{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Plot projectile motion \n", "$$\n", "m\\frac{ d}{dt}\\vec r(t) = -mg \\hat e_3\n", "$$" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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8Mlzy1KrbIiLp23nnMGTk66/h8MPDhCyRhFGhlqtefRVOOgn23hsefRSKimIn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\n", "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+1, ) # numpy array holding the Nstep+1 values of the time\n", "z = np.zeros(Nsteps+1, ) # numpy array holding the Nstep+1 values of the vertical position\n", "for n in range(0,Nsteps+1):\n", " t[n] = Dt*n\n", " z[n] = Zint + Vzint*t[n] - 0.5*g*t[n]**2\n", "#fig, (Plot) = plt.subplots(nrows=1, figsize=(10, 6)) #create a fig object named \"Plot\"\n", "fig = plt.figure(figsize=(10,6))\n", "Plot = fig.add_subplot(111)\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.pdf\") # save the figure as a png file.\n", "plt.show(fig) # Plot the figure here." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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N7hSRbHLuuWHM1OjRof/aqlWxE4kUnAq1bPPrr+G85i67wEMPhSk5CBNEtmoF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\nMHNm/vsXB7H6qN1hZp+a2QygBXAlgLt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Next add x-direction motion\n", "Xint=12\n", "Vxint=10\n", "x = np.zeros(Nsteps+1, ) # numpy array holding the Nstep+1 values of the horizontal position\n", "zz = np.zeros(Nsteps+1, ) \n", "for n in range(0,Nsteps+1):\n", " x[n] = Xint + Vxint*t[n]\n", " zz[n]=z[n]\n", "#Fig2D, (Plot2D) = plt.subplots(nrows=1, figsize=(10, 6)) #create a fig object named \"Plot2D\"\n", "Fig2D = plt.figure(figsize=(10,6))\n", "Plot2D = Fig2D.add_subplot(111)\n", "Plot2D.plot(x,zz,'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, choose a red solid curve.\n", "plt.show(Fig2D)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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 }