring, in the simplest case without friction. The elastic constant of the spring, $k$, determines the restoring force it will apply to the mass when displaced by a distance $x$. The system then oscillates back and forth around its position of equilibrium.\n", "\n", " \n", - "#### Simple spring-mass system, without friction." + "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ + "## Simple spring-mass system, without friction.\n", "Newton's law applied to the friction-less spring-mass system is:\n", "\n", "\\begin{equation}\n", @@ -145,12 +136,7 @@ { "cell_type": "code", "execution_count": 3, - "metadata": { - "collapsed": true, - "jupyter": { - "outputs_hidden": true - } - }, + "metadata": {}, "outputs": [], "source": [ "def springmass(state):\n", diff --git a/notebooks/Projectile_Motion.mp4 b/notebooks/Projectile_Motion.mp4 new file mode 100644 index 0000000000000000000000000000000000000000..5a910d6a45b4e50f2071e4b4fca37aadae9367a8 GIT binary patch literal 10718913 zcmeEP30zIv_uu#4<|H8%rD&o;LW3rXsL((uN>WKQX_5vdNo1%fQ;{enQOP`)sf?M& zGA2o8DfD0Kc8+uSKfmAe-uwB#-}`qzZ@=^1Yp=bgz4qGYo_o6pA+l3LW(WEO4%8v= 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