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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Initial Value Problems - Project\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"![Initial condition of firework with FBD and sum of momentum](../images/firework.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are going to end this module with a __bang__ by looking at the flight path of a firework. Shown above is the initial condition of a firework, the _Freedom Flyer_ in (a), its final height where it detonates in (b), the applied forces in the __Free Body Diagram (FBD)__ in (c), and the __momentum__ of the firework $m\\mathbf{v}$ and the propellent $dm \\mathbf{u}$ in (d). \n",
"\n",
"The resulting equation of motion is that the acceleration is proportional to the speed of the propellent and the mass rate change $\\frac{dm}{dt}$ as such\n",
"\n",
"$$\\begin{equation}\n",
"m\\frac{dv}{dt} = u\\frac{dm}{dt} -mg - cv^2.~~~~~~~~(1)\n",
"\\end{equation}$$\n",
"\n",
"If we assume that the acceleration and the propellent momentum are much greater than the forces of gravity and drag, then the equation is simplified to the conservation of momentum. A further simplification is that the speed of the propellant is constant, $u=constant$, then the equation can be integrated to obtain an analytical rocket equation solution of [Tsiolkovsky](https://www.math24.net/rocket-motion/) [1,2], \n",
"\n",
"$$\\begin{equation}\n",
"m\\frac{dv}{dt} = u\\frac{dm}{dt}~~~~~(2.a)\n",
"\\end{equation}$$\n",
"\n",
"$$\\begin{equation}\n",
"\\frac{m_{f}}{m_{0}}=e^{-\\Delta v / u},~~~~~(2.b) \n",
"\\end{equation}$$\n",
"\n",
"where $m_f$ and $m_0$ are the mass at beginning and end of flight, $u$ is the speed of the propellent, and $\\Delta v=v_{final}-v_{initial}$ is the change in speed of the rocket from beginning to end of flight. Equation 2.b only relates the final velocity to the change in mass and propellent speed. When you integrate Eqn 2.a, you will have to compare the velocity as a function of mass loss. \n",
"\n",
"Your first objective is to integrate a numerical model that converges to equation (2.b), the Tsiolkovsky equation. Next, you will add drag and gravity and compare the results _between equations (1) and (2)_. Finally, you will vary the mass change rate to achieve the desired detonation height. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. Create a `simplerocket` function that returns the velocity, $v$, the acceleration, $a$, and the mass rate change $\\frac{dm}{dt}$, as a function of the $state = [position,~velocity,~mass] = [y,~v,~m]$ using eqn (2.a). Where the mass rate change $\\frac{dm}{dt}$ and the propellent speed $u$ are constants. The average velocity of gun powder propellent used in firework rockets is $u=250$ m/s [3,4]. \n",
"\n",
"$\\frac{d~state}{dt} = f(state)$\n",
"\n",
"$\\left[\\begin{array}{c} v\\\\a\\\\ \\frac{dm}{dt} \\end{array}\\right] = \\left[\\begin{array}{c} v\\\\ \\frac{u}{m}\\frac{dm}{dt} \\\\ \\frac{dm}{dt} \\end{array}\\right]$\n",
"\n",
"Use [two integration methods](../notebooks/03_Get_Oscillations.ipynb) to integrate the `simplerocket` function, one explicit method and one implicit method. Demonstrate that the solutions converge to equation (2.b) the Tsiolkovsky equation. Use an initial state of y=0 m, v=0 m/s, and m=0.25 kg. \n",
"\n",
"Integrate the function until mass, $m_{f}=0.05~kg$, using a mass rate change of $\\frac{dm}{dt}=0.05$ kg/s. \n",
"\n",
"_Hint: your integrated solution will have a current mass that you can use to create $\\frac{m_{f}}{m_{0}}$ by dividing state[2]/(initial mass), then your plot of velocity(t) vs mass(t)/mass(0) should match Tsiolkovsky's_"
]
},
{
"cell_type": "code",
"execution_count": 289,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"plt.rcParams.update({'font.size': 22})\n",
"plt.rcParams['lines.linewidth'] = 3"
]
},
{
"cell_type": "code",
"execution_count": 259,
"metadata": {},
"outputs": [],
"source": [
"def simplerocket(state,dmdt=0.05, u=250):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, without drag or gravity, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" \n",
" Returns\n",
" -------\n",
" derivs: array of three derivatives [v (u/m)*dmdt -dmdt]^T\n",
" '''\n",
" \n",
" dstate = np.array([state[1], ((u/(state[2])*dmdt)), -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 260,
"metadata": {},
"outputs": [],
"source": [
"##Importing R-K2 step for an explicit integration method\n",
"\n",
"def rk2_step(state, rhs, dt):\n",
" '''Update a state to the next time increment using modified Euler's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" \n",
" mid_state = state + rhs(state) * dt*0.5 \n",
" next_state = state + rhs(mid_state)*dt\n",
" \n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 261,
"metadata": {},
"outputs": [],
"source": [
"##Importing step for Implicit integration method (Heun)\n",
"\n",
"def heun_step(state,rhs,dt,etol=0.000001,maxiters = 100):\n",
" '''Update a state to the next time increment using the implicit Heun's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" etol : tolerance in error for each time step corrector\n",
" maxiters: maximum number of iterations each time step can take\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" e=1\n",
" eps=np.finfo('float64').eps\n",
" next_state = state + rhs(state)*dt\n",
" ################### New iterative correction #########################\n",
" for n in range(0,maxiters):\n",
" next_state_old = next_state\n",
" next_state = state + (rhs(state)+rhs(next_state))/2*dt\n",
" e=np.sum(np.abs(next_state-next_state_old)/np.abs(next_state+eps))\n",
" if e<etol:\n",
" break\n",
" ############### end of iterative correction #########################\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 262,
"metadata": {},
"outputs": [
{
"data": {
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pCzyC63C9BtfQ4WpcsJnhpVngLV+GO6ZPwf3IfKaQ2b8f10rxTuCvuOrXLcC//O4v3uHlIYdXc7ISOFdEvsNd0WxS1WCj8LwC3IzrdH8frvbmStzncWU+97AiPSYj9Sruff5PRP4frrbnJgpetfsm7rbJaFwtj/+9a1Q1RUT+BjwmIs28vB/AXbGdjAsunxDcg7j7cV+LyFO4GOM7xh72tp8pIn/G3WOchrtS2437IVRVVR8Jse3luIu2O8X1Iz4S0IbgJVwjwIa482X+wrWQiaU/QrcC7YL79bsO96tnB64KsadfmqNagXrzKuKqDjbgvmBrvQ8/yS9NyFagAXk4EdcQ533f+l6+puBumh/GNWA5JcR7u8Pbz5ogy4K2eMOddDKACwLmD/HSjw2yrXtxAXA3rtpqBe7gTgqWr3Dv2W/Zv3Gt0Lr4zRuE+3W/x/tM1uKaQPf1S3NUK1DcF+1xXDXRQVxft664E9aLAelexlXDZOO1Kgv2WXnzr8JdmabjWnqOBxoEpNkGvBqi3O/Jp2zytAItxPF1eYTfgXzTBztegGq4QJDiHY+Tgfb+7w93cpyIayhxCPfDZTquwZX/Z/0LLuAcwF0J3BhBvucC34RYNsnblq/Vc2/cldIhXCOI+3G3GwK/vyd5eUkPeB9HtQL15jXzjr9dXvpfgIsjyHekx6Tv/NIsYP3HCGj16JX7l7hzwg7cj2Vf69CwrUD9tpGA+7GvwLAw6YbjruhSvfz/7h0H7fzSHNVS0+/7O9Nb54CX3+5Btv8nXLA86O1jEXBJqG3jflS9Su5390CQbc7G/QCLqHWueCsZA4D3q20s0ESDNJYxxpiySNzADOuA/1NXvZ6vuK8CNY7XgrQTrormaQt+xpjywLsH3B43UEMa7io1IhYAjc/nuBE5Psd1uDbGmPLgItxIMetw1fuB3UlCsipQY4wxccm6QRhjjIlLVgVaRPXq1dNWrVpFOxvGGFOuLFy4cKeq1o9mHiwAFlGrVq1YsGBB/gmNMcbkEJH10c6DVYEaY4yJS6UaAEWkg4jcJiJvicgKEckW92DDiIfyCbHdS8U9mHWfuIckLhCRm/Ibbb6w6xljjCn/SrsK9AbgtuLcoIg8hxvpIQ33zLAjuIdXjgOGishFGmRE8MKuZ4wxJjaU9pXOUtyjSS7GPUerSAMKe+N43ogbWug4VT1LVYfjRjj/DTeUz83FtZ4xxpjYUaoBUFVfVdW7VPUDVQ03inqk7vVe71a/EcpVdTvuahPgniBVmoVdzxhjTIwotyd4b5TyXriBgvM8ykVVZ+IeV9IIOL6o6xljjIkt5TYAAr5nYi1T1cMh0swPSFuU9YrVnoMZ3Pnhr+w6EOzRfcYYY0paee4H2Np7DdeXZENA2qKsV2yWbNrH9W8tZPPew2zdd5gJY/qRmCAlsStjjDEhlOcrwGre68EwaXwPnqxeDOvlEJFrvS4TC1JSUvLNaKAdqWls3usuPmev3sVTX60s8DaMMcYUTXkOgL5LpoKO5l3Y9XKo6suq2ltVe9evX/CRfIZ2asitJ7fNmX5+xhq+WhbsYdTGGGNKSnkOgKnea7UwaXzLUv3mFXa9YnXbKe05sX1u8Lzjg19ZuzPcRakxxpjiVJ4D4DrvtWWYNM0D0hZlvWKVmCA8c3F3mtaqDEBqeibXT1zIoYzMktqlMcYYP+U5AP7svXYRkcoh0vQJSFuU9Ypd7aoVePHyXlRIch/Dyu2p3DtpCfaMRmOMKXnlNgCq6kZgEVAB90Tgo4jIYKAZbrSXOUVdr6R0bVaTh87tkjP96S9bmDAn6oOkG2NMzCvzAVBEHvUGzn40yGLfvMdFpK3fOg2A573Jx1Q1u5jWKxEX92nByD7Nc6Yf+mw5C9fvLo1dG2NM3Crtp0H0FJG5vj+gp7fokYD5/hoDHbzXo6jqR8ALuFFblojIFBGZBKwCOgOTcYNbF8t6JenBc7rQtWlNADKzlRvfXkRKqnWSN8aYklLaV4A1gH5+f75+du0C5kdMVW8ELsNVaw4GhgGrcYNZXxDqiQ6FXa+kVEpO5IXLe1KrSjIA2/enc/M7iziSVSoXocYYE3fEGlwUTe/evbU4nwj//e8pXPnGPHwfy+gBrXjwnC7hVzLGmHJGRBaqau9o5qHM3wOMNye2r88dp7bPmR7/4zo+mL8xijkyxpjYZAGwDLppSFvO6NooZ/q+yUtZtGFPFHNkjDGxxwJgGSQiPHFhNzo2crdIM7KyuX7iQrbvT4tyzowxJnZYACyjqlZM4pVRvXMaxexITefaiQtJO1KqbXOMMSZmWQAsw5rXqcLzl/bMeVTSrxv38rdPltpIMcYYUwwsAJZxA9rW474zO+VMf7xoE2/MXhe9DBljTIywAFgOjB7Qiot6NcuZfvjz35i9emcUc2SMMeWfBcByQET45/Bj6d68FgBZ2cpN7yxiw65DUc6ZMcaUXxYAy4mKSYm8dEUvGlSvCMDeQ0cY8+Z89qcdiXLOjDGmfLIAWI40rFGJl67IfXzS6h0HuOntRWTacGnGGFNgFgDLmR4tavPEhcflTM9atZN/fLY8ijkyxpjyyQJgOXRu96bcOrRdzvSEOet588d10cuQMcaUQxYAy6k/n9KOs47LfULU36csY8bKHVHMkTHGlC8WAMspEeHJi7rRzWsZmq1w8zs/s3JbapRzZowx5YMFwHKsUnIir4zqRZOalQA4kJ7J2Dfns/OAPUjXGGPyYwGwnGtQvRKvje5D1QqJAGzac5jrbMxQY4zJlwXAGNCpcQ2evaQH4oYMZeH6Pdz98WIbM9QYY8KwABgjhnZqyN/OyB0z9NNftvDkVyujmCNjjCnbLADGkLEntObSfi1ypp+bvoZ3ftoQxRwZY0zZZQEwhogI/zinC0M61M+Zd/+nS5m+wrpHGGNMIAuAMSYpMYFxl/bk2KY1gNyBs5ds2hflnBljTNliATAGVa2YxOuj+9C0VmUADmVkcdX4+WzcbU+PMMYYHwuAMapB9Uq8OaYPNSsnA7DzQDqj35jHvkP29AhjjAELgDGtbYPqvHxFLyokuo95TcpBrpm4gPRM6yNojDEWAGNcvzZ1eXJEt5zpeWt3c+eHi8nOtj6Cxpj4ZgEwDpzTrQn3/qljzvSUX7fw8Oe/WUd5Y0xcswAYJ649sQ2j+rfMmX7th7W8OPOPKObIGGOiywJgnBAR/u/sLpzepVHOvMenreCD+RujmCtjjIkeC4BxJDFBeHpkd45vUydn3j2TFvP18u1RzJUxxkSHBcA44x6h1JsuTVxHefccwUX89MeuKOfMGGNKlwXAOFS9UjLjr+pLy7pVAEjPzObqCQtYvmV/lHNmjDGlxwJgnKpfvSITx