diff --git a/README.md b/README.md
index b26bad5..3219cdb 100644
--- a/README.md
+++ b/README.md
@@ -1,4 +1,54 @@
# Computational Mechanics 03- Initial Value Problems
+## Learning to frame engineering equations as numerical methods
-![Warning: Under
-Construction!!](https://publicdomainvectors.org/photos/under-construction_geek_man_01.png)
+Welcome to Computational Mechanics Module #3! In this module we will explore
+some more data analysis, find better ways to solve differential equations, and
+learn how to solve engineering problems with Python.
+
+[01_Catch_Motion](./notebooks/01_Catch_Motion.ipynb)
+
+* Work with images and videos in Python using `imageio`.
+* Get interactive figures using the `%matplotlib notebook` command.
+* Capture mouse clicks with Matplotlib's `mpl_connect()`.
+* Observed acceleration of falling bodies is less than $9.8\rm{m/s}^2$.
+* Capture mouse clicks on several video frames using widgets!
+* Projectile motion is like falling under gravity, plus a horizontal velocity.
+* Save our hard work as a numpy .npz file __Check the Problems for loading it back into your session__
+* Compute numerical derivatives using differences via array slicing.
+* Real data shows free-fall acceleration decreases in magnitude from $9.8\rm{m/s}^2$.
+
+[02_Step_Future](./notebooks/02_Step_Future.ipynb)
+
+* Integrating an equation of motion numerically.
+* Drawing multiple plots in one figure,
+* Solving initial-value problems numerically
+* Using Euler's method.
+* Euler's method is a first-order method.
+* Freefall with air resistance is a more realistic model.
+
+[03_Get_Oscillations](./notebooks/03_Get_Oscillations.ipynb)
+
+* vector form of the spring-mass differential equation
+* Euler's method produces unphysical amplitude growth in oscillatory systems
+* the Euler-Cromer method fixes the amplitude growth (while still being first
+* order)
+* Euler-Cromer does show a phase lag after a long simulation
+* a convergence plot confirms the first-order accuracy of Euler's method
+* a convergence plot shows that modified Euler's method, using the derivatives
+* evaluated at the midpoint of the time interval, is a second-order method
+* How to create an implicit integration method
+* The difference between _implicit_ and _explicit_ integration
+* The difference between stable and unstable methods
+
+[04_Getting_to_the_root](./notebooks/04_Getting_to_the_root.ipynb)
+
+* How to find the 0 of a function, aka root-finding
+* The difference between a bracketing and an open methods for finding roots
+* Two bracketing methods: incremental search and bisection methods
+* Two open methods: Newton-Raphson and modified secant methods
+* How to measure relative error
+* How to compare root-finding methods
+* How to frame an engineering problem as a root-finding problem
+* Solve an initial value problem with missing initial conditions (the shooting
+* method)
+* _Bonus: In the Problems you'll consider stability of bracketing and open methods._
diff --git a/images/.ipynb_checkpoints/damped-spring-checkpoint.png b/images/.ipynb_checkpoints/damped-spring-checkpoint.png
new file mode 100644
index 0000000..cb78d51
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diff --git a/images/.ipynb_checkpoints/double_pendulum_animation-checkpoint.gif b/images/.ipynb_checkpoints/double_pendulum_animation-checkpoint.gif
new file mode 100644
index 0000000..81f5a58
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diff --git a/images/.ipynb_checkpoints/pendulum_spring-checkpoint.png b/images/.ipynb_checkpoints/pendulum_spring-checkpoint.png
new file mode 100644
index 0000000..323f0de
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diff --git a/images/bisection.png b/images/bisection.png
