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@Nirav-Madhani
Last active July 6, 2021 12:10
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Untitled3.ipynb",
"provenance": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 625
},
"id": "WmUKUvA_eEB_",
"outputId": "6722138b-f18d-4bf9-c1d5-96279b832536"
},
"source": [
"import numpy as np\n",
"from scipy.integrate import odeint\n",
"import matplotlib.pyplot as plt\n",
"import sys,math\n",
"from scipy.integrate import simps\n",
"from sklearn.metrics import auc\n",
"from scipy.interpolate import interp1d\n",
"\n",
"g= 9.81\n",
"m0 = 500\n",
"F = 2.5*9.81*m0\n",
"n = 5\n",
"b=.3\n",
"\n",
"sqrt = np.sqrt\n",
"t = np.linspace(0,m0/n-1,1000)\n",
"\n",
"def v0Function(ve):\n",
"\n",
" def velocity(v,t):\n",
" return (m0*g-b*v*v)/m0 #Changed Here\n",
" def height_diff(x,t):\n",
" return np.sqrt(g*m0/b)*np.tanh(t*np.sqrt(b*g*m0))\n",
" v0,y0 = ve,0 \n",
" v = odeint(velocity,v0,t)\n",
" return v.ravel() \n",
"\n",
"def find_h1_with_drag(v0,info=False):\n",
" v0 = abs(v0)\n",
" def b_velocity(v,t):\n",
" return g - (b*v*v + F)/(m0-n*t)\n",
" v_b = odeint(b_velocity,v0,t)\n",
" pt = np.argmin(abs(v_b))\n",
" height = auc(t[:pt],v_b[:pt])\n",
" if info:\n",
" return height, pt, v_b\n",
" return height\n",
"\n",
"def find_h(h,ve):\n",
" \n",
" v_free = v0Function(ve)\n",
" plt.plot(t,v_free)\n",
" plt.show()\n",
" def vt(y,tt):\n",
" pt = np.argmin(abs(t-tt))\n",
" return v_free[pt]\n",
" y = odeint(vt,0,t)\n",
" plt.plot(t,y)\n",
" plt.show()\n",
" pt = np.argmin(h-y)\n",
" for i in range(pt,-1,-1):\n",
" h0,v0 = y[i],v_free[i]\n",
" h1 = find_h1_with_drag(v0)\n",
" if h1 > 0 and h1+h0<h:\n",
" return h0,max(h1,h-h0)\n",
"\n",
"print(find_h(3000,1000))\n",
"print(F)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
},
{
"output_type": "stream",
"text": [
"/usr/local/lib/python3.7/dist-packages/scipy/integrate/odepack.py:248: ODEintWarning: Excess work done on this call (perhaps wrong Dfun type). Run with full_output = 1 to get quantitative information.\n",
" warnings.warn(warning_msg, ODEintWarning)\n"
],
"name": "stderr"
},
{
"output_type": "stream",
"text": [
"(array([356.45014909]), array([2643.54985091]))\n",
"12262.500000000002\n"
],
"name": "stdout"
}
]
}
]
}
numpy
scipy
matplotlib
sklearn
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