/SjfvWKAKSmZXLlG/PYsMtGizHGxAcLgHGsRd0qTBjTl+qVkgBISU1n1Os/kZJqT5Q3xsQ+C4BxrlPjGrw6qjcVktyhsG7XIa58fR77DtuQacaY2GYB0NCvTV3GXdKDBO+J8su37mfM+PkcTM+MbsaMMaYEWQA0AJzWpRGPXXBczvTC9Xu4ZsIC0o7YuKHGmNhkAdDkGNG7OQ+e3Tln+sc1u7j5nUUcycqOYq6MMaZkWAA0Rxk9sDV/HdYhZ/qb33bw5/d/IcsGzzbGxBgLgCaPm4a05caTjsmZ/mzxVu6dZE+QMMbEFguAJqi/DuvA6AGtcqY/WLCJf3y23J4gYYyJGRYATVAiwgNndebCXs1y5o3/cR1PfrUyirkyxpjiYwHQhJSQIDx+wXGceVzjnHnPTV/Dc9NXRzFXxhhTPCwAmrASE4T/jOjOyR0b5Mx74suVvDBjTRRzZYwxRWcB0OSrQlICz1/Wk4Ft6+bMe3zaCl7+3oKgMab8sgBoIlIpOZFXR/Whf5vcIPjI5yt4dZY9Vd4YUz5FJQCKyKUiMktE9onIARFZICI3iUjE+RGRk0REI/xrEbDu+HzSryj+d13+Va6QyGuje9Ovde4Ddf859Tde+2FtFHNljDGFk1TaOxSR54AbgTTgW+AIMBQYBwwVkYtUNZLxt7YBb4ZZ3hfoBKwBNoZIMxsI1qJjawT7j0tVKiTx+ug+XPXGfOat2w3AQ58tJ1FcJ3pjjCkvSjUAisgFuOC3DThRVVd58xsC04HhwM3AM/ltS1VXAKPD7GuZ9+/rGrrz2quqOj7S/BunasUk3riqD6PfmMf8dXsAeHDKchIShFH9W0U3c8YYE6HSrgK913u92xf8AFR1O3CDN3lPQapCgxGR/kBnIIvwV4mmkFwQ7EuvlrVz5j3w6TImzl0fxVwZY0zkSi0AikgzoBeQAXwYuFxVZwKbgUbA8UXc3RjvdZqqbi7itkwI1SomMf6qPvRoUStn3v2TlzJhzrqo5ckYYyJVmleAPbzXZap6OESa+QFpC0xEqgAXe5Ov5ZN8iIj8W0ReFpGHRGRYUa8+4031Ssm8OaYv3ZrnBsEHPl1mrUONMWVead4D9LWQCFdHtiEgbWFcBFQHdgCf5ZN2VJB5y0VkpKouKUIe4kqNSslMGNOX0W/M4+cNewHXOjQ9M5ubhrSNcu6MMSa40rzaqea9HgyT5oD3Wr0I+/FVf05Q1SMh0vwC3Ap08fLVBDgL+BV37/AbEWkaagcicq3XdWNBSkpKEbIaO2pWTmbi2H70bZXbReKJL1fy769W2gDaxpgyqTQDoHivJXY2FJG2wIne5Ouh0qnq06r6X1VdrqoHVXWrqk7FdZ2YCzQgt8FOsPVfVtXeqtq7fv36xfkWyrVqFZMYP6bPUSPGPPvdah6btsKCoDGmzCnNAJjqvVYLk8a3LDVMmnB8V39zVPW3gq6sqhnAo97kGYXMQ1yrUiGJ167sw0kdcn8YvDTzD/4+xR6lZIwpW0ozAK7zXluGSdM8IG3ERCSR3Ht6+TV+Ccc3CkzIKlATXqXkRF66ohendm6YM2/8j+v42+Sl9lBdY0yZUZoB8GfvtYuIVA6Rpk9A2oIYhgtaB4H3C7G+j6/+7kDYVCasikmJPH9ZT87smvsopXd+2sBfP1pMZlZ2FHNmjDFOqQVAVd0ILAIq4FpqHkVEBgPNcKPEzCnELsZ6r++ralGC1wjvdX7YVCZfyYkJPDOyO8N75F5Mf7xoEze/8zPpmZGMdmeMMSWntPu8+e6vPe41WAFARBoAz3uTj6lqtt+yR0VkhYg8SggiUg/XihPyqf4Uke4icpZXZeo/P0lE/oJrHQrwn4jekQkrKTGBJy/qxsW9m+fMm7ZsG2PGz+dgemYUc2aMiXcFCoAiUk1EmolIuIYsIanqR8ALuNFelojIFBGZBKzCdT+YjBsU219joIP3GsoVuCvLFar6Yz7ZaAVMAXaIyBwR+VBEpuH6Jz7lpblbVb+M/J2ZcBIThEfP78rYE3K7d85evYvLXv2JvYcyopgzY0w8yzcAisixIvJfEfkD2IfrrL5PRNaIyDgR6VqQHarqjcBluOrQwbh7d6txg2BfEOGTIAJd5b2G7Prg51fcYNsrgRbA2V4+DgFvAH1V9V+FyIMJIyFBuO/MTtx5Wvuceb9s3MuIl+awfX9aFHNmjIlXEq5puoi8i+ss/h4wA/gN10WhOu5RQ4OBS4DlqjqypDNbFvXu3VsXLFgQ7WyUKxPmrOOBT5flTDevU5m3xvajZd2q0cuUMaZUichCVe0dzTzkdwX4jqoep6qPqOqPqrpHVTO91x9V9VFVPQ54qzQya2LDqP6tePri7iQmuLERNu4+zIUvzmHFtv1RzpkxJp6EDYCqOiWSjahqfmNuGnOU83o05eUrelExyR2CKanpjHhxDgvX74lyzowx8SKiRjAiUtcb//IZEXnde71WROrmv7YxwQ3t1JAJY/pSvaIbk31/WiaXvTqXb3/bHuWcGWPiQSSNYIbiGqlc7qXfghvX8zJglYgMKdEcmpjWr01d3r32eOpWrQBA2pFsrpmwgPfmbchnTWOMKZpIHof0X2Csqk4KXCAiw3H99zoVd8ZM/Di2aU0+vL4/o16fx6Y9h8lWuGfSErbtT+O2oe0Qkfw3YowxBRRJFWhLYGqIZZ8TfmxPYyLSpn41Jt04gC5NauTMe/qbVdw7aYkNnWaMKRGRBMCfgH+KyFFt1L3ph7zlxhRZg+qVeOq5y/UAACAASURBVP+6/gxqVy9n3nvzN3LdxIUcyrBRY4wxxSuSAHgVMBDYKSLLRORHEVkKpAAnAFeWZAZNfKlW0T1OyX/80G9X7ODSV35i14H0KObMGBNrwnaEPyqhSDtyn6B+AFimqqtKMG/lgnWELxmqyr++XMkLM9bkzGtdrypvXtWXFnWrRDFnxpjiUB46wudQ1VWqOllV3/Je4z74mZIjItx9ekf+fk4XfG1g1u48yPkvzObnDdZX0BhTdGEDoIhMEpE++aTp4w1obUyxu3JAK567tCcVvA7zOw9kMPLluXy+ZGuUc2aMKe/y6wbxIvC8iNQAZuIGkPaNBdoeOAnYC9xXgnk0ce6Mro2pV60i105cwN5DR0jPzObGtxdx1+kduGHwMdZNwhhTKPkNhfaVqvbBdXrfCPQDLgT64p4KMVJV+6nq1yWeUxPX+rauwyc3DqR1vdzGyP+atpJ7Pl7CEesmYYwphIgbwZjgrBFM6dpzMIPr3lrIvLW7c+YNOKYuL1zWi5pVkqOYM2NMQZSLRjAi0iK/v9LIqDEAtatWYOLYvpzfM7ebxI9rdnH+C7PZsOtQFHNmjClvImkFug5Y6/2tC/K3tgTyZUxIFZMSeeqibtxxau7DddekHGT487NZuH53mDWNMSZXJAFwMbAK19ClJZAc8FehxHJnTAgiwi1D2/HMyO45LUR3Hczgkld+4uOFm6KcO2NMeZBvAFTV7riGL3WAH3Djf44EKqhqlqpmlWwWjQnt3O5NefeaftTxniaRkZnNHR/+ysNTl5OVbfe3jTGhRdQRXlWXqupfgdbAv4GzgK0i0rMkM2dMJHq1rMPkGwfSvmG1nHmvzFrLmPHz2Xf4SBRzZowpyyIeCcbTDhgM9Ad+BmxIDlMmtKhbhUk3DuTUzg1z5s38PYXhz81mTcqBKObMGFNWRdIKtI6I3CQi84DJuHFAT1TVIapqDWBMmVGtYhIvXd6LW05umzPvj50HOe+52UxfuSOKOTPGlEX59gMUkTRcS8+JwNxgaVT1u+LPWvlg/QDLps8Wb+HOD38l7YjrJJ8gcM+fOnLNoDY2cowxZUBZ6AcYSQBcB4RLpKrapjgzVZ5YACy7lm7ex7UTFrBlX1rOvPN7NOWR87tSKTkxijkzxpSLAGjCswBYtqWkpnPDWwtZsD73dnWXJjV48fJeNK9jj1UyJlrKQgAsaCMYY8qV+tUr8s41xzOyT/Ocecu27Oes//7ADLsvaExcswBoYl6FpAQePb8r/zzvWJIT3f2/fYePcNX4+Tz77Sqyrb+gMXHJAqCJCyLC5ce35IPr+tOoRiUAVOHfX//ONRMWWH9BY+JQJN0g7EaJiRk9WtTms1tP4Pg2dXLmfbtiB+eM+4Hftu6PYs6MMaUtkivA9SLylYjcLiLtSjxHxpSwetUq8tbYflx3Ym7j5fW7DjH8+dl8+svmKObMGFOaIgmATYDHgebA/0RklYg8IyKniYgNhG3KpaTEBO49oxPPX9aTqhVcl4i0I9nc9t4vPPDpUtKO2BC3xsS6SAbDPqKq36rqHaraCTgN93SI24HNIvI/EbleRBqG35IxZc8ZXRvz6c0DaVM/90nzE+as58IXf2T9roNRzJkxpqQVuBGMqq5V1XGqegbuqvAloCtwdnFnzpjS0LZBdT69aSBndG2UM2/p5v2c9ewPTF28NYo5M8aUJOsIX0TWET52qCoT567nn5/9RkZWds78Uf1b8v/O6GSjxxhTjKwjvDFliIgwqn8rPr5hAC38RomxKlFjYpMFQGMCdG1Wk89uPYE/HWtVosbEMguAxgRRo1Iyz1/Wk3+c24UKie5rkpqeyU3vLOL+ydZK1JhYEHEAFJFkETlWRE7wXpNLMmPGRFuoKtGJc9dzzrgfWLHNOs4bU55FMhLMmSIyBdgHzAbe8173ichnInJWCefRmKjyVYn6txL9ffsBzhk3mzdmr8UakhlTPoUNgCIyG7gBeBdoq6o1VbWZqtYEjgHeBq730hkTs2pUSua5S3vyyPCuVEp2X5uMzGz+PmU5Y8bPZ+eB9Cjn0BhTUGG7QYhIV1Vdku9GRI5V1aXFmrNywrpBxJ/VOw5w67s/s9xv7NB61Srw5EXdOKlDgyjmzJjyo8x3g/APfiJyUbA0InJhvAY/E5/aNqjGJzcN4JpBrXPm7TyQweg35vP3KcusgYwx5URBWoG+FmL+y8WREWPKk4pJifztzM5MGNOX+tUr5sx/Y/Y6zntuNiu3pUYxd8aYSETSCKaNiLQBEkSktW/a+zsFSCv5bBpTNp3Yvj7TbhvE0I65VZ8rtqVy9n9/4KWZa8iyh+0aU2blOxSaiGQDCkiQxduAB1U1bq8C7R6ggdxh1B6e+hvpmbnDqPVpVZsnL+pGy7pVw6xtTPwp8/cAAVQ1QVUTgVne//5/TeI5+Bnj4+sz+NktJ9C1ac2c+fPX7eFPz8zi7Z/WW3cJY8qYiO8Bqurg4tqpiFwqIrNEZJ+IHBCRBSJyk4gUaGQaERkvIhrmb0Vp5MMYn3YNqzPpxgHcfko7EhNcpcmhjCz+9slSRr8xn2377I6BMWVFfv0AJ4lIn3zS9BGRSZHuUESew/Uf7A3MAr4G2gPjgI9EpDBD7s8G3gzy90kp58MYkhMTuP2U9nxy4wDaNqiWM3/m7ykMe/p7Pv1ls10NGlMG5NcP8DTgYaAGMBNYCaQC1XHB4iRgL3Cfqn6d785ELgA+wt07PFFVV3nzGwLTgU7A7ar6TESZFxkPXAlcparjI1mnuPNh9wBNOGlHsnjyy5W8Nnst/l+1M7s25h/ndqFutYqhVzYmhpX5e4Cq+pWq9gEuAzYC/YALgb7ABmCkqvaLJPh57vVe7/YFHW8/23EjzgDcUwpVkGUlHybGVUpO5L6zOvPuNcfTrHblnPlTl2zl1P98z/9+3WJXg8ZESak9EFdEmuGCaAZQS1UPB0mzCWgKDFTVHyPY5ngKeAVY3PmwK0ATqQPpmfzzs+W8N3/jUfNP6dSQh4cfS8MalaKUM2NKX1m4AkzKL4GItMgvjapuiGBfPbzXZcGCjmc+LvD0APINgH6GiMhxQDVgO/AD8LWqZgdJW5L5MCakahWTeOyC4/hT18bc+/FitngNYr75bTs/rd3F/Wd25qLezRAJ1uPIGFPc8g2AwDpcP0AI3hdQgUgajPjGjVofJo0vkLYOkyaYUUHmLReRkUHGMi3JfBiTr8Ht6/Pln0/k8WkreGuuO9RS0zK56+PFTFm8hUeGd6W53+OXjDElI5J7XIuBVcB9QEsgOeCvQoT78jWHOxgmzQHvtXqE2/wFuBXo4m2/CXAW8CvQGfhGRJoWdz5E5Fqvy8SClJSUCLNqTK7qlZL553ldee/a42lZNzfYzVq1k2FPf8+EOevItlFkjClRkXSE745r+FIHV7X4OTASqKCqWaoa6ci/vqvHYvtWq+rTqvpfVV2uqgdVdauqTsU10pkLNCC3wUux5UNVX1bV3qrau379+oXdjDEc36Yu0247kWsGtcbrNsihjCwe+HQZI16aw6rtNqaoMSUlolaOqrpUVf+KqxL8N+4qa6uI9CzAvnzf5Gph0viWFelbr6oZwKPe5BnRyocxkahcwQ2s/dENR/cbXLB+D2c8O4snv1xpT5gwpgQUtJl/O2Aw0B/4GdhTgHXXea8tw6RpHpC2KHyjwARWgZZ2PoyJSM8WtZl66wnccnJbkrzLwSNZyrjpqxn29PfMWmXV7cYUp0ieBlHHGx5sHjAZd3/sRFUdoqprC7Cvn73XLiJSOUSaPgFpi6Ku93ogYH5p58OYiFVMSuSO0zow9dZB9GpZO2f++l2HuOK1edz23s+kpNrT540pDpFcAW4BbsYFv5tw99baisjJvr9IdqSqG4FFuEYzeR6uKyKDgWa40VnmRJb9sEZ4r/OjnA9jCqxDo+p8eF1/Hj2/KzUq5TbW/vSXLQx9agbv/LTBGskYU0SRPA5pHeEbjKiqtoloZyIXAh/igssgVV3tzW+AG4KsMwFDkInIo8Bw4BNVvddvfndcoPrCvyGOiCThWoY+gQvwp6vql0XNRyjWEd6UtJTUdB6eupzJv2w5an6vlrV5ZHhXOjSKtNG0MWVHWegIX2ojweTsUOR53HBjacA3wBFgKG680cnAhQEBbTxutJc3VXW03/zzcINd7wZ+Bzbhui10xXWHyAbuVdV/FUc+QrEAaErLrFUp3Dd5Ket3HcqZl5ggXNm/Fbef2o4alZKjmDtjCqYsBMBSH+tSVW/EjS26CNegZhiwGlfNekEBulX8CjyDG6C7BXC2t71DwBtA31DBr5jzYUypGNSuPl/efiI3D2lLcqJrJJOVrbw+ey0nPzmTjxdusmpRYwqg1K8AY41dAZpoWLU9lQc+XcacP3YdNb9Xy9r849wudGlSM8SaxpQNcXkFaIwpunYNq/PONf347yU9aOQ3iPbC9Xs4+78/cP/kpew9lBHFHBpT9lkANKacEhHO7taEb+8YzA0nHZNTLZqtMHHuek5+aibvzbPWosaEYgHQmHKuasUk7j69I9NuP5FB7erlzN99MIN7Ji3h3OdmM2/t7ijm0JiyyQKgMTHimPrVmDCmLy9e3oumtXLHeFiyeR8jXprDjW8vZOPuQ2G2YEx8sQBoTAwREU4/thHf/GUwt57clopJuV/xz5dsY+hTM3n0i99ITTsSxVwaUzZYADQmBlWukMhfTuvAd3eexDndmuTMz8jK5qWZfzDkSTeaTJbdHzRxzAKgMTGsaa3KPHtJDz6+YQDdm9fKmb/zQAb/75MlnPnsLGav3hnFHBoTPRYAjYkDvVrWZtINA3j64u40rpnbbWLFtlQue/Unxoyfz8pt9vQvE1+sI3wRWUd4U94czsjilVl/8MKMNRz2e85ggsAFPZvx51Pb06RWqAelGFM8ykJHeAuARWQB0JRX2/al8cSXK5n08yb8TwMVkxIYPbAVNw5uS80qNr6oKRkWAGOABUBT3i3fsp/Hp61g5u9HP3C3ZuVkbhpyDKP6t6JScmKUcmdilQXAGGAB0MSKH1fv5NEvVrBk876j5jepWYm/nNaB4T2akug9qd6YorIAGAMsAJpYkp2tfL50K098ufKoxy4BdGxUnb+c2p5TOzdExAKhKRoLgDHAAqCJRRmZ2bw3fwPPfLOKXQePHlT7uGY1+cup7Rncvr4FQlNoFgBjgAVAE8sOpGfy6qw/ePn7PziUcfQjMnu1rM0dp7VnwDH1QqxtTGgWAGOABUATD3YeSOfFGWuYOHc96ZnZRy3r36Yud5zWnt6t6kQpd6Y8sgAYAywAmniyfX8az01fzbvzNnAk6+hzx+D29bnjtPYc16xWiLWNyWUBMAZYADTxaNOeQ4z7bjUfLtyUZzzRUzo15NahbS0QmrAsAMYAC4Amnq3beZBnv13FJ79sJvBUclKH+txycjt6tawdncyZMs0CYAywAGgMrN6Ryn++WcXUxVvzLBvYti63nNyO49vUjULOTFllATAGWAA0JtfKbamMm76azxZvyXNF2LdVHW4Z2pYT2taz7hPGAmAssABoTF5rUg7w3PTVfPrLljz3CLs3r8WtQ9sypEMDC4RxzAJgDLAAaExo63cd5IUZa/ho4SYyAwJhp8Y1uH5wG87s2pikRHsyW7yxABgDLAAak7/New/z4ow1vD9/IxlZR/cjbFa7Mlef0JoRfZpTpUJSlHJoSpsFwBhgAdCYyG3fn8ZLM//g3XkbjnoWIUDtKslcOaAVo/q3ok7VClHKoSktFgBjgAVAYwpuz8EMJsxZz5tz1rE7YKzRysmJXNynOWNPaE3zOlWik0FT4iwAxgALgMYU3uGMLD5cuJGXv/+DTXsOH7UsMUE467jGXDOoDcc2rRmlHJqSYgEwBlgANKboMrOymbpkKy/O/IPftu7Ps7xv6zqMGdiaUzs3tGcSxggLgDHAAqAxxUdVmbVqJy/OXMOPa3blWd68TmVGD2jNiN7NqF4pOQo5NMXFAmAMsABoTMlYvGkvr/2wlqmLt+bpQlGtYhIjejfnqoGt7D5hOWUBMAZYADSmZG3bl8aEOet4Z94G9h46ctSyBIFTOzdk7Alt6NOqtnWsL0csAMYAC4DGlI7DGVl8vGgTr89eyx8pB/Ms79KkBlcc35JzuzelcoXEKOTQFIQFwBhgAdCY0pWdrcxclcLrP6xl1qqdeZbXqJTEhb2ac/nxLWhTv1oUcmgiYQEwBlgANCZ6ft+eyhuz1zJp0eY8T6oHGNSuHlcc35Khnaz1aFljATAGWAA0Jvr2HsrgwwWbeOun9azfdSjP8qa1KnNpvxZc3Kc59apVjEIOTSALgDHAAqAxZUd2tvL9qhTemrueb1fsyPNIpuRE4U/HNuaSvi04vk0dazQTRRYAY4AFQGPKpo27D/HOvA28P39jnuHWAFrXq8rFfZpzQc9m1K9uV4WlzQJgDLAAaEzZlnYkiy+WbmXCnPX8vGFvnuVJCcKpnRsysm8