{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Plot projectile motion \n", "$$\n", "\\frac{ d}{dt}\\vec r(t) = -mg \\hat e_3\n", "$$" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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BxhslTsbbxZ26b73F5gMHUn3GDOZtvTVTzziDXwsLVZyVQT8z66bSH3+w6fDhNHn0Udab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\nRETyQ/v20LYt9OoFCxfGTpMWFWoiIiK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "#work in MKS units\n", "T = 10 #seconds\n", "g = 9.8 #m/sec**2\n", "Dt = 0.1 #seconds\n", "Zint = 5 #fix initial position\n", "Vzint = 40 #fix initial velocity\n", "Nsteps = int(T/Dt)\n", "t = np.zeros(Nsteps, ) # numpy array holding the Nstep+1 values of the time\n", "z = np.zeros(Nsteps, ) # numpy array holding the Nstep+1 values of the vertical position\n", "for n in range(0,Nsteps):\n", " t[n] = Dt*n\n", " z[n] = Zint + Vzint*t[n] - 0.5*g*t[n]**2\n", "fig = plt.figure(figsize=(10,6)) #create a fig object named \"fig\"\n", "Plot = fig.add_subplot(111) #create an axis object within \"fig\" named \"Plot\"\n", "Plot.plot(t,z,'r-') #Add a curve described by the arrays t and z to Plot, choose a red solid curve.\n", "Plot.set(xlabel='time (t)', ylabel='vertical position (z)', # add a tile and axis labels.\n", " title='One-dimensional motion') \n", "Plot.grid() #superimpose a grid on Plot\n", "#fig.savefig(\"test.png\") # save the figure as a png file.\n", "plt.show(fig) # Plot the figure here.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Next add x-direction motion" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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q1HJZv36hCrvrLqhX7383f/klHHpoqOPGj4eddoqYUUSkkJ15JtxzD4wdC2ec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\nzZpB584wZ07sNBJLOoXaytS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jMvI5ss3ixYupWLFi7BiyFp2X5NK5SSadl+QqynOzYEFp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\nOhM4hHKnb36PJ0vfATzxGsqOiDbKgNKI2NtmATf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Xint=12\n", "Vxint=10\n", "x = np.zeros(Nsteps, ) # numpy array holding the Nstep+1 values of the horizontal position\n", "for n in range(0,Nsteps):\n", " x[n] = Xint + Vxint*t[n]\n", "#Fig2D, (Plot2D) = plt.subplots(nrows=1, figsize=(10, 6)) #create a fig object named \"Plot2D\"\n", "Fig2D = plt.figure(figsize=(10,6)) #create a fig object named \"Fig2D\"\n", "Plot2D = Fig2D.add_subplot(111) #create an axis object within FIg2D named \"Plot2D\"\n", "Plot2D.plot(x,z,'b-') #Add a curve described by the arrays x and z to Plot2D, choose a blue solid curve.\n", "Plot2D.set(xlabel='horizontal position (x)', ylabel='vertical position (z)', # add a tile and axis labels.\n", " title='Two-dimensional motion') \n", "Plot2D.grid() #superimpose a grid on Plot\n", "#fig.savefig(\"test.png\") # save the figure as a png file.\n", "#plt.show(Fig2D) # Plot the figure here.\n", "#\n", "Points_X = np.zeros(2, )\n", "Points_Z = np.zeros(2, )\n", "Points_X[0] = Xint\n", "Points_Z[0] = Zint\n", "DeltaX=15\n", "Points_X[1] = Points_X[0] + DeltaX\n", "Points_Z[1] = Points_Z[0] + DeltaX*Vzint/Vxint\n", "Plot2D.plot(Points_X,Points_Z,'r-') #Add this line to Plot2D axis object, choose a red solid curve.\n", "plt.show(Fig2D)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }