{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Nutation and Precession of a gyroscope\n", "\n", "From the IB Dynamics course, the [equations of motion for a symmetric top](http://www-teach.phy.cam.ac.uk/dms/dms_getFile.php?node=9980) can be written as:\n", "\n", "$$\n", "\\frac{1}{2}I_1 \\dot{\\theta}^2 = E - \\frac{(J_z-J_3 \\cos \\theta)^2}{2I_1 \\sin^2 \\theta} - mgh\\cos\\theta - \\frac{J_3^2}{2I_3}\n", "$$\n", "\n", "$$\n", "I_1\\ddot{\\theta} = mgh\\sin\\theta-\\frac{J_3(J_z-J_3 \\cos \\theta)}{I_1 \\sin \\theta}+\\frac{(J_z-J_3 \\cos \\theta)^2\\cos\\theta}{I_1 \\sin^3\\theta}\n", "$$\n", "\n", "$$\n", "\\dot{\\phi} = \\frac{J_z-J_3 \\cos \\theta}{I_1 \\sin^2 \\theta}\n", "$$\n", "\n", "$$\n", "\\dot{\\chi} = \\frac{J_3}{I_3}+\\frac{J_3\\cos^2\\theta-J_z\\cos\\theta}{I_1 \\sin^2\\theta}\n", "$$\n", "\n", "By integrating the second equation, which is the time derivative of the first, to find $\\dot{\\theta}$, the angle $\\theta(t)$ can be found and this can be used to integrate both $\\chi$ and $\\phi$.\n", "\n", "First suitable values for the free parameters must be found. By writing the energy equation as the following:\n", "\n", "$$\n", "\\frac{1}{2}I_1 \\dot{\\theta}^2 = E - \\frac{(J_z-J_3 \\cos \\theta)^2}{2I_1 \\sin^2 \\theta} - mgh\\cos\\theta - \\frac{J_3^2}{2I_3} = E - U_{eff}(\\theta)\n", "$$\n", "\n", "The effective potential can be used to find the range of $\\theta$ values for a given energy." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "from scipy.integrate import odeint\n", "\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib.patches import FancyArrowPatch\n", "from mpl_toolkits.mplot3d import proj3d\n", "from matplotlib.animation import FuncAnimation\n", "%matplotlib inline\n", "\n", "from pycav import display\n", "\n", "E = 71.\n", "# I_1 and I_3\n", "I = [0.1,0.05]\n", "# J_z and J_3\n", "J = [2.,2.5]\n", "m = 1.\n", "h = 1.\n", "\n", "def Ueff(theta,I,J,m,h):\n", " return (J[0]-J[1]*np.cos(theta))**2/(2*I[0]*(np.sin(theta))**2)+m*9.81*h*np.cos(theta)+J[1]**2/(2*I[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Effective Potential plot\n", "\n", "By looking at the plot below, one can find the maximum and minimal values of $\\theta$ for the given energy value, $E$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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REckPLBMynIjvvhnj7392yU2bNhEWFsbTTz+Ni4sLFSpUYMGCBbz22mvWfbp160bdunUB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\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta = np.linspace(0.2,np.pi/2.,1000)\n", "fig1 = plt.figure(figsize = (15,9));\n", "ax1 = fig1.add_subplot(111);\n", "ax1.plot(theta,Ueff(theta,I,J,m,h));\n", "ax1.plot(theta,(J[0]-J[1]*np.cos(theta))**2/(2*I[0]*(np.sin(theta))**2)+J[1]**2/(2*I[1]));\n", "ax1.plot(theta,m*9.81*h*np.cos(theta));\n", "ax1.axhline(E,c = 'k',ls = '-.');\n", "ax1.set_xlim((theta.min(),theta.max()));\n", "ax1.set_xlabel('Theta');\n", "ax1.legend(('Effective Potential','Ang. Mom. Term','Gravitational