LTmhbz+4VlhILgDHAAqAx5cfSzft4b/4GPv15C6npmXmWN61VmRG9mzOiTzMa16wchRzGDwuAMcACoDHlz6GMTKYu3sr78zeyYP2ePMsTBAa3r8/FfZpzcseGVEiyB/YWNwuAMcACoDHl26rtqbw3fyOTFm1iT8BIM+CeU3hOtyZc0KsZXZvWtIYzxcQCYAywAGhMbEjPzOKrZdt5b/4GZq/OOxA3QLsG1bigVzOG92hKwxqVSjmHscUCYAywAGhM7Nmw6xAfLtzIpEWb2bz3cJ7lCQIntKvPBT2bMqxLIyol29BrBWUBMAZYADQmdmVnK3PX7uLjhZv5YulWDmVk5UlTvWISZx7XmPN7NqN3y9okWCvSiMRtABSRS4EbgOOARGAF8AbwgqrmHc8o+DaSgROBM4CBQEugLpACzAHGqeqMEOuOB64Ms/mVqtoxknxYADQmPhxMz+SLpdv4eOEm5vwRvIq0Sc1KnN29Ced2a0qnxtXtfmEYcRkAReQ54EYgDfgWOAIMBaoDnwAXqWren1l5t3MK8LU3uQ1YCBwEOgPHevMfUtUHgqw7HhcAZwOrg2x+q6reG8n7sQBoTPzZtOcQnyzazMeLNrEuyNBrAG0bVOPcbk04p3sTWtatWso5LPviLgCKyAXAR7iAdaKqrvLmNwSmA52A21X1mQi2dTIukD6jqrMCll0MvI27ujxZVacHLB+PC4BXqer4orwnC4DGxC9VZeH6PXy8yFWRBj6v0Kdb81qc260JZx3XmAbWeAaIzwC4AOgFXKmqEwKWDQZm4IJj00irQsPs61VgLPC6qo4NWDYeC4DGmGKUkZnNrFUpfPrLFr5evp3DR/JWZCUI9D+mLud0a8KwLo2oVaVCFHJaNpSFAJhUWjsSkWa44JcBfBi4XFVnishmoClwPPBjEXf5s/farIjbMcaYfFVISmBop4YM7dSQQxmZfL18O1N+3cKMlSlkZrsLjWyF2at3MXv1Lv72yVL6H1OXM7s25rQujahTNX6DYbSUWgAEenivy1Q1b7tiZz4uAPag6AGwnfe6NUyaISJyHFAN2A78AHxd1KtPY0x8q1IhiXO7N+Xc7k3ZczCDL5Zu43+/buantbtznlCRma3MWrWTWat28rfJS+nfpi5/6tqIYV0a2SObSklpBsDW3uv6MGk2BKQtFBFpBIz2Jj8Ok3RUkHnLRWSkqi4pSh6MMQagdtUKXNqvBZf2a8G2fWl8tngLU5dsPWpg7qxs5YfVO/lh9U7un7yUfq3rckbXRgw7thENqts9w5JSmgGwmvd6MEyaA95r9cLuRESSgLeAmsC3qjolSLJfcK1Gv8UF5BpAT+BhoBvwjYj0VNXNhc2HMcYEalSzElcPasPVg9qwee9hpi3dxudLtrLQbzzSbIU5f+xizh+7eOB/y+jTqg7DujTitM4NaV6nShRzH3tKMwD6OsSUdKubF3HdKjYClwdLoKpPB8w6CEwVka+Bmbh7kPcCNwdbX0SuBa4FaNGiRfHk2hgTV5rWqszYE1oz9oTWbNuXxhdLt/LFkm3MX59bTaoK89buZt7a3Tz02XI6NqrOaV4w7NKkhvUzLKLSDICp3mu1MGl8y1LDpAlJRJ7BtfzcBgxV1W0FWV9VM0TkUeBTXAf7UOleBl4G1wq0MHk1xhifRjUrcdXA1lw1sDXb96fx5bJtTF28lXnrdh/1VPsV21JZsS2VZ79dRZOalTi1c0NO7dyIfm3qkJxoT6woqNIMgOu815Zh0jQPSBsxEXkKuBU3EsxQXx/DQljhvTYt5PrGGFNoDWtUYlT/Vozq34odqWl8vXw7Xy/fzo+rd5GRlds+b8u+NN6cs54356ynRqUkhnRswGmdGzG4Q32qVSzNU3v5VWr9AEWkOa6RSwZQK1hLUBHZiOu2cIKqzi7Atv8F/BXYhQt+vxYhn/1xLVB3q2rd/NJbP0BjTGk4kJ7J97+n8PXy7Xz723b2p+V9oC9AhcQE+rWpw5AODTi5YwNa1Subo9CUhX6Apd0RfiGusUmxdYQXkceAu4E9uOD3cz6r5Le9/wC3A1+q6un5pbcAaIwpbUeyspm/djdfeVeHwZ5Y4dO6XlWGdGjAkI716du6DhWTysaTK+IxAF6I6wS/DRikqqu9+Q1wQ6F1JmAoNO+e3HDgk8DxOUXkIeA+YC9wiqoujCAP3XFXmV/4jznqtR69FXgCSABOV9Uv89ueBUBjTDSpKsu37s+pKl22ZX/ItFUqJDLgmHqc3LEBJ3WoT5NalUsxp0eLuwAIICLP454EkQZ8Q+5g2DWAycCFAYFpPG7YsjdVdbTf/HNwjVUAFgDLQuxyhao+5rfeebhBt3cDvwObcN0uugJNgGzgXlX9VyTvxwKgMaYs2bL3MDNWpvDdih3MXr0z6JBsPh0bVWdIxwac1L4+PVrUpkJS6TWkicsACDmPQ7oJF3R8j0N6nSCPQwoTAEfjHqGUn5mqepLfeq2B24C+5D5CSXGBcBbwXCRXkj4WAI0xZVXakSzmrd3N9JU7mL5iR8gnVwBUrZDI8W3qMqhdPQa1r0+belVLtJtF3AbAWGIB0BhTXqzdeZDvVuxgxsod/PTH7qNalQZqUrMSg9rVZ1D7egw8ph61i3msUguAMcACoDGmPDqYnsns1TuZvjKF739PCduQRgS6Nq3prg7b1adnMVSXWgCMARYAjTHlnaqybtchfliVwverdjJnzS4OpAfvZgGuMU3f1nUYeEw9Tu3csFBdLcpCALTeksYYE+dEhNb1qtK6XlWu6N+KI1nZ/LpxL9+v2skPq1L4ZeNesv2ulQ5lZDFjZQozVqYgAlcPahO9zBeBBUBjjDFHSU5MoHerOvRuVYe/nNqefYePMGfNzpzHN23YnduYZmDbelHMadFYADTGGBNWzcrJnH5sY04/tjEAG3cfYvbqnfy8YS8dGhb64T1RZwHQGGNMgTSvU4WRfVswsm/5fhqODR9ujDEmLlkANMYYE5csABpjjIlLFgCNMcbEJQuAxhhj4pIFQGOMMXHJAqAxxpi4ZGOBFpGIpADrC7l6PWBnMWYn1ll5FYyVV+SsrAqmOMqrparWL47MFJYFwCgSkQXRHgy2PLHyKhgrr8hZWRVMrJSXVYEaY4yJSxYAjTHGxCULgNH1crQzUM5YeRWMlVfkrKwKJibKy+4BGmOMiUt2BWiMMSYuWQA0xhgTlywARoGIXCois0Rkn4gcEJEFInKTiMTk5yEiHUTkNhF5S0RWiEi2iKiIXBjBuoUqq/JYxiKSLCJDReQpEZkrIltFJENENovIRyJyUj7rx01Z+YjILSLygYj8JiK7ROSIiKSIyDcicrmISJh14668AonII953UUXkzjDpYrOsVNX+SvEPeA5Q4DDwGfAJsN+bNwlIjHYeS+A9P+29v8C/C0uirMprGQOn+JXNVi/v7wNL/Ob/w8rqqPxvAjKARcAU4D1gDpDtvYfJQIKVV9D30gfI9CurO+Pt2Ir6hxBPf8AFfie3dn7zGwLLvWW3RTufJfC+rwb+BYwAjgFm5BcAC1tW5bmMgZOBj4BBQZZd7J2sFBgS72Xll9cTgKpB5ncBtnnv4SorrzzvpSKwDNjsBaagATDWyyrqH0Q8/QELvA9+VJBlg/0OmDy/WGPpL8IAWKiyiuUyBl718v+alVVE5XW/9x7esfLKk9/HvfyeDYwPEwBjuqyi/kHEyx/QzPvQ04HKIdJs8tIMiHZ+S7gswgbAwpZVrJcxcJOX9y+trCIqr3u9/L9u5XVUPvvhahPe9qaDBsB4KKuycSMyPvTwXpep6uEQaeYHpI1XhS2rWC/jdt7rVr95VlZBiEhr4HpvcorforguLxGpBLwJ7AZuyyd5zJdVUjR3Hmdae6/hnhyxISBtvCpsWcVsGYtII2C0N/mx3yIrK0BErsJVrSXjrkAG4Fq5P6qqn/gljffyehjoAIxU1fye5hDzZWUBsPRU814PhklzwHutXsJ5KesKW1YxWcYikgS8BdQEvlVV/ysaKytnIHCl33Qm7h7gvwPSxW15icgA4HZgsqq+H8EqMV9WVgVaenz9kTSquSgfCltWsVrGLwJDgY3A5QHLrKwAVb1aVQWogmsB+jTwIDBXRJr4JY3L8hKRysAbuG4IN0a6mvcas2VlAbD0pHqv1cKk8S1LDZMmHhS2rGKujEXkGWAsrkn/UFXdFpDEysqPqh5W1eWq+ldcI5huwDi/JPFaXo8A7YG/qOrW/BJ7Yr6srAq09KzzXluGSdM8IG28Wue9FrSsCrtemSQiTwG3Aim44LcqSLJ13mtcl1UIbwBPAmeLSLKqHiF+y2s4rsP7lSJyZcCyjt7rDSJyFrBaVa8mDsrKAmDp+dl77SIilUO0juoTkDZeFbasYqaMReRfwF+AXcCpqro8RNK4L6sw9uLuBSYBdYDtxHd5JeAaCoXSxvurSeDXGgAABcZJREFU5U3HfllFu09KPP0BCykHnUNLoRxmkH9H+EKVVSyUMfCYl8/dQI+SOq5ioazyKZeTvPewB79ht6y88uR9PKE7wsd0WUW98OPpD7jQ74Nv6ze/AW5YIqUMDA9UCuUQSQAsVFmV9zIGHvI7afcqyeMqBspqEHAZUDHIsoHAGu89PGnlFbYcwwXAmC6rqBd+vP0Bz3sf/mFcB91JwD5v3ieUgQFiS+A99wTm+v35BsT93X9+cZVVeS1j4Bwvj4rrKDw+xN898V5WXt5Hk/tj4VvgbeB/fidYxQ3CnGc0kngsrzDlOJ4QATDWyyrqhR+Pf8ClwGwvEBzEVRfcRDmrOinA+z3J74QU8q84y6o8lrHfCT2/vxnxXlZevlsD/wCm47qIHAbScA0rPgLOK4n3XV7LK8z7CRsAY7msxMukMcYYE1esH6Axxpi4ZAHQGGNMXLIAaIwxJi5ZADTGGBOXLAAaY4yJSxYAjTHGxCULgMYYY+KSBUBjSomInCQim4q4jRYickBEEospTwdEpE1xbMuY8sYCoDEREpEvReQfQeafKyLbvCe3lyhV3aCq1VQ1y9v3DBG5ugjbq6aqfxRfDsMTkZdF5NrS2p8x4VgANCZy44ErREQC5l8BvK2qmaWfpXLndODzaGfCGLAAaExBTMY9V26Qb4aI1AbOAiZ40xVF5EkR2SAi20XkRRGpHGxjItLJu4LbKyLLROQcv2WVReQpEVkvIvtE5AdvXisRURFJEpGHvbyM86oyx4nIc96DdP33M0VEbg+RBxWRtt7/4731p4pIqoj8JCLHhFjPl4+rRGSjiOwRketFpI+ILPbe07iAdY4D9qrqJhFpKyIzvfe2U0Tez7f0jSlmFgCNiZC6B3t+AIzymz0CWKGqv3rTjwPtge5AW6Ap8EDgtkQkGTdC/le4R8TcArwtIh28JE8CvYABuKB7F+6J3v75+RswC7jZq8q8GXgTuEREErz91AOGAu9G+DYvAf4O1AZWAw/nk74f0A64GHga+BtwCtAFGCEig/3SngFM9f5/yHvvtYFmwH8jzJ8xxcYCoDEF8yZwkd9V3ShvHl7V6DXAn1V1t6qmAo8AI4Ns53igGvCYqmao6ne4R/f4gtcY3PPSNqtqlqr+qKrp+WVOVefhHjkz1Js1Evf0iO0Rvr9JqjrPq859GxfIw3lIVdNU9SvcaP/vquoOVd2MC849/NKeSW715xGgJdDEW/+HCPNnTLGxAGhMAXgn6hTgXK/1ZB/gHW9xfaAKsNCrAtwLTPPmB2oCbFRV/6u69bgrxnpAJdwDXQvjTeBy7//LgYkFWHeb3/+HcEE6HP/AejjIdDUAEakFdAR+9JbdBQgwz6v+HVOAPBpTLEq81ZoxMWgC7sqvA/CV39XVTtxJv4t3BRTOFqC5iCT4BcEWuIcE78Q91+4Y4NcQ6/sEe57ZW8BSEekGdMLdu4y2YcC3vtarqroNd7WMiJwAfCMi36vq6ijm0cQZuwI0puAm4O5zXYNX/QngBbJXgP+ISAMAEWkqIsOCbOMnXJXhXSKSLCInAWcD73nbeR34t4g0EZFEEekvIhWDbGc7cFQ/PlXdhHui/ETgY+/eZbT5V38iIheJSDNvcg8ukGdFI2MmflkANKaAVHUdriqvKvC/gMV34xqPzBWR/cA3/7+9O1RtIAjiMP7Nm9RGRDYyLpCYquq8Qkx9niEhRMXkcQJ1NXV9g4pQVTMRe4HjqKkoW26/nzyOZTg4/szsHkfpFIdrfANPwIrS8R2BdWa+d7e8AG+UIPukHK756X3dAc/dKcx97/oZmPK78eef6PZGF5Rx8N0jcImIL8oz3GTmR4361C7/CC+NUETMKaPQh8E+Y41aZsAhM2c165CG7AClkek+sdgAp9rh17OtXYA0ZAcojUhETIBXyuGZZWZeK5ck/VsGoCSpSY5AJUlNMgAlSU0yACVJTTIAJUlNMgAlSU26AW9LFdS6mnPgAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"## Now defining the Tsiolkovski equation 2.b\n",
"m_0 = 0.25 #kg\n",
"u = 250 #m/s\n",
"time = np.linspace(0,4,1000)\n",
"dt = time[1] - time[0]\n",
"m_Tsiolkovsky = np.zeros(len(time))\n",
"m_Tsiolkovsky[0] = 0.25\n",
"for i in range(1, len(m_Tsiolkovsky)):\n",
" m_Tsiolkovsky[i] = m_Tsiolkovsky[i-1] - 0.05*dt\n",
"v_Tsiolkovsky = -u*np.log(m_Tsiolkovsky / m_0)\n",
"##Checking Tsiolkovsky Equation results\n",
"plt.plot(v_Tsiolkovsky,m_Tsiolkovsky/m_0)\n",
"plt.xlabel('Velocity in m/s', fontsize = 12)\n",
"plt.ylabel('M(t) / M(0)', fontsize = 12)\n",
"plt.title('Tsiolkovkys Relation for Mass Ratio and Velocity', fontsize = 16);"
]
},
{
"cell_type": "code",
"execution_count": 263,
"metadata": {},
"outputs": [],
"source": [
"N = int(4/dt)\n",
"#Setting up Explicit numerical solution data set using the rk-2 step method\n",
"num_sol_simple_explicit = np.zeros([N,3]) \n",
" #Setting intial conditions\n",
"y0_simple = 0 #m\n",
"v0_simple = 0 #m/s\n",
"m0_simple = 0.25 #kg\n",
"num_sol_simple_explicit[0,0] = y0_simple\n",
"num_sol_simple_explicit[0,1] = v0_simple\n",
"num_sol_simple_explicit[0,2] = m0_simple \n",
"for i in range(N-1):\n",
" num_sol_simple_explicit[i+1] = rk2_step(num_sol_simple_explicit[i],simplerocket, dt)\n",
"# Now, num_sol_simple_explicit stores the numerical solution using the rk2 integration method.\n"
]
},
{
"cell_type": "code",
"execution_count": 264,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Comparing this solution to Tsiolkovskys equation\n",
"velocity_rk2_simple = num_sol_simple_explicit[:,1]\n",
"mass_rk2_simple = num_sol_simple_explicit[:,2]\n",
"plt.plot(v_Tsiolkovsky,m_Tsiolkovsky/m_0, label = 'Tsiokolvskys Equation', linestyle = '-', color = 'r')\n",
"plt.plot(velocity_rk2_simple, mass_rk2_simple/m_0, label = 'RK2 Explicit Integration', linestyle = '--', color = 'k')\n",
"plt.xlabel('Velocity in m/s', fontsize = 12)\n",
"plt.ylabel('M(t) / M(0)', fontsize = 12)\n",
"plt.title('Comparing Explicit Integration and Tsikolvsky for Convergence', fontsize = 16);\n",
"plt.legend(fontsize = 8);"
]
},
{
"cell_type": "code",
"execution_count": 265,
"metadata": {},
"outputs": [],
"source": [
"N = int(4/dt)\n",
"#Setting up Implicit numerical solution data set using the heun step method\n",
"num_sol_simple_implicit = np.zeros([N,3]) \n",
" #Setting intial conditions\n",
"y0_simple = 0 #m\n",
"v0_simple = 0 #m/s\n",
"m0_simple = 0.25 #kg\n",
"num_sol_simple_implicit[0,0] = y0_simple\n",
"num_sol_simple_implicit[0,1] = v0_simple\n",
"num_sol_simple_implicit[0,2] = m0_simple \n",
"for i in range(N-1):\n",
" num_sol_simple_implicit[i+1] = heun_step(num_sol_simple_implicit[i],simplerocket, dt)\n",
"# Now, num_sol_simple_implicit stores the numerical solution using the heun step integration method."