new file mode 100644
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diff --git a/images/bisection.svg b/images/bisection.svg
new file mode 100644
index 0000000..61715ca
--- /dev/null
+++ b/images/bisection.svg
@@ -0,0 +1,299 @@
+
+
+
+
diff --git a/images/shooting.png b/images/shooting.png
new file mode 100644
index 0000000..8bb9983
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diff --git a/images/shooting.svg b/images/shooting.svg
new file mode 100644
index 0000000..b494211
--- /dev/null
+++ b/images/shooting.svg
@@ -0,0 +1,937 @@
+
+
+
+
diff --git a/notebooks/.ipynb_checkpoints/02_Step_Future-checkpoint.ipynb b/notebooks/.ipynb_checkpoints/02_Step_Future-checkpoint.ipynb
index bde138e..a103501 100644
--- a/notebooks/.ipynb_checkpoints/02_Step_Future-checkpoint.ipynb
+++ b/notebooks/.ipynb_checkpoints/02_Step_Future-checkpoint.ipynb
@@ -374,7 +374,7 @@
},
{
"cell_type": "code",
- "execution_count": 199,
+ "execution_count": 310,
"metadata": {},
"outputs": [],
"source": [
@@ -391,7 +391,7 @@
},
{
"cell_type": "code",
- "execution_count": 200,
+ "execution_count": 311,
"metadata": {},
"outputs": [],
"source": [
@@ -401,7 +401,7 @@
},
{
"cell_type": "code",
- "execution_count": 201,
+ "execution_count": 312,
"metadata": {},
"outputs": [],
"source": [
@@ -419,7 +419,7 @@
},
{
"cell_type": "code",
- "execution_count": 202,
+ "execution_count": 314,
"metadata": {},
"outputs": [],
"source": [
@@ -429,7 +429,7 @@
},
{
"cell_type": "code",
- "execution_count": 203,
+ "execution_count": 315,
"metadata": {},
"outputs": [
{
@@ -438,7 +438,7 @@
"array([ 1.6 , -0.00981])"
]
},
- "execution_count": 203,
+ "execution_count": 315,
"metadata": {},
"output_type": "execute_result"
}
@@ -452,7 +452,7 @@
},
{
"cell_type": "code",
- "execution_count": 204,
+ "execution_count": 316,
"metadata": {},
"outputs": [],
"source": [
@@ -469,7 +469,7 @@
},
{
"cell_type": "code",
- "execution_count": 205,
+ "execution_count": 317,
"metadata": {},
"outputs": [
{
@@ -504,7 +504,7 @@
},
{
"cell_type": "code",
- "execution_count": 206,
+ "execution_count": 318,
"metadata": {},
"outputs": [
{
@@ -595,7 +595,7 @@
},
{
"cell_type": "code",
- "execution_count": 207,
+ "execution_count": 319,
"metadata": {},
"outputs": [],
"source": [
@@ -632,7 +632,7 @@
},
{
"cell_type": "code",
- "execution_count": 208,
+ "execution_count": 320,
"metadata": {},
"outputs": [],
"source": [
@@ -643,7 +643,7 @@
},
{
"cell_type": "code",
- "execution_count": 209,
+ "execution_count": 321,
"metadata": {},
"outputs": [],
"source": [
@@ -653,7 +653,7 @@
},
{
"cell_type": "code",
- "execution_count": 210,
+ "execution_count": 322,
"metadata": {},
"outputs": [],
"source": [
@@ -664,7 +664,7 @@
},
{
"cell_type": "code",
- "execution_count": 230,
+ "execution_count": 323,
"metadata": {},
"outputs": [],
"source": [
@@ -681,7 +681,7 @@
},
{
"cell_type": "code",
- "execution_count": 231,
+ "execution_count": 324,
"metadata": {},
"outputs": [
{
@@ -719,7 +719,7 @@
},
{
"cell_type": "code",
- "execution_count": 232,
+ "execution_count": 325,
"metadata": {},
"outputs": [
{
@@ -784,6 +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/.ipynb_checkpoints/03_Get_Oscillations-checkpoint.ipynb b/notebooks/.ipynb_checkpoints/03_Get_Oscillations-checkpoint.ipynb
index 9a34693..bea1f08 100644
--- a/notebooks/.ipynb_checkpoints/03_Get_Oscillations-checkpoint.ipynb
+++ b/notebooks/.ipynb_checkpoints/03_Get_Oscillations-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 R.C. Cooper"
]
},
{
@@ -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",
@@ -31,23 +31,20 @@
{
"cell_type": "code",
"execution_count": 1,
- "metadata": {
- "collapsed": true
- },
+ "metadata": {},
"outputs": [],
"source": [