]
},
{
"cell_type": "code",
"execution_count": 266,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Comparing this solution to Tsiolkovskys equation\n",
"velocity_heun_simple = num_sol_simple_implicit[:,1]\n",
"mass_heun_simple = num_sol_simple_implicit[:,2]\n",
"plt.plot(v_Tsiolkovsky,m_Tsiolkovsky/m_0, label = 'Tsiokolvskys Equation', linestyle = '-', color = 'r')\n",
"plt.plot(velocity_heun_simple, mass_heun_simple/m_0, label = 'Heun Implicit Integration', linestyle = ':', color = 'b')\n",
"plt.xlabel('Velocity in m/s', fontsize = 12)\n",
"plt.ylabel('M(t) / M(0)', fontsize = 12)\n",
"plt.title('Comparing Implicit Integration and Tsikolvsky for Convergence', fontsize = 16);\n",
"plt.legend(fontsize = 10);"
]
},
{
"cell_type": "code",
"execution_count": 267,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Now plotting all three charts together to solidify the convergence to the same solution\n",
"plt.figure(figsize=(10,10))\n",
"plt.plot(v_Tsiolkovsky,m_Tsiolkovsky/m_0, label = 'Tsiokolvskys Equation', linestyle = '-', color = 'r')\n",
"plt.plot(velocity_rk2_simple, mass_rk2_simple/m_0, label = 'RK2 Explicit Integration', linestyle = '--', color = 'k')\n",
"plt.plot(velocity_heun_simple, mass_heun_simple/m_0, label = 'Heun Implicit Integration', linestyle = ':', color = 'b')\n",
"plt.xlabel('Velocity in m/s', fontsize = 12)\n",
"plt.ylabel('M(t) / M(0)', fontsize = 12)\n",
"plt.title('Comparing Both Integration Methods to Tsikolvsky for Convergence', fontsize = 16);\n",
"plt.legend(fontsize = 10);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, we can clearly see that both integration solutions converge to the Tsiolkovsky equation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. You should have a converged solution for integrating `simplerocket`. Now, create a more relastic function, `rocket` that incorporates gravity and drag and returns the velocity, $v$, the acceleration, $a$, and the mass rate change $\\frac{dm}{dt}$, as a function of the $state = [position,~velocity,~mass] = [y,~v,~m]$ using eqn (1). Where the mass rate change $\\frac{dm}{dt}$ and the propellent speed $u$ are constants. The average velocity of gun powder propellent used in firework rockets is $u=250$ m/s [3,4]. \n",
"\n",
"$\\frac{d~state}{dt} = f(state)$\n",
"\n",
"$\\left[\\begin{array}{c} v\\\\a\\\\ \\frac{dm}{dt} \\end{array}\\right] = \n",
"\\left[\\begin{array}{c} v\\\\ \\frac{u}{m}\\frac{dm}{dt}-g-\\frac{c}{m}v^2 \\\\ \\frac{dm}{dt} \\end{array}\\right]$\n",
"\n",
"Use [two integration methods](../notebooks/03_Get_Oscillations.ipynb) to integrate the `rocket` function, one explicit method and one implicit method. Demonstrate that the solutions converge to equation (2.b) the Tsiolkovsky equation. Use an initial state of y=0 m, v=0 m/s, and m=0.25 kg. \n",
"\n",
"Integrate the function until mass, $m_{f}=0.05~kg$, using a mass rate change of $\\frac{dm}{dt}=0.05$ kg/s, . \n",
"\n",
"Compare solutions between the `simplerocket` and `rocket` integration, what is the height reached when the mass reaches $m_{f} = 0.05~kg?$\n"
]
},
{
"cell_type": "code",
"execution_count": 268,
"metadata": {},
"outputs": [],
"source": [
"def rocket(state,dmdt=0.05, u=250,c=0.18e-3):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, with drag, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" c : drag constant for a rocket set to 0.18e-3 kg/m\n",
" Returns\n",
" -------\n",
" derivs: array of three derivatives [v (u/m*dmdt-g-(c/m)*v^2) -dmdt]^T\n",
" '''\n",
" g = 9.81\n",
" dstate = np.array([state[1], ((u/state[2])*dmdt - g - (c/(state[2]))*state[1]**2),-dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 269,
"metadata": {},
"outputs": [],
"source": [
"N = int(4/dt)\n",
"#Setting up Explicit numerical solution data set using the rk-2 step method\n",
"num_sol_rocket_explicit = np.zeros([N,3]) \n",
" #Setting intial conditions\n",
"y0_rocket = 0 #m\n",
"v0_rocket = 0 #m/s\n",
"m0_rocket = 0.25 #kg\n",
"num_sol_rocket_explicit[0,0] = y0_rocket\n",
"num_sol_rocket_explicit[0,1] = v0_rocket\n",
"num_sol_rocket_explicit[0,2] = m0_rocket \n",
"for i in range(N-1):\n",
" num_sol_rocket_explicit[i+1] = rk2_step(num_sol_rocket_explicit[i],rocket, dt)\n",
"# Now, num_sol_rocket_explicit stores the numerical solution using the rk2 integration method for rocket."
]
},
{
"cell_type": "code",
"execution_count": 270,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Comparing this solution to Tsiolkovskys equation\n",
"velocity_rk2_rocket = num_sol_rocket_explicit[:,1]\n",
"mass_rk2_rocket = num_sol_rocket_explicit[:,2]\n",
"plt.plot(v_Tsiolkovsky,m_Tsiolkovsky/m_0, label = 'Tsiokolvskys Equation', linestyle = '-', color = 'r')\n",
"plt.plot(velocity_rk2_rocket, mass_rk2_rocket/m_0, label = 'RK2 Explicit Integration - Rocket', linestyle = '--', color = 'k')\n",
"plt.xlabel('Velocity in m/s', fontsize = 12)\n",
"plt.ylabel('M(t) / M(0)', fontsize = 12)\n",
"plt.title('Comparing Explicit Integration (Rocket) and Tsikolvsky for Convergence', fontsize = 16);\n",
"plt.legend(fontsize = 8);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see these solutions __do not__ converge because we have now taken into account drag and gravity into our equations which was neglecting when deriving Tsiolkovskys equation."
]
},
{
"cell_type": "code",
"execution_count": 271,
"metadata": {},
"outputs": [],
"source": [
"N = int(4/dt)\n",
"#Setting up Implicit numerical solution data set using the heun step method\n",
"num_sol_rocket_implicit = np.zeros([N,3]) \n",
" #Setting intial conditions\n",
"y0_rocket = 0 #m\n",
"v0_rocket = 0 #m/s\n",
"m0_rocket = 0.25 #kg\n",
"num_sol_rocket_implicit[0,0] = y0_rocket\n",
"num_sol_rocket_implicit[0,1] = v0_rocket\n",
"num_sol_rocket_implicit[0,2] = m0_rocket \n",
"for i in range(N-1):\n",
" num_sol_rocket_implicit[i+1] = heun_step(num_sol_rocket_implicit[i],rocket, dt)\n",
"# Now, num_sol_simple_implicit stores the numerical solution using the heun step integration method for rocket function."
]
},
{
"cell_type": "code",
"execution_count": 272,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Comparing this solution to Tsiolkovskys equation\n",
"velocity_heun_rocket = num_sol_rocket_implicit[:,1]\n",
"mass_heun_rocket = num_sol_rocket_implicit[:,2]\n",
"plt.plot(v_Tsiolkovsky,m_Tsiolkovsky/m_0, label = 'Tsiokolvskys Equation', linestyle = '-', color = 'r')\n",
"plt.plot(velocity_heun_rocket, mass_heun_rocket/m_0, label = 'Heun Implicit Integration - Rocket', linestyle = ':', color = 'b')\n",
"plt.xlabel('Velocity in m/s', fontsize = 12)\n",
"plt.ylabel('M(t) / M(0)', fontsize = 12)\n",
"plt.title('Comparing Implicit Integration (Rocket) and Tsikolvsky for Convergence', fontsize = 16);\n",
"plt.legend(fontsize = 10);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again, we can see that the solution using the heun integration step for this rocket taking into account both gravity and drag __does not__ converge with the simplified analysis of Tsiolkovskys equation. When we plot all three, we would expect both numerical integratiosn to follow the same trend (as they both make the same assumptions). This will be shown below. "
]
},
{
"cell_type": "code",
"execution_count": 273,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Now plotting all three charts together to solidify the convergence to the same solution for integration methods\n",
"plt.figure(figsize=(10,10))\n",
"plt.plot(v_Tsiolkovsky,m_Tsiolkovsky/m_0, label = 'Tsiokolvskys Equation', linestyle = '-', color = 'r')\n",
"plt.plot(velocity_rk2_rocket, mass_rk2_rocket/m_0, label = 'RK2 Explicit Integration - Rocket', linestyle = '--', color = 'k')\n",
"plt.plot(velocity_heun_rocket, mass_heun_rocket/m_0, label = 'Heun Implicit Integration - Rocket', linestyle = ':', color = 'b')\n",
"plt.xlabel('Velocity in m/s', fontsize = 12)\n",
"plt.ylabel('M(t) / M(0)', fontsize = 12)\n",
"plt.title('Comparing Both Integration Methods to Tsikolvsky for Convergence', fontsize = 16);\n",
"plt.legend(fontsize = 10);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The above plot shows that we have achieved the expected results in relation to the comparisons with Tsiolkovskys equation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__ANSWER__: Comparing the simplerocket case to the rocket case, we see that neglecting gravity and drag allows for the rocket to achieve much greater velocities as more fuel is used up in propulsion. As such, we expect that there will be a much lower final height associated to the case which takes into account gravity and drag. We can find the height associated to this condition where m_f = 0.05 by recalling that this is the stopping point for each of the solution sets. Thus, it is simply a matter of retrieving the last state vector associated to each solution. Since both of our integrations converged, it does not matter which one we pick to get these values. I will use the explicit Rk2 data sets from each solution for uniformity in obtaining the height data. "
]
},
{
"cell_type": "code",
"execution_count": 274,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The data supports the above statement, with the rocket function yielding an associated height of 424.53266 meters while simple rocket yielded a greater height of 596.03084 meters at m_f = 0.05.\n"
]
}
],
"source": [
"simple_height_mf = num_sol_simple_explicit[-1,0]\n",
"rocket_height_mf = num_sol_rocket_explicit[-1,0]\n",
"print('The data supports the above statement, with the rocket function yielding an associated height of {:.5f} meters while simple rocket yielded a greater height of {:.5f} meters at m_f = 0.05.'.format(rocket_height_mf, simple_height_mf))"
]
},
{
"cell_type": "code",
"execution_count": 275,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(6,6))\n",
"plt.plot(time[0:-1], num_sol_simple_explicit[:,0], label = 'simplerocket solution')\n",
"plt.plot(time[0:-1], num_sol_rocket_explicit[:,0], label = 'rocket solution')\n",
"plt.title('Comparision of simplerocket and rocket Functions for Height', fontsize = 14)\n",
"plt.xlabel('Time (s)', fontsize = 10)\n",
"plt.ylabel('Height (m)', fontsize = 10)\n",
"plt.legend(fontsize = 14);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Solidified above, we see the solution considering drag and gravity to have a much lower maximum height than the simple solution. Major divergence in the solutions begins at just under one second which also makes sense as the effects of drag and gravity would be expected to have a more profound effect later in the solution (since it is affecting the acceleration of the rocket and therefore would compound over time)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3. Solve for the mass change rate that results in detonation at a height of 300 meters. Create a function `f_dm` that returns the final height of the firework when it reaches $m_{f}=0.05~kg$. The inputs should be \n",
"\n",
"$f_{m}= f_{m}(\\frac{dm}{dt},~parameters)$\n",
"\n",
"where $\\frac{dm}{dt}$ is the variable we are using to find a root and $parameters$ are the known values, `m0=0.25, c=0.18e-3, u=250`. When $f_{m}(\\frac{dm}{dt}) = 0$, we have found the correct root. \n",
"\n",
"Plot the height as a function of time and use a star to denote detonation at the correct height with a `'*'`-marker\n",
"\n",
"Approach the solution in two steps, use the incremental search [`incsearch`](../notebooks/04_Getting_to_the_root.ipynb) with 5-10 sub-intervals _we want to limit the number of times we call the function_. Then, use the modified secant method to find the true root of the function.\n",
"\n",
"a. Use the incremental search to find the two closest mass change rates within the interval $\\frac{dm}{dt}=0.05-0.4~kg/s.$\n",
"\n",
"b. Use the modified secant method to find the root of the function $f_{m}$.\n",
"\n",
"c. Plot your solution for the height as a function of time and indicate the detonation with a `*`-marker."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 3 Part A"
]
},
{
"cell_type": "code",
"execution_count": 276,
"metadata": {},
"outputs": [],
"source": [
"def f_m(dmdt,m0=0.25, c=0.18e-3, u=250, height_desired = 300):\n",
" ''' define a function f_m(dmdt) that returns \n",
" height_desired-height_predicted[-1]\n",
" here, the time span is based upon the value of dmdt\n",
" \n",
" arguments:\n",
" ---------\n",
" dmdt: the unknown mass change rate in kg/s\n",
" m0: the known initial mass\n",
" c: the known drag in kg/m\n",
" u: the known speed of the propellent\n",
" \n",
" returns:\n",
" --------\n",
" error: the difference between height_desired and height_predicted[-1]\n",
" when f_m(dmdt)= 0, the correct mass change rate was chosen\n",
" '''\n",
" mdif = m0 - 0.05\n",
" seconds = mdif/dmdt\n",
" times = np.linspace(0,seconds, 1000)\n",
" dt = times[1] - times[0]\n",
" N = int(seconds/dt)\n",
" #Setting up Explicit numerical solution data set using the rk-2 step method\n",
" num_sol_rocket_explicit_temp = np.zeros([N,3]) \n",
" #Setting intial conditions\n",
" y0_rocket = 0 #m\n",
" v0_rocket = 0 #m/s\n",
" m0_rocket = 0.25 #kg\n",
" num_sol_rocket_explicit_temp[0,0] = y0_rocket\n",
" num_sol_rocket_explicit_temp[0,1] = v0_rocket\n",
" num_sol_rocket_explicit_temp[0,2] = m0_rocket \n",
" for i in range(N-1):\n",
" num_sol_rocket_explicit_temp[i+1] = rk2_step(num_sol_rocket_explicit_temp[i],lambda state: rocket(state, dmdt = dmdt,u=250,c=0.18e-3) , dt)\n",
" # Now, num_sol_rocket_explicit_temp stores the numerical solution using the rk2 integration method for rocket.\n",
" error = height_desired - num_sol_rocket_explicit_temp[-1,0]\n",
" return error\n"
]
},
{
"cell_type": "code",
"execution_count": 277,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"229.25528480165963"
]
},
"execution_count": 277,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"##Checking function works b using parameters in the sample: should yield -124\n",
"f_m(0.4)\n",
"##Function appears to be working appropriately."
]
},
{
"cell_type": "code",
"execution_count": 278,
"metadata": {},
"outputs": [],
"source": [
"##Importing the incsearch function from notebook 4\n",
"def incsearch(func,xmin,xmax,ns=50):\n",
" '''incsearch: incremental search root locator\n",
" xb = incsearch(func,xmin,xmax,ns):\n",
" finds brackets of x that contain sign changes\n",
" of a function on an interval\n",
" arguments:\n",
" ---------\n",
" func = name of function\n",
" xmin, xmax = endpoints of interval\n",
" ns = number of subintervals (default = 50)\n",
" returns:\n",
" ---------\n",
" xb(k,1) is the lower bound of the kth sign change\n",
" xb(k,2) is the upper bound of the kth sign change\n",
" If no brackets found, xb = [].'''\n",
" x = np.linspace(xmin,xmax,ns)\n",
" f = np.zeros(ns)\n",
" for i in range(ns):\n",
" f[i] = func(x[i])\n",
" sign_f = np.sign(f)\n",
" delta_sign_f = sign_f[1:]-sign_f[0:-1]\n",
" i_zeros = np.nonzero(delta_sign_f!=0)\n",
" nb = len(i_zeros[0])\n",
" xb = np.block([[ x[i_zeros[0]+1]],[x[i_zeros[0]] ]] )\n",
"\n",
" \n",
" if nb==0:\n",
" print('no brackets found\\n')\n",
" print('check interval or increase ns\\n')\n",
" else:\n",
" print('number of brackets: {}\\n'.format(nb))\n",
" return xb"
]
},
{
"cell_type": "code",
"execution_count": 279,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n",
"[[0.08888889]\n",
" [0.05 ]]\n"
]
}
],
"source": [
"##Using incsearch function to determine the range of dmdt that yields the closest response to zero between\n",
"## 0.05 and 0.4 kg/s \n",
"two_closest = incsearch(f_m, 0.05, 0.4, ns = 10) \n",
"print(two_closest)"
]
},
{
"cell_type": "code",
"execution_count": 286,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using the incsearch function, we find that the mass change rate to achieve the desired detonation height is between [0.05] and [0.08888889] kg/s, respectively.\n"
]
}
],
"source": [
"print('Using the incsearch function, we find that the mass change rate to achieve the desired detonation height is between {} and {} kg/s, respectively.'.format(two_closest[1\n",
"], two_closest[0]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 3 Part B"
]
},
{
"cell_type": "code",
"execution_count": 196,
"metadata": {},
"outputs": [],
"source": [
"## Importing the modified secant function to use for this part of the problem.\n",
"def mod_secant(func,dx,x0,es=0.0001,maxit=50):\n",
" '''mod_secant: Modified secant root location zeroes\n",
" root,[fx,ea,iter]=mod_secant(func,dfunc,xr,es,maxit,p1,p2,...):\n",
" uses modified secant method to find the root of func\n",
" arguments:\n",
" ----------\n",
" func = name of function\n",
" dx = perturbation fraction\n",
" xr = initial guess\n",
" es = desired relative error (default = 0.0001 )\n",
" maxit = maximum allowable iterations (default = 50)\n",
" p1,p2,... = additional parameters used by function\n",
" returns:\n",
" --------\n",
" root = real root\n",
" fx = func evaluated at root\n",
" ea = approximate relative error ( )\n",
" iter = number of iterations'''\n",
"\n",
" iter = 0;\n",
" xr=x0\n",
" for iter in range(0,maxit):\n",
" xrold = xr;\n",
" dfunc=(func(xr+dx)-func(xr))/dx;\n",
" xr = xr - func(xr)/dfunc;\n",
" if xr != 0:\n",
" ea = abs((xr - xrold)/xr) * 100;\n",
" else:\n",
" ea = abs((xr - xrold)/1) * 100;\n",
" if ea <= es:\n",
" break\n",
" return xr,[func(xr),ea,iter]"
]
},
{
"cell_type": "code",
"execution_count": 198,
"metadata": {},
"outputs": [],
"source": [
"## Using modified secant function with a guess that is about close to the range derived in the previous problem.\n",
"dmdt_found_secant, extra = mod_secant(lambda x: f_m(x), 0.00001, 0.1)"
]
},
{
"cell_type": "code",
"execution_count": 243,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The modified secant function yields a value for dmdt of 0.07890353 kg/s with an approximate error of 1.46088e-09 after 6 iterations.\n",
"This is effectively the root of the f_m function.\n"
]
}
],
"source": [
"print('The modified secant function yields a value for dmdt of {:.8f} kg/s with an approximate error of {:.5e} after {} iterations.'.format(dmdt_found_secant, extra[1], extra[2]))\n",
"print('This is effectively the root of the f_m function.')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 3 Part C"
]
},
{
"cell_type": "code",
"execution_count": 244,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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B25yL+yLNjeTcwV0rfxF3Pufi/hc+xyWPwdsqrm1L4LL93n9c8jkTd03f35MmzPt6IL0qfA/fe/spbnTPhBBlYnDJeZq3/S7v76dwNRG+7a7F1fLkEdDTCZfgPYI7h3O96SMU7VHie+5Xh4n3pIBlp+DaJGThLn/cFOb1CPn+EdSrwlt2ODDFe27Z3rlxRpjPhbig5eMo4TPqYH+I90SNqVAi8hLuy6yhhr/MYUpBRI7G/fK7VFUnRDseY0z1ZpcqTLnzRmSrj/s1nYDrwnUd8LQlDWUjIu1xDQln4mopjsANdLUa+DCKoRljaghLHExF2IOrTj8UVyW/Gvfl9nQ0g6omsnDtTC7FXQ75A9dW4k51bRGMMaZC2aUKY4wxxkTMumMaY4wxJmKWOBhjjDEmYtbGIQKNGzfWdu3aRTsMY4wxptL88ssv21S1SfBySxwi0K5dO+bMmVPyhsYYY0w1ISJrQy23SxXGGGOMiZglDsYYY4yJmCUOxhhjjImYJQ7GGGOMiZg1jiyDgoICtm3bxs6dO8nPL8tNF40x5SE2NpYGDRrQuHFjYmLsd5ExFaFSEwcRuRE4AegKNAWScXeMS8PdUWyihhnKUkSGAn/D3ZI2FncnvzeB0aoa9nbCpS0XiQ0bNiAitGvXjvj4eESkLLszxpSBqpKbm8uWLVvYsGEDbdu2jXZIxlSO7dth2DCYOBEaNarww1V2Sn4H7tamWbj7qH+Iuz3xKbjbIE8Wkf1i8u6sOBFIxd3c50vcvdFH4e4LHxvqYKUtF6k9e/bQqlUrEhISLGkwJspEhISEBFq1asWePXuiHY4xlWfcOPj8c3jrrUo5XGUnDhcBh6hqL1U9W1UvUtW+uBqILcA5wGWBBURkMHA9sBnopqpnqeogoCOwBBgE3BB8oNKWO1Blqg7dvh3OOMNNjTHlwi5RmBpFFZ57zv393HNuvoJV6n+Yqn6nqvv9FFDVRcBL3uypQavv8qZ3qOqKgDJbcJcgAO4MUVNR2nKVp5KzRGOMMdXMzJmwa5f7e+dO+O67Cj9kVUrN87xptm+BiLQGegM5wPvBBVR1BpAONAf6lLVcpYpClniwmThxIqeddlq0wzDGmKrr+efBd2luz57C75UKVCUSBxFpD1znzX4csKqnN12kqllhis8O2rYs5SpPJWSJ7dq1o06dOtSrV48GDRpw7LHH8sorr1BQEFmb0G+++YbWrVuXe1yhrFmzBhEhLy/Pv2zYsGF88cUXlXL8QCeddBJjxowpdfk1a9Zw8sknk5iYSOfOnZk2bVo5Ruc8//zzdOjQgeTkZFq2bMktt9xS5LUrKYZJkyaRkpJCUlIS5557Ljt27Ah7rHbt2pGQkMC2bduKLO/Rowciwpo1a0qMtzLPJWOqrXPOAZGij6lTC394qrr54G3OOadcw4hK4iAiV4jIOBGZKCIzgOVAa+BxVZ0csGl7bxpyvGzPuqBty1Ku8lRSlvjxxx+ze/du1q5dy5133smTTz7JVVddVSHHMs7FF19Mz5492b59O48++ihDhgxh69at5XqMs88+m7lz55KRkcHChQtJS0vjxRdfjCiGRYsWce211zJhwgS2bNlCYmIi119/fbHHa9++Pe+8845/fsGCBWRlhcvJy19gUmRMjfXYY9C2LdSuXbgsJ6foNoHztWtDSoorV55UtdIfwBhAAx65wN1A7aDt7vbWv13Mvh71tnm1rOWC1l8DzAHmtG3bVkNZvHhxyOX7GThQ1eWChY+EhOLnwZUrg5SUFP3yyy+LLPvpp59URHTBggWqqpqdna233nqrtmnTRps2barXXnut7t27VzMzM7V27doqIpqUlKRJSUmanp6u2dnZevPNN2uLFi20RYsWevPNN2t2draqqk6fPl1btWqlzzzzjDZp0kSbN2+ub7zxhv/Yn3zyifbo0UPr1aunrVu31vvvv9+/rk2bNgr4jzVr1ix988039bjjjvNv8/3332tqaqomJydramqqfv/99/51/fr103vvvVePPfZYrVu3rp566qm6devWkK/Ljh07dMCAAdq4cWNt0KCBDhgwQNevX6+qqnfffbfGxMRorVq1NCkpSUeMGLFf+TPPPFNffPHFIsu6du2qkydP1mXLlmlCQoJmZGT41x1//PE6evToYt+rsti2bZv2799f//a3v6mqlhjDXXfdpRdffLF/3cqVKzU+Pr7I9oFSUlL04Ycf1tTUVP+yW2+9VR955BEFdPXq1ap64OdSfn6+Pv7449qhQwdt2LChnn/++bp9+3ZVVV29erUCOmbMGG3Tpo2ecMIJmpWVpcOGDdOGDRtq/fr1NTU1VTdv3hwy5oj/N4052GRmql5wgWpi4v7fGYGPxETVCy9025cSMEdDfD9GpcZBVa9WVQESgS7A88ADwI8i0jJgU18fxwNtAFDacoExvqaqqaqa2qTJfncVPTBVJUsEjjnmGFq3bs3MmTMBuOOOO1i+fDnz5s1j5cqVpKen89BDD5GUlMRnn31Gy5YtyczMJDMzk5YtW/Loo4/y448/Mm/ePNLS0vj555955JFH/PvfvHkzu3btIj09nbFjxzJixAj++OMPAJKSkhg/fjw7d+5k6tSpjB49milTpgDw7bffArBz504yMzPp27dvkbh37NjBgAEDuOmmm9i+fTv/+Mc/GDBgANsDeqRMmjSJN998k99//52cnByeeeaZkK9BQUEBV1xxBWvXrmXdunXUqVOHG25wHWweffRRTjjhBEaNGkVmZiajRo3ar/xll13G22+/7Z9PS0sjPT2dM888k0WLFtGhQwfq1avnX9+9e3cWLVoUMpZJkybRoEGDsI9169aFLOcrm5ycTOPGjUlLS+Paa68FKDGGRYsW0b17d/+6Qw89lISEBJYvXx72WH369CEjI4MlS5aQn5/Pu+++yyWXXFJkmwM9l1588UWmTJnCjBkz2LhxI4cccggjRowoss8ZM2awZMkSPv/8c9566y127drF+vXr2b59O6+88gp16tQJG7Mx1VJSErz7Ljz7LFqrVuhtatWCZ5+F//zHbV/OotrGQVWzVHWxqv4T1wuiO26MBZ/d3rRuMbvxrdsdsKy05SpGly6weDEMHAiJicVvm5jorkctWuTKVYCWLVuyY8cOVJXXX3+d5557joYNG1KvXj3uvvtu/vOf/4QtO3HiREaOHEnTpk1p0qQJ999/PxMmTPCvj4+PZ+TIkcTHx3PmmWdSt25dli1bBri2A127diUmJoZu3bpx8cUXM2PGjIhinjp1Kh07dmT48OHExcVx8cUX07lzZz7+uLBJzBVXXEGnTp2oU6cOF1xwAfPmzQu5r0aNGjF48GASExOpV68e99xzT8RxAJxzzjmsWLGCFStcZ50JEyZw4YUXkpCQQGZmJvXr1y+yff369dm9O/RpNnToUHbu3Bn2UdwgRkOHDiUjI4Ply5dz3XXX0axZM4ASYzjQGH2GDx/O+PHj+fLLL+ncuTOtWrXyryvNufTqq6/y6KOP0rp1a2rVqsUDDzzABx98UOSyxAMPPEBSUhJ16tQhPj6e7du3s3LlSmJjY+nduzfJycnFxmxMtdWrF9kSZgzHWrWgd+8KO3SVaBzpedObni0i8d7fa7xpSjHl2gRtW5ZyFScgSyRKWaJPeno6DRs2ZOvWrezdu5fevXv7f+GeccYZxV6P37hxIykphS9rSkoKGzdu9M83atSIuLjCkzkxMZHMzEwAfvrpJ04++WSaNGlC/fr1eeWVV/ZrcBfpcX3HTk9P9883b9485HGD7d27l2uvvZaUlBSSk5M58cQTD2jY8Fq1anHBBRfw9ttvU1BQwDvvvMPw4cMBqFu3LhkZGUW2z8jIKPLrv7x17NiRLl26+NsplBRDaWMcPnw4kyZNYty4cVx66aVF1pXmXFq7di2DBg3yb3/EEUcQGxvLli1b/Nu0adPG//fw4cM5/fTTueiii2jZsiW33347ubm5xcZsTHW15OOvwUuyCxDya9dxDSEBcnNhzpwKO