- "import numpy\n",
- "from matplotlib import pyplot\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
- "pyplot.rc('font', family='serif', size='14')"
+ "plt.rcParams.update({'font.size': 22})\n",
+ "plt.rcParams['lines.linewidth'] = 3"
]
},
{
"cell_type": "code",
"execution_count": 2,
- "metadata": {
- "collapsed": true
- },
+ "metadata": {},
"outputs": [],
"source": [
"def eulerstep(state, rhs, dt):\n",
@@ -76,13 +73,14 @@
"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",
@@ -115,7 +113,7 @@
"\\dot{v} &=& -\\omega^2 x\n",
"\\end{eqnarray}\n",
"\n",
- "Like we did in [Lesson 2](http://go.gwu.edu/engcomp3lesson2) of this module, we write the state of the system as a two-dimensional vector,\n",
+ "Like we did in [Lesson 2](./02_Step_Future.ipynb) of this module, we write the state of the system as a two-dimensional vector,\n",
"\n",
"\\begin{equation}\n",
"\\mathbf{x} = \\begin{bmatrix}\n",
@@ -138,10 +136,8 @@
},
{
"cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "collapsed": true
- },
+ "execution_count": 42,
+ "metadata": {},
"outputs": [],
"source": [
"def springmass(state):\n",
@@ -154,10 +150,10 @@
" \n",
" Returns \n",
" -------\n",
- " derivs: array of two derivatives [v - ω*ω*x]^T\n",
+ " derivs: array of two derivatives [v - w*w*x]^T\n",
" '''\n",
" \n",
- " derivs = numpy.array([state[1], -ω**2*state[0]])\n",
+ " derivs = np.array([state[1], -w**2*state[0]])\n",
" return derivs"
]
},
@@ -170,14 +166,12 @@
},
{
"cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "collapsed": true
- },
+ "execution_count": 43,
+ "metadata": {},
"outputs": [],
"source": [
- "ω = 2\n",
- "period = 2*numpy.pi/ω\n",
+ "w = 2\n",
+ "period = 2*np.pi/w\n",
"dt = period/20 # we choose 20 time intervals per period \n",
"T = 3*period # solve for 3 periods\n",
"N = round(T/dt)"
@@ -185,7 +179,7 @@
},
{
"cell_type": "code",
- "execution_count": 5,
+ "execution_count": 44,
"metadata": {},
"outputs": [
{
@@ -211,21 +205,17 @@
},
{
"cell_type": "code",
- "execution_count": 6,
- "metadata": {
- "collapsed": true
- },
+ "execution_count": 45,
+ "metadata": {},
"outputs": [],
"source": [
- "t = numpy.linspace(0, T, N)"
+ "t = np.linspace(0, T, N)"
]
},
{
"cell_type": "code",
- "execution_count": 7,
- "metadata": {
- "collapsed": true
- },
+ "execution_count": 46,
+ "metadata": {},
"outputs": [],
"source": [
"x0 = 2 # initial position\n",
@@ -234,22 +224,18 @@
},
{
"cell_type": "code",
- "execution_count": 8,
- "metadata": {
- "collapsed": true
- },
+ "execution_count": 47,
+ "metadata": {},
"outputs": [],
"source": [
"#initialize solution array\n",
- "num_sol = numpy.zeros([N,2])"
+ "num_sol = np.zeros([N,2])"
]
},
{
"cell_type": "code",
- "execution_count": 9,
- "metadata": {
- "collapsed": true
- },
+ "execution_count": 48,
+ "metadata": {},
"outputs": [],
"source": [
"#Set intial conditions\n",
@@ -266,10 +252,8 @@
},
{
"cell_type": "code",
- "execution_count": 10,
- "metadata": {
- "collapsed": true
- },
+ "execution_count": 49,
+ "metadata": {},
"outputs": [],
"source": [
"for i in range(N-1):\n",
@@ -285,40 +269,40 @@
},
{
"cell_type": "code",
- "execution_count": 11,
- "metadata": {
- "collapsed": true
- },
+ "execution_count": 67,
+ "metadata": {},
"outputs": [],
"source": [
- "x_an = x0*numpy.cos(ω * t)"
+ "x_an = x0*np.cos(w * t)"
]
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": 68,
"metadata": {},
"outputs": [
{
"data": {
- "image/png": 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oFRn2lFRw6mNzmTGiK38+fViwsxMSampdlFTU0CExzufL1oFBmifi7pCVUqop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\n",
+ "image/png": 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\n",
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