3ZVShx24rpkxgENvWW/etMuIhKuTvLooG3LUq7i9epVfOJQgVkiwOzZs0lPT+f444+ncePG1KlTh0WLFvl/4e7atcv/hRtqNMyWLVuydm1hm9N169bRsmXL/bYLZejQoQwcOJD169eza9currvuOl97khJH3gw+ru/Ygb96I/Xss8+ybNkyfvrpJzIyMvyXSSKNBdzliokTJ/LVV1+RmJjov7TSpUsXfvvttyK/3tPS0ugSpvZo4sSJ1K1bN+yjuEsVgfLy8li1alVEMXTp0oW0tDT/ut9++419+/bRqVOnYo+RkpJC+/bt+fTTTznvvPOKrCvNudSmTRs+++yzIjUs2dnZRd7TwHLx8fHcf//9LF68mFmzZvHJJ58wfvz4iF4fY6qTvTl5bPi/L6iTt4+suAR2NWlO7DuToE0bd6k7K8v13KsgVSlxOBGXNOwEtgGo6npgLpAAnB9cQET64XpjbAZ+8C0vbblKMWeOywZdIO7SRCVkiRkZGXzyySdcdNFFXHLJJf5LBn/961+55ZZb+P333wFXG/H5558D0KxZM7Zv384uX7dRXGv9Rx55hK1bt7Jt2zYeeuih/a51h7N7924aNmxI7dq1+fnnn5k0aZJ/XZMmTYiJieG3334LWfbMM89k+fLlTJo0iby8PN59910WL17MWWeddcCvxe7du6lTpw4NGjRgx44dPPjgg0XWN2vWLGwcPn379iUmJoZbb73VX9sA0KlTJ3r06MGDDz5IdnY2kydPZv78+QwePDjkfoYNG+a/7h/qEe5SxZgxY/zv2eLFi3n88cfp379/RDEMGzaMjz/+mJkzZ7Jnzx5GjhzJeeedF1GtyNixY/n6669JCqoRK825dN1113HPPff4E8KtW7fy0UcfhT329OnTWbBgAfn5+SQnJxMfH09sbJlGjTfmoPT8tBUcvnYxeRLDjM59YeEiOPfcwkvisbHw008VF0CoFpMV8cDd3GoYUCvEuuOAVbjGjM8ErRviLd8EHBawvCmwyFt3c4h9lqpcqEfv3r1DtjgtVcvtiy5yLV5r11ZNSVGdPFm1bVs3D6oBrd3LKiUlRWvXrq1169bV5ORk7dOnj44aNUrz8vL822RlZeldd92l7du313r16mnnzp31hRde8K+/4oor/K3Y09PTNSsrS2+88UZt3ry5Nm/eXG+88UbNyspS1cJeFcEx+Hp2vP/++9q2bVutW7euDhgwQEeMGKHDhg3zb3vfffdp48aNtX79+vrDDz/s16ti5syZ2qtXL01OTtZevXrpzJkz/ev69eunr7/+un8+uGyg9PR07devnyYlJWnHjh31lVdeUUBzc3NVVXXWrFnasWNHbdCggd54441hX9+HH35YAV21alWR5atXr9Z+/fpp7dq1tVOnTvv1bCkPl19+uTZt2lQTExM1JSVFb7vtNv/7EEkMEydO1DZt2mhiYqIOHDjQ35shlFC9c1RVc3Nzi/SqONBzKT8/X5999lnt1KmT1q1bVzt06KB33XWXP/7A90RVddKkSdqpUydNTEzUpk2b6o033lhkfSDrVWGqq0Xpu7TDXVP1qw6peutfbtb356zff6OxY1XPPLPMxyJMrwpRrZwRC0Xkclw7hp242oDNQD3gUOBIb7OpwPkaNGiTiLyMGyY6G5iG677ZH3d3zSnAEFXd7wJ1acsFS01N1TkhagKWLFnCEUccUVLxojp0gHXrYMgQGDvWtWXYsweuvBI+/ND1pvCqnE3VNn78eF577TW+q4QhXs2BKdX/pjFVXEGBct7oWcxbvxOAPh0a8s5f+1TYTRZF5BdVTQ1eXpmXKmYADwPzcHeoPA84DUjC3SVzkLobUe03qoyqXo+rrZgL9ANOx91V8wZgcLgv/9KWq1BHHAGvvVa0AaSv4eRrr0HnzpUekjlwe/fu5eWXX+aaa66JdijGmBpi4s/r/ElDfKzwyLldo3Jn5jB9Ocqfqq4GRpah/CRgUokbllO5CjN1avh1V17pHqZK+/zzzznvvPP485//zNChQ6MdjjGmBvh9dzZP/W+pf/5v/Q7lsKbFjThQcSotcTCmujj99NPZs2e/m7waY0yFefiTJezOdt0v2zVK5Pp2heIAACAASURBVPqTD4taLFWpV4Uxxhhjgny7fCsfpxWOl/PIuV2pHR+9HkWWOJRRpHeaNMZUDvufNNVJdm4+905Z6J8/t0dLju/YOIoRWeJQJklJSaSnp5OTk0Nl9U4xxoSmquTk5JCenr7fOBPGHKxGfb2SdTv2ApBcO457BhxZQomKZ20cyqB169Zs27aNtWvX2m1/jakC4uLiqF+/Po0bR/cXmTHlYeXvu3n128Lu+Xf+5Qia1Asz8nAlssShDGJiYmjatClNmzaNdijGGGOqEVXl7skLyc13tdm9Uw7hoqPblFCqctilCmOMMaaKef+XDfy8egcAcTHCo4OOIiam8sdsCMUSB2OMMaYK2bEnh8c/XeKfv+qE9nRuXnVuIW+JgzHGGFOFPDJ1MX/sdTdDbNWgDjf37xjliIqyxMEYY4ypIr5dvpX/zk33zz98bhcSE6pWc0RLHIwxxpgqYG9OHvdMWeCfP7t7S07p3CyKEYVmiYMxxhhTBTz35XLW73D3eaxfJ56RZ0V/zIZQLHEwxhhjomzBhl2M/W61f/7eAVVjzIZQLHEwxhhjoig3v4A7PpxPgTcA8XGHNWJI79bRDaoYljgYY4wxUTRm5moWb8oAoFZcDI8N6opI1RizIRRLHIwxxpgoWbNtD89PW+6fv+XUTqQ0qtr3WrHEwRhjjIkCN6z0AvbluTu6dmmZzNXHt49yVCWzxMEYY4yJgvd/2cCsVdsBiI0RnhzcjbjYqv+1XPUjNMYYY6qZrbv38ejUgGGlj2/PUa3qRzGiyFniYIwxxlSyBz9exK4sN6x024aJ3PLnTlGOKHKWOBhjjDGV6KslW/hk/ib//KODjqJOQmwUIzowljgYY4wxlSRzXx73Tlnonx/cqzUndGwSxYgOnCUOxhhjTCV58rOlbNqVDUCjpATuHXBElCM6cJY4GGOMMZXgx9+2M+HHtf75kWcfySFJCVGMqHQscTDGGGMqWFZOPnd8ON8//+cjmjKwe8soRlR6ljgYY4wxFeyZL5axdvteAOrVjuPRKj6sdHEscTDGGGMq0C9rd/DG94V3vrzvrCNpllw7ihGVjSUOxhhjTAXJzs3nnx/MR707X57YqQnnV+E7X0bCEgdjjDGmgjw/bQW/bd0DQN1acTx+3sF7icLHEgdjjDGmAqSt38lr367yz991ZmdaNagTxYjKhyUOxhhjTDnLySvg9g/mU+BdoujboREXH902ukGVE0scjDHGmHI2avpKlm3ZDUCd+FieHNyNmJiD+xKFT6UlDiISLyL9ReRZEflRRDaJSI6IpIvIByJyUphy40REi3ksLeG4Q0VkpojsEpFMEZkjIiNExJImY4wx5W7xxgxenr7SP3/7GYfTtlFiFCMqX3GVeKx+wJfe35uBX4A9wJHAYGCwiDysqiPDlP8eWBli+aYQywAQkZeA64Fs4CsgF+gPjAL6i8j5qppfiudijDHG7Cc3v4B/fpBGnneNIjXlEC7r2y66QZWzykwcCoAPgRdUdWbgChG5EJgI3Cci01V1eojyY1R1XKQHE5HBuKRhM3Ciqq7wljcDpgODgBuAF0rxXIwxxpj9vPbtbyzamAFArbgYnhpSfS5R+FRadb2qfq2qQ4KTBm/du8A4b/aScjrkXd70Dl/S4B1rC/A3b/ZOu2RhjDGmPCzfspsXpvm/bvjHqZ3o0KRuFCOqGFXpS/NXb1rmkTFEpDXQG8gB3g9er6ozgHSgOdCnrMczxhhTs+XmF3Dre2nk5BcA0L1NA64+oUOUo6oYlXmpoiQdvWm4Ngsni0g3oC6wBfgO+FJVC0Js29ObLlLVrDD7mw208radVbqQjTHGGBj9zSoWpO8CICE2hqeHdCO2ml2i8KkSiYOINAcu92Y/DLPZpSGWLRaRi1R1QdDy9t50bXCBAOuCtjXGGGMO2ML0Xbz4VeEliltP60SnZvWiGFHFivqlChGJA94G6gNfqerHQZvMA24CuuBqG1oCZwFpuB4Z00SkVVAZ30WlPcUcOtObVt931xhjTIXal5fPbe8X9qLonXJItb1E4VMVahxewXWRXE+IhpGq+nzQoj3AVBH5EpiBa6NwF66HhI+vfkhLG5SIXANcA9C2bfUY7csYY0z5emHaCpZudgM91Y6P4Znzu1fbSxQ+Ua1xEJEXgKtwXSb7q+rmSMuqag7wuDd7ZtDq3d60uOasvnW7Q61U1ddUNVVVU5s0aRJpWMYYY2qIX9f9wSszCu9FcecZnWnfOCmKEVWOqCUOIvIs7hLEVlzSsKKEIqH4Ro0MvlSxxpumFFO2TdC2xhhjTESycvK59b20IveiuLSaDfQUTlQSBxF5CvgHsB04VVUXl3JXjbxpZtByX9fOLiIS7lZkRwdta4wxxkTk6c+X8du2wttlV8eBnsKp9MRBRJ4A/gn8gUsa0sqwuwu86ezAhaq6HpgLJADnh4ihH268iM3AD2U4vjHGmBrmx9+28+as1f75ewccQZuG1edeFCWp1MRBRB4G7gB24pKGYn/ti0gPETlLRGKDlseJyD9wlzoAngtR3Nf+4UkROSygbFPgZW/2iTDjQBhjjDH72bMvj39+kIZ6lyhOOrwJFx7dpvhC1Uyl9aoQkYHAvd7sSuBGkZDVOktV9Qnv73bAZGCHiCwHNuC6T3bFdcsswA0p/XnwTlT1AxEZjRteeoGITKPwJlfJwBTcza6MMcaYiDz26RLW73DjCibXjuPJwd0I811WbVVmd8yGAX+neo9QZgC+xCENdxOqY3ANHXviulhuAN4EXlLVX8IdUFWvF5HvgBG4u3PG4hpUvgGMttoGY4wxkZqxfCsTf1rnn3/onKNollw7ihFFR6UlDt6dLccdYJnVwN/LeNxJwKSy7MMYY0zNtisrlzs+mO+fP71LM87p0TKKEUVP1EeONMYYY6q6+z9ayOaMbAAaJiXw6KCuNe4ShY8lDsYYY0wxPk7byJR5G/3zjw06isZ1a0UxouiyxMEYY4wJY9OuLO6ZXHgfxcG9WnPGUS2iGFH0WeJgjDHGhFBQoNz2fhoZ2XkAtD6kDg8MPDLKUUWfJQ7GGGNMCG/OWsP3K7cDIAL/uqAH9WrHRzmq6LPEwRhjjAmybPNunvzfUv/8df0O5Zj2DYspUXNY4mCMMcYE2JeXz9/fnUdOnhvqp0vLZG75c6coR1V1WOJgjDHGBPjXl8tZsikDgFpxMTx/YQ8S4uzr0sdeCWOMMcbz42/bee3b3/zzd/6lMx2b1YtiRFWPJQ7GGGMMkJGdy63vFd7A6oSOjbmsb7uoxlQVWeJgjDHGAA98tIj0ne4GVvXrxPP0kO7ExNTM0SGLY4mDMcaYGm/q/E3899d0//xjg7rSvH7Nu4FVJCxxMMYYU6Nt3JnF3QGjQw7q2YoB3Wr26JDFscTBGGNMjZVfoNzy7jx2ZeUC0KpBHR48p0uUo6raLHEwxhhTY43+ZiU/rd4BQIzA8xf1INlGhyyWJQ7GGGNqpLnr/uC5aSv88zee0pGj29nokCWxxMEYY0yNk5Gdy83/+ZX8Atf3MjXlEG485bAoR3VwsMTBGGNMjTNyykLW73BdL+vVjuP5i3oQF2tfiZGwV8kYY0yN8t+5G5gyb6N//vHzutL6kMQoRnRwscTBGGNMjbF2+x7um7LQP39+79ac1a1lFCM6+FjiYIwxpkbIzS/gpv/MY09OPgDtGyfxwEDrenmgLHEwxhhTIzz35XLS1u8EID5WePGiniTViotyVAcfSxyMMcZUe7NWbmP0jFX++X+efjhdW9ePYkQHL0scjDHGVGt/7MnhlvfmFbnr5dXHd4huUAcxSxyMMcZUW6rKbe+nsSVjHwANkxJ49ny762VZWOJgjDGm2hr73Wq+Wvq7f/6Z87vRNNnuelkWljgYY4ypln5d9wdPfLbUP3/18e05pXOzKEZUPVjiYIwxptrZtTeXGyb9Sp43pHT3Ng24/YzOUY6qerDEwRhjTLWiqtz+YRrpOwuHlB51cU8S4uwrrzzYq2iMMaZaGf/DWj5ftMU///SQbrRpaENKlxdLHIwxxlQbC9N38ejUJf75y/qmcMZRLaIYUfVjiYMxxphqYXd2LiMmzSUnvwCAo1olc/eAI6IcVfVjiYMxxpiDnqpy138XsHb7XgDq1opj1MW9qBUXG+XIqp9KSxxEJF5E+ovIsyLyo4hsEpEcEUkXkQ9E5KQSyg8VkZkisktEMkVkjoiMEJFin0NpyxljjDl4vPPzej6Zv8k//9h5XWnXOCmKEVVflfnl2Q+YBvwDSAF+ASYDO4DBwHQReShUQRF5CZgIpAIzgS+BTsAo4AMRCZlSlracMcaYg8eSTRk8+PEi//zFx7RlYHe7VXZFqczEoQD4EDhRVVuo6lmqeqGqdgUuAvKB+0Tk5MBCIjIYuB7YDHTzyg0COgJLgEHADcEHK205Y4wxB4/MfXmMmDSXfXmuXUPn5vW4/+wjoxxV9VZpiYOqfq2qQ1R1Zoh17wLjvNlLglbf5U3vUNUVAWW2AH/zZu8McemhtOWMMcYcBFSVOz6cz29b9wBQJz6WUUN7UTveKpMrUlX60vzVm7b2LRCR1kBvIAd4P7iAqs4A0oHmQJ+yljPGGHPwGDdrDVOLtGs4isOa1o1iRDVDVUocOnrTTQHLenrTRaqaFabc7KBty1LOGGPMQeCXtX8UGa9h2J/aMqhn62JKmPJSJRIHEWkOXO7Nfhiwqr03XVtM8XVB25alnDHGmCpue+Y+bpg0138fim6t6zPS2jVUmqgnDiISB7wN1Ae+UtWPA1b76pz2FLOLTG9arxzKBcZ1jdd1c87WrVuL2Y0xxpjKkl+g/P3deWzalQ1A/TrxvDTUxmuoTFFPHIBXgP7AevZvGCneVA9wn6Ut56eqr6lqqqqmNmnSpLS7McYYU45e+GoFM1ds888/d2F3uw9FJYtq4iAiLwBX4bpM9lfVzUGb7PamxbV28a3bHbCstOWMMcZUUd8s+51/f+3vJMcNJx/GKZ2bRTGimilqiYOIPAvcBGzFJQ0rQmy2xpumFLOrNkHblqWcMcaYKih9ZxZ/f3ce6tUjH3dYI245tVN0g6qhopI4iMhTuBEktwOnquriMJv6umh2EZE6YbY5OmjbspQzxhhTxezLy+f6iXPZuTcXgGbJtXjhop7ExkgJJU1FqPTEQUSeAP4J/IFLGtLCbauq64G5QAJwfoh99cON+7AZ+KGs5YwxxlQ9j01dQtr6nQDExQgvDe1F47q1ohxVzVWpiYOIPAzcAezEJQ2R/Np/3Js+KSKHBeyrKfCyN/uEqhaUUzljjDFVxEfz0nnrh8Ke9Xf+pTOp7RpGMSITV1kHEpGBwL3e7ErgRpGQ1UxLVfUJ34yqfiAio3HDRC8QkWlALq4nRjIwBXfTqiJKW84YY0zVsHhjBnd8ON8//5ejmnPV8Tb0TrRVWuIABKaIqd4jlBnAE4ELVPV6EfkOGIG7y2YssBR4AxgdrtagtOWMMcZE1869OVz79hyyc93HdIcmSTw1pBthfnCaSiSqpR7qoMZITU3VOXPmRDsMY4ypEfILlMvf/Nk/XkPdWnFMGXGc3YeikonIL6q634/8qjAAlDHGGOP37BfLigzy9OwF3S1pqEIscTDGGFNlfLZgEy9/s8o/f8PJh3F6l+ZRjMgEs8TBGGNMlbBiy25ue7+wh/5JhzexQZ6qIEscjDHGRF1Gdi7XTPiFPTn5AKQ0SuSFC22Qp6rIEgdjjDFRVVCg/OPdeaze5m5oXCc+lleH96Z+YnyUIzOhWOJgjDEmqv799UqmLfndP//UkG50bp4cxYhMcSxxMMYYEzVfLdnCc9OW++evObEDZ3dvGcWITEkscTDGGBMVq7Zm8vd35/nnjzusEbeffngUIzKRsMTBGGNMpdu1N5er35rD7uw8AFo1qMO/L+5FXKx9LVV19g4ZY4ypVHn5Bdzwztz9GkM2TEqIcmQmEiXeq0JEmgGnAd2BBrg7W6YBX6rq5ooNzxhjTHXz2KdLi4wM+cz53TmqVf0oRmQORNgaBxE5QkQ+ABYDw4F4YLM3HQ4sEpEPROTISonUGGPMQe+92et54/vV/vmb+ndkQLcWUYzIHKjiahzGAU8Dw1R1X/BKEUkAzgHGAn0rJDpjjDHVxpw1O7hnygL//BldmvP3/h2jGJEpjbCJg6r+qbiCqpoDvO89jDHGmLDSd2Zx3du/kJvv7sjcuXk9nr2gOzE2MuRBxxpHGmOMqVB7c/L461tz2JaZA0CjpATGXJZKUq0Sm9mZKiiixEFEuovI1yKyQ0RyvEeuiORUdIDGGGMOXqrKP9+fz+JNGQDExQijL+lN60MSoxyZKa1I0713gA+Bm4CsigvHGGNMdfLvr1cydcEm//zD5x7FMe0bRjEiU1aRJg7NgZGqqhUZjDHGmOrjfws38a8vC4eTvvzYdlx8TNsoRmTKQ6RtHN4ChlZkIMYYY6qP+Rt27jec9L0DjohiRKa8RFrj8ATwg4jcDWwJXKGqp5R7VMYYYw5aG3dmcdVbc8jOLQCgXaNERtlw0tVGpInDB8BqYDLWxsEYY0wYmfvyuHLcbLbudsP/1K8TzxuXH80hNpx0tRFp4tADaOSN3WCMMcbsJy+/gBsnzWXp5t0AxMcKrw7vTYcmdaMcmSlPkdYbzQRsaGljjDFhPTJ1CdOXbfXPPzaoK306NIpiRKYiRFrjsBr4QkQms38bh5HlHpUxxpiDyluz1jBu1hr//IiTD+X81DbRC8hUmEgTh0RgKpAABJ4J1j3TGGNquOlLf+fBjxf55wd0bcGtpx4exYhMRYoocVDVKyo6EGOMMQefJZsyuGHSXAq8n5E92jSwe1BUc8XdVrtpJDsQkWblF44xxpiDxe+7s7lq3Gz25OQD0KpBHV6/NJXa8bFRjsxUpOIaR04XkZdFpK+IFNlORGJEpI+IvAx8VbEhGmOMqWqycvL561tz2LgrG4C6teIYe3kqTerVinJkpqIVlzj0BBYDrwG7RWSBiMwSkQXAbuAVYAHQq+LDNMYYU1Xk5Rdw4ztzSduwC4AYgVFDe9K5eXKUIzOVIWwbB2/MhlHAKBFpA3QFGgB/APNVNb1yQjTGGFNVqCoPfLyIaUt+9y97cGAXTjo8oqvbphqItHHkemB9BcdijDGmihs9YxVv/7jOP39dv0MZ3rdd9AIylc4GDjfGGBORKb+m89T/lvnnz+nRkttPt26XNU2lJg4icriI3Cwib4vIUhEpEBEVkSHFlBnnbRPusbSEYw4VkZkisktEMkVkjoiMCG7waYwxJrxZK7fxzw/S/PN9OjTkqSHdrNtlDRTpAFDl5W/AzaUs+z2wMsTyTeEKiMhLwPVANq73Ry7QH9d2o7+InK+q+aWMxxhjaoSlmzO4dsIv5Oa7wRo6NavLq8NTqRVn3S5roogSBxG5TVWfCbH8H6r6rwM43kLgaWAO8AswFugXYdkxqjou0gOJyGBc0rAZOFFVV3jLmwHTgUHADcALke7TGGNqmk27srj8jdns3pcHQLPkWoy74hjq14mPcmQmWiKtrg93P4p7D+RgqjpGVW9X1fdUddWBlC2Fu7zpHb6kwYthC67mA+BOu2RhjDGhZWTncsWbs9mcUThWw7grjqFlgzpRjsxEU7E1DiJyivdnrIicDARezOqAG8+hyhGR1kBvIAd4P3i9qs4QkXSgFdAHmFW5ERpjTNW2Ly+fv739i/8W2XEx7hbZR7SwsRpqupIuVYz1prWBNwKWK+4SwI0VEVQYJ4tIN6Au7g6d3wFfqmpBiG17etNFqpoVZn+zcYlDTyxxMMYYv/wC5db30vh+5Xb/sqeGdOO4wxpHMSpTVRSbOKhqewARGa+ql1ZOSGGFOv5iEblIVRcELW/vTdcWsz9fR+T2xWxjjDE1iqry4MeL+GR+Ybvz207rxHm9WkcxKlOVRHR9PzBp8O5T4X9UXGh+84CbgC642oaWwFlAGnAkME1EWgWVqetN9xSz30xvWq/8QjXGmIPbi1+tZPwPhb+5Lj+2HSNOPiyKEZmqJqIvfhHpJSI/iMgeXJfGXCDPm1YoVX1eVf+tqotVdY+qblLVqcAxwI9AUwobQvpD9hUv7XFF5BpvzIc5W7duLe1ujDHmoDHhx7U8N225f35g95aMPOtIRGysBlMo0hqDt3BdGFNxjSI74Kr4O1RQXCXy7qXxuDd7ZtBqX6PNuoTnWxeygaeqvqaqqaqa2qRJk9IHaowxB4Gp8zcx8qOF/vkTOjbmmfO72wBPZj+RDgCVAtyjqqX+BV9BfKNGBl+qWONNU4op2yZoW2OMqZG+W7GNv7/7K75P+O5tGvDKJb1JiLPe6mZ/kZ4Vk4HTKjKQUmrkTTODlv/qTbuISLgOx0cHbWuMMTXO/A07uXbCHP+okB2aJPHm5UeTVKuyBxY2B4uwZ4aITKCwjUAtYLKIfIfrhukX5d4WF3jT2YELVXW9iMwFegHnA+MD14tIP6A17rn8UAlxGmNMlfPb1kwuf3M2e3LcyPvNk2sz4ao/0TApIcqRmaqsuJQy+L4QiysykFBEpAfuC/6zwHtKiEgcrqfFTd6i50IUfxw3+NOTIjJLVVd6ZZsCL3vbPBFmHAhjjKnWNu/KZvjYn9mxJweA+nXimXDVMbSyUSFNCcImDqr6YHkfTER6UfilDa47JcBjInJbwLH7eH+2w10m2SEiy4ENuO6TXXHdMgtwQ0p/HiL+D0RkNG546QUiMo3Cm1wlA1NwN7syxpgaZXvmPoaN+ZH0nW58vDrxsbxx+dF0bGa9003JIr3J1SlhVu0DNqhqcQMtBUoG/hRieccw26fhbkJ1DK6hY0/c5ZMNwJvAS6r6S7iDqer13uWVEbibacXiGlS+AYy22gZjTE2zKyuX4WN/ZtVWN8xNXIzw8iW96J1ySJQjMwcLiaSjhIisxv3CB9hOYaPE34HmwHzgosCbSVUnqampOmfOnGiHYYwxZbJnXx7Dx/7E3HU7AYgR+PfFvRjQrUWUIzNVkYj8oqqpwcsj7VUxFngRaKCqLYEGuJqAV7y/Z1P0EoQxxpgqJDs3n2smzPEnDQBPnNfNkgZzwCLtb3Mz0EJV8wBUNUtE7gE2quqjInIr7vKBMcaYKiY3v4AbJv1a5KZV9599JBcc3aaYUsaEFmmNwx4Kxz3w6Q3s9f62tgLGGFMF5Rcot72fxrQlW/zLbjutE1ccZ/f3M6UTaY3DSOALEfk/YD2ui+TZFN5Wuz/wQfmHZ4wxprRUlXunLOSjeRv9y67t18FuWmXKJKLEQVXHi8gcYDCukeRyoK+qLvbWfwJ8UmFRGmOMOSCqymOfLuGdn9f5l13Spy13ntHZblplyiTiMUW9JKHSB4Eyxhhz4J6btoLXZ672z5/XsxUPDTzKkgZTZsUNOf2aql7j/R04/HQRUR5y2hhjTJAXv1rBi18V9o4/vUsznhrSze50acpFcTUOqwP+Dh5+2hhjTBX00vSV/OvL5f75fp2a8OLFPYmLtTtdmvJR3JDTjwf8Xe7DTxtjjClfr327iqc/X+afP6FjY14d3ptacbFRjMpUNxGnoCJyqoiMFZGPvfnUYoaiNsYYU4nGfreaxz5d6p8/9tBGvH5pKrXjLWkw5SuixEFEbgRGAyuAE73FWcAjFRSXMcaYCL01aw0Pf1LYdv1P7Rsy5jJLGkzFiLTG4e/An1X1CQoHe1oKHF4hURljjInI2z+u5f7/W+SfP7rdIbxx+dEkJkTcac6YAxJp4lAPN/ATFPauiAdyyj0iY4wxEfnPz+u4d8pC/3yvtg1484pjSKplSYOpOJEmDt8CdwYtuwmYXr7hGGOMicR7c9Zz1+QF/vnubRow7spjqGtJg6lgkZ5hNwIfi8hfgXoisgzIwA07bYwxphJN+mkddwckDV1b1Wf8lceQXDs+ilGZmiLSIac3icjRwDFAW9xli59V1W5uZYwxlWj8D2sY+VFhm4YuLZOZcNUx1K9jSYOpHAcy5LQCP3kPY4wxleyN71bzUEDviW6t6zPhyj9RP9GSBlN5ik0cRGQmYYaa9lHVE4tbb4wxpuxe+3ZVkXEaerRpwFtXWk2DqXwl1TiMCfhbgJeA6ysuHGOMMcFemr6yyIiQqSmH8OYVR1PP2jSYKCg2cVDVtwLnReRfwcuMMcZUnBemreC5aYX3nvhT+4a8cfnR1uXSRI2decYYUwWpKv/6cjn//rrwHoPHHtqIMZel2uBOJqrs7DPGmCpGVXnis6W8+u1v/mUndGxs954wVUJJjSODb2IVJyIn49o7AKCqX1dEYMYYUxPlFyj3fbSQST+t8y87+fAmjL6ktyUNpkooqcZhbND8duCNgHkFOpRrRMYYU0Pl5hdw2/tpfDRvo3/ZqUc2Y9TQnnZrbFNllNQ4sn1lBWKMMTVZdm4+N0yay7Qlv/uXDerZiqeGdCM+NtK7AxhT8ayNgzHGRNmefXn8dfwcZq3a7l92SZ+2PDTwKGJipJiSxlQ+SxyMMSaKdu7N4fI3ZzNv/U7/suv6HcodZxyOiCUNpuqxxMEYY6Lk993ZXDr2Z5Zu3u1fdvsZh3P9SYdFMSpjimeJgzHGREH6ziwuGfMTq7ft8S97+JwuDO/bLnpBGRMBSxyMMaaSLd+ym8ve+JlNu7IBiI0Rnh7SjfN6tY5yZMaUzBIHY4ypRL+s3cGV4+awKysXgITYGF68uCdnHNU8ypEZExlLHIwxppJMW7yFEZPmsi+vAICkhFheHZ7K8R0bRzkyYyJniYMxxlSC92av567JC8gvUAAa101g3BXHcFSr+lGOzJgDU6mjiojI4SJys4i8LSJLRaRARFREhkRQdqiIzBSRXSKSKSJzRGSEiBT7HEpbzhhjyoOq8tL0ldz+4Xx/0tC2YSIfXHesJQ3moFTZNQ5/A24+0EIi8hJwPZANfAXkAv2BUUB/ETlfVfPLq5wxBErDpgAAHfNJREFUxpSHggLloU8WM27WGv+yI1skM+7Ko2lar3b0AjOmDCr7V/dC4GngQuAwYEZJBURkMO7LfzPQTVXPUtVBQEdgCTAIuKG8yhljTHnYl5fPTf/5tUjScOyhjXj32j6WNJiDWqUmDqo6RlVvV9X3VHVVhMXu8qZ3qOqKgH1twdVgANwZ4tJDacsZY0yZ7MrK5Yo3Z/PJ/E3+ZQO6tuDNK46mXu34KEZmTNlV6S9NEWkN9AZygPeD16vqDCAdaA70KWs5Y4wpq/SdWZz/yqwi9524tG8KL15sd7g01UOVThyAnt50kapmhdlmdtC2ZSlnjDGltjB9F+e+9D3Lt2T6l912WiceHNiFWLtZlakmqnp3TN9tvdcWs826oG3LUs4YY0rl66VbuGHSr+zNce2t42OFp4Z0Y1BPGw3SVC9VPXGo6033FLONL7WvVw7l/ETkGuAagLZt2xYfpTGmRpvw41ru/2ghXm9LkmvH8erwVPoe2ii6gRlTAap64uCr29NKKuenqq8BrwGkpqaWej/GmOqroEB54n9Lee3b3/zLWh9Sh3FXHM1hTUP+JjHmoFfVEwffvWbrFrONb93ugGWlLWeMMRHJzs3nH+/N49MFm/3LurWuz5jLUq27panWqnrisMabphSzTZugbctSzhhjSrQtcx/XjJ/D3HU7/ctOPbIZL1zUg8SEqv6xakzZVPUz/Fdv2kVE6oTpIXF00LZlKWeMMcVasimDq9+aQ/rOwo+Vy49tx31nHWk9J0yNUKW7Y6rqemAukACcH7xeRPoBrXGjQ/5Q1nLGGFOcLxZtZvDoWf6kQQTuO+tIHrDulqYGqdKJg+dxb/qkiBzmWygiTYGXvdknVLWgnMoZY0wRqsrob1Zx7du/+Ltb1q0Vx9jLUrnqeOvRbWoWUa28DgMi0ovCL22AI3HdIVcAO3wLVbVPULmXccNEZwPTKLxZVTIwBRgS5iZXpSoXLDU1VefMmRPx8zTGVB/ZufncPXkB/52b7l/WpmEdxl52NJ2aWc8JU32JyC+qmhq8vLLbOCQDfwqxvGNxhVT1ehH5DhgB9ANigaXAG8DocLUGpS1njDEAW3fv49oJRRtBHtOuIa8M703DpIQoRmZM9FRqjcPBymocjKl5Fm/M4K/jizaCvCC1NY+c25WEuIPhKq8xZVNVahyMMabK+3TBJm57P83fniFG4O4zj+Cq49sjYo0gTc1miYMxxnjyC5RnvljG6G9W+ZfVrRXHvy/u+f/t3Xl81dWd//HXJ/tO2AIhhEUIsski4NKqiOivrrUuoLXWdqaOrWvtzPiztp1fZ9q6dqryq2jrtOr8pmqnYrXtuBUULbiD7BAB2ULYE0L2/fz+uN+QhSTeJHfJvff9fDzu45uc75LzPRyS9+O7nMO8iTlhrJlI/6HgICIClFXXc/vza1ix7cjxstGD0/iPG2brIUiRNhQcRCTmbdlfzk3/tYqi0tbnGc49eSiLrpnJgLTEMNZMpP9RcBCRmPbndfu4e8l6ahpa38y+bd54vnfBBA3qJNIJBQcRiUmNTc089Man7Wa2TE+K5xcLZ3Dh1OFhrJlI/6bgICIxp7SqnjueX8PK7a3PM5w0JJ1ff30WBXqeQaRbCg4iElNW7y7l1mfXcKC89njZ+ZNyePiaGWSl6HkGkc+j4CAiMcE5x29X7uSB1wppbG4d+O7O8wu447wC4vQ8g4hfFBxEJOodq2ngfy9ZxxubDh4vy05L5JGFMzQ+g0gPKTiISFTbWHyMW579hD2l1cfLZuRns/hrp5KXnRrGmolEJgUHEYlKzjme/6iIf/3LJuobW+ez++YXxvCDiydpvgmRXlJwEJGoU13fyI9e2sgf17ROhZ2RnMCDV03jkmm5YayZSORTcBCRqLJp3zFuf34NOw5XHS+bODyTx792KicNzQhjzUSig4KDiEQF5xzPvLeL+18tpL6p9dbEglkj+cnlU0lNig9j7USih4KDiES8kso67lqynrcKDx0vS0uK5yeXT+XqWSPDWDOR6KPgICIR7b3tR7jzv9dyqKLueNnUvCz+77UzdWtCJAgUHEQkIjU0NfPosq08/vZnuNbxnLjxrLHcdeHJJCfo1oRIMCg4iEjEKSqt5o7fr2HNnrLjZYPTk/j3BdM1oJNIkCk4iEjEcM7xwqq9/NtfNlFV3zoN9lnjh/DwwunkZKWEsXYisUHBQUQiwpHKOu754waWbm4dNjohzvin/3Uy3z7nJM01IRIiCg4i0u8t3XyQe/64niOV9cfLThqSzsPXzGBGfnYYayYSexQcRKTfqqxr5Gf/s5nff1zUrvwbZ47m+xdN0tgMImGg4CAi/dKqXaV87w9rKSqtOV6Wk5nMzxdMZ+6EoWGsmUhsU3AQkX6ltqGJR5Zt5T/+toPmNq9ZXjItl3u/MpXstKTwVU5EFBxEpP9YvbuUu5asbzfPRGZKAj/7ylS+PH0EZnoAUiTcFBxEJOxq6pv4979+ylPv7mw3mNMXxw/m51dPZ0R2avgqJyLtKDiISFh9uKOEu19cz66S6uNlGckJ3HPxRK47bZSuMoj0MwoOIhIWVXWNPPR6If/5/u525WcXDOGBq6aRp6sMIv2SgoOIhNy7249w94vr2Xu09Y2JzJQE/uWSySyYPVJXGUT6MQUHEQmZkso67n1lC39cU9yu/LyJOdx3xSkMH6Aho0X6OwUHEQk65xxLVu/lvle3cLS64Xj5gNREfnzZZK6YmaerDCIRIiKCg5k9A3yjm00+dc5N7GLf64CbgWlAPFAIPA084ZxrDnBVRaSDzw5X8sOXNvDBjtJ25ZdMy+XHl00mJ1NXGUQiSUQEhzbeBbZ3Ur6/s43NbDFwC1ALvAk0APOBx4D5ZrbAOdfU2b4i0jd1jU386u0dLF6+nfqm1oyel53Kz74yVdNfi0SoSAsOv3HOPePPhmZ2Fb7QcAA4xzm3zSsfBiwHrgBuAxYFp6oiseuDHSX88KUNfNZmIKf4OOPGs8by3fMLSEuKtF89ItIimv/33uMt724JDQDOuYNmdjPwNvB9M/ulblmIBMbB8lruf3ULL6/d1658+sgB3HflKUwZMSBMNRORQInK4GBmI4FZQD3wQsf1zrl3zKwYyAPOAN4LbQ1Fokt9YzPPvLeTRcu2UVXfevcvIzmBu750MtefMZr4OD38KBINIi04zDOzaUAGcBBYCSzt5IrBTG+5yTlXQ+c+xhccZqLgINJrK7cd4cd/3tjutgT4Hn780SWTyB2ggZxEokmkBYcbOinbbGbXOuc2tCkb6y13d7J9iz0dthWRHiguq+HeVzbz6oYD7coLcjL4ty9P4Qvjh4SpZiISTJESHNYCq/G9GbEbyAJOBe4FpgPLzOxU51zLqDIZ3rKq44HaqPSWmYGvrkj0qm1o4jcrdrB4+WfUNLS/LXHn+QV84wtjSIyPC2MNRSSYIiI4OOce7VBUBbxiZkuBd/A9p3APvrckAFpupjp6ycxuAm4CGDVqVG8PIxI1nHP8ed0+Hnr9U4rL2t8BvHJmHt+/aCI5WRqTQSTaRURw6Ipzrt7M7gf+BFzcZlWFt8w4ca/jWtZVdLbSOfck8CTA7Nmzex1ARKLB6t2l/PR/trC2qKxd+aTcLH5y+RTmjBkUppqJSKhFdHDwFHrLvDZlu7zl6G72y++wrYh0UFRazQOvF/LK+vZjrA1OT+J7F0zg2jn5JOi2hEhMiYbgMNhbVrYpW+Mtp5hZahdvVszpsK2IeMprG1i8fDtPr9zVbtTHpIQ4vnXWWG45dxyZKYlhrKGIhEs0BIeF3vLjlgLnXJGZfYLvAcoFwP9ru4OZzQVG4htV8v0Q1VOk36trbOLZD/bw2PLtlFbVt1t36bRc7r5wIvmD0sJUOxHpD/p9cDCzGfj+yL/Wdl4JM0sA7vA+AI902PV+fIM/PWhm7znntnv75QCPe9s8oFEjRaCp2fHSmmIeWbr1hAcfZ+Rn8y+XTmbW6IFhqp2I9Cf9PjgAY4CXgFIz2wrsxfcK5SnACKAZ37DSb7TdyTm3xMyewDcz5gYzW0brJFdZwMv4JrsSiVnOOZZuPsjP3/iUbYcq263Ly07l7osmctm0XE15LSLHRUJwWIdvIqrT8D3sOBPfa5Z78U2Pvdg5t7qzHZ1zt5jZSuBWYC6t02o/habVlhj3wY4SHny9kDV72r8pMTg9idvOG891p48iOSE+TLUTkf6q3wcH59xO4M4+7P8c8FzgaiQS2dYVlfHw0q28s/Vwu/L0pHj+4ZyTuPHsk8hI7ve/GkQkTPTbQSRGrCsqY9Gb23ir8FC78qT4OK4/YzS3zhvH4IzkMNVORCKFgoNIlFu/t4xHl50YGOIMrjx1JHeeX8DIgXpTQkT8o+AgEqXW7y1j0bJtvNkhMJjBpdNGcMd54ykYpqlaRKRnFBxEosyaPUdZvHw7y7YoMIhI4Ck4iEQB5xwrth3h8be388GO0nbrzOCSU3K5Y34BExQYRKSPFBxEIlhTs+P1jQd44p3tbCwub7dOgUFEgkHBQSQC1TU28dInxfz6bzvYeaSq3br4OOPy6SP4zrnjFBhEJOAUHEQiSFl1Pc99tIf/fG8XB8vr2q1LTojj2jn5/MM5J+ktCREJGgUHkQjw2eFKnn53Jy+uLqamoanduqyUBG44cwzf/OIYhmgcBhEJMgUHkX7KOcd7n5Xw25U7TxiDASAnM5kbzx7LV08bpSmuRSRkFBxE+pnahib+vHYfT727k8IDFSesnzg8k2+dNZYvzxihuSREJOQUHET6id0lVTz74R5eWFXE0eqGduvMYP7EHP7+i2M5c9xgzVYpImGj4CASRo1NzbxVeIjffbiHv3WYdAogNTGeBbNH8ndfHMvYIelhqKGISHsKDiJhcKiilv/+qIjnP9rDvmO1J6zPy07l62eO5qtzRjEgTc8viEj/oeAgEiJNzY6/bTvMC6uK+OumgzQ2u3brzeDcCUO5/ozRnHtyDvFxuh0hIv2PgoNIkO06UsULq4t4cXUxB8pPvLowKD2JhbPz+drpo8gfpPEXRKR/U3AQCYLq+kZe3XCAP6wq4qOdpZ1uM2fMQK4/YzQXTh2utyNEJGIoOIgESFOz48MdJby8tphX1u+nqr7phG2GZCRx5akjWTBrpGaoFJGIpOAg0gfOOTbtK+flNcX8Zf2+E4aBBt/cEfNOzmHh7JHMm5hDYnxcGGoqIhIYCg4ivbC7pIo/rd3Hn9YW89nhqk63GTc0nYWz87ni1DxyMlNCXEMRkeBQcBDxU1FpNa9t3M+rGw6wtqis022GZCRx6bQRXD5jBDPyszVQk4hEHQUHkW7sOFzJaxsP8NrG/WwsLu90m7SkeL40ZTiXzxjBWeOHkKBbESISxRQcRNpwzrH1YCWve2Ghs7kiABLijLkThnL5zDwumDSM1CS9FSEisUHBQWJeXWMTH+4o5a3CQ7xZeJCi0ppOt0uMN84uGMqFU4dzwaRhDExPCnFNRUTCT8FBYtKRyjreKjzEW1sOsWLb4U5fnQRITohj7oShXHxKLudNyiFL01eLSIxTcJCY0NjUzLq9ZazYdoS3Pz3Mur1lONf5thnJCcydMJSLThnOvJNzSE/WfxMRkRb6jShRyTnH7pJqVmw/woqth3n/sxIq6hq73H7UoDTmT8rh/EnDmDNmEEkJesBRRKQzCg4SNQ5X1PHRzlJWbj/Cim2H2Xu082cVAOIMZo8exPxJOcyflMO4oRl6dVJExA8KDhKx9pXV8NHOUj7cWcqHO0vY0cVATC1yB6Rw1vghnFUwhLkThpKdpocbRUR6SsFBIkJzs2PHkSo+2X30eFDo7ooCQHpSPGeOG+yFhaGMG5quqwoiIn2k4CD9UmlVPWuLjrJ2TxlrispYV1RGeW3XzygAJMXHMSM/mzNOGsRZBUOZOSpb80KIiASYgoOEXUVtA1v2V7Bp3zHWFpWxtqiM3SXVn7tfamI8s0YP5PSxgzht7CCm52eTkqiBmEREgknBQULGOcfB8jo27z/GpuJyNu8vZ9O+cvaUfn5IABicnsSM/GzmjB3E6WMHMTVvgK4oiIiEWEwEBzO7DrgZmAbEA4XA08ATzrnmcNYtGjnnKKmqZ9vBSrYfqmD7oUq2Hark0wMVlFTV+3WMpPg4puRlMSM/m5mjBjIzP5uRA1P1jIKISJhFfXAws8XALUAt8CbQAMwHHgPmm9kC51znwwZKt2obmth7tJrdJdXsKqlm+6HWoHC0usHv4yTEGQXDMpmcm8UpeVnMHDWQSblZGktBRKQfiurgYGZX4QsNB4BznHPbvPJhwHLgCuA2YFHYKtmPNTc7jlTWsf9YLXuP1rCrpIo9JdXsLvUt95fXdjn6YlcykhOYlJvJlBEDmJybxeQRWRQMyyA5Qc8miIhEgqgODsA93vLultAA4Jw7aGY3A28D3zezX8baLYvq+kZKKus5UlnHoYo6DhyrZd+xGvaX1bL/WA37j9VysLyWhqYeJgNPWlI8BTkZjMvJoCAnk4KcDAqGZZA/MI24ON1uEBGJVFEbHMxsJDALqAde6LjeOfeOmRUDecAZwHuhrWFg1DY0UV7bQHlNIxW1DZTXekvv+7KaBkoq63whoar++Nc1DX2/OxNnMCI7ldGD0xg1KJ1xQ9MZn5NBwbBMcrNSFBBERKJQ1AYHYKa33OSc62qkoI/xBYeZhCA4NDY188iyrTQ1Q7NzNDX7Pi1ft5ZBU3MztQ3N1DY2UVPfRG1jM3UNTdQ0NFHb0ERtQzM19U3UNwX3Qkl2WiK5A1LJy05h1KB0X0gYnMboQWmMHJim5xBERGJMNAeHsd5ydzfb7OmwbVA5YPHyz0Lxoz5XUkIcQ9KTGJyRzJCMJIYPSGXEgBRys1PJHZDifVJJTdKzByIi0iqag0OGt+xuAoNKb5nZcYWZ3QTcBDBq1KiAVCg+CK8SJsQZWamJZKUkeMtEMlMSyEpJJCvVtxyckczgjCSGZCQxON33dUZygl5tFBGRHovm4NDyV7FXT/c5554EngSYPXt2754Q7CAuzvinCyYQF2fExxnxZr6vDeLjWr72LRPijJTEeFIS40hJiCc5MZ7Ulu8T40lp870CgIiIhEo0B4cKb5nRzTYt6yq62Sagbp9fEKofJSIiEnDR/GTbLm85uptt8jtsKyIiIt2I5uCwxltOMbPULraZ02FbERER6UbUBgfnXBHwCZAELOi43szmAiPxjSr5fmhrJyIiEpmiNjh47veWD5rZ+JZCM8sBHve+fSDWRo0UERHprWh+OBLn3BIzewLfzJgbzGwZrZNcZQEv45vsSkRERPwQ1cEBwDl3i5mtBG4F5tI6rfZTaFptERGRHon64ADgnHsOeC7c9RAREYl00f6Mg4iIiASQgoOIiIj4TcFBRERE/KbgICIiIn5TcBARERG/mXMBmfgxqpnZYWB3AA85BDgSwOPFIrVh36j9+kbt1zdqv74JVfuNds4N7Vio4BAGZrbKOTc73PWIZGrDvlH79Y3ar2/Ufn0T7vbTrQoRERHxm4KDiIiI+E3BITyeDHcFooDasG/Ufn2j9usbtV/fhLX99IyDiIiI+E1XHERERMRvCg59ZGbXmdkKMztmZpVmtsrMbjWzXrVtoI8XCQJ1zmb2jJm5bj6FwTqHcDCzk83su2b2OzMrNLNm7zyv7uNxY6IPBrr9Yqn/mVmimc03s1+Y2Qdmtt/M6s2s2MyWmNm5fTh21Pe/YLRfKPtfTMyOGSxmthi4BagF3gQagPnAY8B8M1vgnGsK1/EiQZDO+V1geyfl+/tS137oZuC7gTxgjPXBgLefJxb631xgqff1AWA1UAVMBq4CrjKznzrn/k9PDhpD/S8o7ecJfv9zzunTiw++f1zn/WMUtCkfBmz21n03XMeLhE8Q2vAZb59vhvvcQtR+NwIPAQuBccDb3vlf3R/+Pfr7JwjtFzP9DzgPWAKc3cm6a4BGry3m9eCYMdP/gtR+Iet/YW/ASP0Aq7x/pBs6WTe3zX+AuHAcLxI+QWjDmPnF3cX59/UPX8z1wQC3X0z3vw5t8RuvLX7bg31iuv8FoP1C1v+i5p5RKJnZSGAWUA+80HG9c+4doBgYDpwR6uNFglg85/5M/x4SYGu85Uh/Nlb/O0GP2i/U9IxD78z0lpucczVdbPMxkOdt+16IjxcJgnnO88xsGpABHARWAkudc829rWwMiMU+GCzqf1DgLf29r67+115P26+toPc/BYfeGestu5v4ak+HbUN5vEgQzHO+oZOyzWZ2rXNuQw+PFStisQ8GS0z3PzMbDnzT+/ZFP3dT//P0sv3aCnr/062K3snwllXdbFPpLTPDcLxIEIxzXgvcAUzxjj8CuBRYh+9p5WVmltfzqsaEWOyDgRbz/c/MEoDfAQOAN51zf/FzV/U/+tR+EML+pysOvWPeMlDDbgb6eJEg4OfsnHu0Q1EV8IqZLQXewXdv9B7gtkD9zCgSi30woNT/APgVvtcni4Dre7Cf+p9Pb9svpP1PVxx6p8JbZnSzTcu6im62CdbxIkHIztk5Vw/c7317cV+OFcVisQ+GRKz0PzNbBHwL37gE851zB3qwe8z3vz62X5eC0f8UHHpnl7cc3c02+R22DeXxIsEubxmqc24ZNS2qLxX3wS5vGUt9MJSiuv+Z2S/wXSY/jO+P3rYeHmKXt4zJ/heA9vs8Ae1/Cg690/KqzBQzS+1imzkdtg3l8SJBqM95sLes7Har2BWLfTCUorb/mdlDwD8CJcAFzrnNvThMzPa/ALXf5wlo/1Nw6AXnXBHwCZAELOi43szm4nv/9gDwfqiPFwnCcM4LveXHAThW1InFPhhiUdn/zOwB4C7gKL4/eut6c5xY7X+Baj8/BLb/hXuErEj9AFfTOpLZ+DblOcAmOhkeFd99pkLg/kAcL9I/gWxDYAa+J4jjO5Qn4EvzTd7xvhTu8w5ie77N54x8qD4YnPaLxf4H/NQ7p6PALD/3Uf8LQvuFuv/prYpecs4tMbMn8E2Us8HMltE6IUsW8DK+iVnaygVO9paBOF5EC3AbjgFeAkrNbCuwF99rW6fgey2pGbjbOfdGcM4m9MzsVODxNkWTveV9ZvbPLYXOubYj7akPegLcfmOIof5nZl8GfuR9ux243cw627TQOfdAm+/V/whK+40hhP1PwaEPnHO3mNlK4FZ8Y6nH40uDTwFPuB6O1BXo40WCAJ7zOmARcBq+B6xm4kvYe4GngcXOudUBrn64ZQGnd1Je0EmZX2KsDway/WKt/w1q8/Vs79OZd4AHulh3ghjqf4Fuv5D2P/MuZ4iIiIh8Lj0cKSIiIn5TcBARERG/KTiIiIiI3xQcRERExG8KDiIiIuI3BQcRERHxm4KDiIiI+E3BQUSCxsx+YGa/CeHPe9fMZn7ONsPMbIuZJYeqXiLRRCNHikivmVnb2fbSgDp84+IDfNs5d18I63IZUOGc63b2ROfcQTNbDtwE/DIklROJIrriICK95pzLaPkAe4DL2pQ9G+LqfAf4Lz+3fRb4dhDrIhK1FBxEJGjM7F/N7Hfe12PMzJnZ35lZkZkdNbPvmNkcM1tvZmVm9liH/f/eu61w1MzeMLPRXfycJOA8fGP7t5SdZmarzKzczA6a2cNtdvkQOKmr44lI1xQcRCTUTsc3kdQ1wKPAD4HzgSnAQjObC2BmXwF+AFwJDAVWAM93ccwCoNk5t7dN2SJgkXMuCxgH/KFlhXOuEd+shNMDd1oisUHBQURC7afOuVrn3F+BKuB559wh51wxvnDQ8nDjt4H7nXNbvD/09wEzurhKkA1UdChrAMab2RDnXKVz7oMO6yu8/USkBxQcRCTUDrb5uqaT7zO8r0cDi7xbGGVAKWBAXifHPApkdij7FjABKDSzj83s0g7rM4Gy3p2CSOzSWxUi0l8VAff6+ZDlNsDMLM+7coFzbhvwVTOLw3e7Y4mZDXbOVZlZAjAeWBesyotEK11xEJH+6lfAPWY2BcDMBpjZgs42dM41AMuAuS1lZna9mQ11zjXTemWh5VXR04BdzrndQau9SJRScBCRfsk59xLwIPB7MysHNgIXdbPLr4Gvt/n+QmCTN9bEIuBa51ytt+5r+IKJiPSQOefCXQcRkYAws5XA7d0NAmVmOfhe25zZJkiIiJ8UHERERMRvulUhIiIiflNwEBEREb8pOIiIiIjfFBxERETEbwoOIiIi4jcFBxEREfGbgoOIiIj4TcFBRERE/Pb/AbVDQgq8MSr7AAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"## Solution set with the required dmdt for detonation at 300 meters\n",
"mdif = 0.25 - 0.05\n",
"dmdt = 0.07890353\n",
"seconds = mdif/dmdt\n",
"times = np.linspace(0,seconds, 1000)\n",
"dt = times[1] - times[0]\n",
"N = int(seconds/dt)\n",
"#Setting up Explicit numerical solution data set using the rk-2 step method\n",
"num_sol_rocket_300 = np.zeros([N,3]) \n",
" #Setting intial conditions\n",
"y0_rocket = 0 #m\n",
"v0_rocket = 0 #m/s\n",
"m0_rocket = 0.25 #kg\n",
"num_sol_rocket_300[0,0] = y0_rocket\n",
"num_sol_rocket_300[0,1] = v0_rocket\n",
"num_sol_rocket_300[0,2] = m0_rocket \n",
"for i in range(N-1):\n",
" num_sol_rocket_300[i+1] = rk2_step(num_sol_rocket_300[i],lambda state: rocket(state,0.07890353,u=250,c=0.18e-3) , dt)\n",
"# Now, num_sol_rocket_300 stores the numerical solution using the rk2 integration method for rocket\n",
"\n",
"y0_position_300 = num_sol_rocket_300[:,0]\n",
"time_to_300 = times[:-1]\n",
"plt.figure(figsize=(8,6));\n",
"plt.plot(time_to_300, y0_position_300);\n",
"plt.title('Height of Designed Rocket Until Detonation', fontsize = 16);\n",
"plt.xlabel('Time (s)', fontsize = 12);\n",
"plt.ylabel('Height (m)', fontsize = 12);\n",
"plt.plot(time_to_300[-1], y0_position_300[-1], '*', color = 'r', markersize = 14, label = 'Detonation at y0 = 300 Meters');\n",
"plt.legend(fontsize = 12);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## References\n",
"\n",
"1. Math 24 _Rocket Motion_. <https://www.math24.net/rocket-motion/\\>\n",
"\n",
"2. Kasdin and Paley. _Engineering Dynamics_. [ch 6-Linear Momentum of a Multiparticle System pp234-235](https://www.jstor.org/stable/j.ctvcm4ggj.9) Princeton University Press \n",
"\n",
"3. <https://en.wikipedia.org/wiki/Specific_impulse>\n",
"\n",
"4. <https://www.apogeerockets.com/Rocket_Motors/Estes_Motors/13mm_Motors/Estes_13mm_1_4A3-3T>"
]
}
],
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