Term','Energy'));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using odeint from SciPy to numerically integrate our equations of motion\n", "\n", "With suitable free parameters chosen, the equations can be integrated using SciPy's odeint function to give us the angles as functions of time\n", "\n", "Here we define $\\omega = \\dot{\\theta}$ so the set of first order differential equations we are solving are:\n", "\n", "$$\n", "\\dot{\\omega} = \\frac{1}{I_1} \\left( mgh\\sin\\theta-\\frac{J_3(J_z-J_3 \\cos \\theta)}{I_1 \\sin \\theta}+\\frac{(J_z-J_3 \\cos \\theta)^2\\cos\\theta}{I_1 \\sin^3\\theta} \\right)\n", "$$\n", "\n", "$$\n", "\\dot{\\theta} = \\omega\n", "$$\n", "\n", "$$\n", "\\dot{\\phi} = \\frac{J_z-J_3 \\cos \\theta}{I_1 \\sin^2 \\theta}\n", "$$\n", "\n", "$$\n", "\\dot{\\chi} = \\frac{J_3}{I_3}+\\frac{J_3\\cos^2\\theta-J_z\\cos\\theta}{I_1 \\sin^2\\theta}\n", "$$\n", "\n", "odeint takes a list of starting values, [$\\omega_0$, $\\theta_0$, $\\phi_0$, $\\chi_0$], and takes a function which returns a list of the time derivatives, [$\\dot{\\omega}$, $\\dot{\\theta}$, $\\dot{\\phi}$, $\\dot{\\chi}$], and returns a list containing the input variables evaluated at the times given, [$\\omega(t)$, $\\theta(t)$, $\\phi(t)$, $\\chi(t)$]\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def omega_dot(theta,E,I,J,m,h):\n", " return (1/I[0])*(m*9.81*h*np.sin(theta)-\n", " (J[1]*(J[0]-J[1]*np.cos(theta)))/(I[0]*np.sin(theta))+\n", " (J[0]-J[1]*np.cos(theta))**2*np.cos(theta)/(I[0]*(np.sin(theta))**3))\n", "\n", "def theta_dot(theta,E,I,J,m,h):\n", " rot_energy = E-Ueff(theta,I,J,m,h)\n", " return np.sqrt(2*rot_energy/I[0])\n", "\n", "def phi_dot(theta,E,I,J,m,h):\n", " return (J[0]-J[1]*np.cos(theta))/(I[0]*(np.sin(theta))**2)\n", "\n", "def chi_dot(theta,E,I,J,m,h):\n", " return (J[1]*(np.cos(theta))**2-J[0]*np.cos(theta))/(I[0]*(np.sin(theta))**2)+J[1]/I[1]\n", "\n", "def derivatives(q,t,E,I,J,m,h):\n", " omega = q[0]\n", " theta = q[1]\n", " dqdt = [omega_dot(theta,E,I,J,m,h),omega,phi_dot(theta,E,I,J,m,h),chi_dot(theta,E,I,J,m,h)]\n", " return dqdt\n", "\n", "starting_angles = [0.8,0.,0.]\n", "q0 = [theta_dot(starting_angles[0],E,I,J,m,h),starting_angles[0],starting_angles[1],starting_angles[2]]\n", "t = np.linspace(0.,3.5,500)\n", "\n", "sol = odeint(derivatives,q0,t,args = (E,I,J,m,h))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting the motion of the gyroscope\n", "\n", "Converting these angles into Cartesian coordinates allows us to plot the trajectory of the centre of the mass" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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g4MCBuP32240VcNy9G7jmmp73Z2YCRUVAVZWpNt5///2Gn5cKEyZMQG5uLu6+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\nWRYOhwN2u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iwTCAQAKpUC1CioJAnhjz90Mb9mDeLatZGvBb8ftUMHpHbt0Dp2RD77bF3o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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta = sol[:,1]\n", "phi = sol[:,2]\n", "chi = sol[:,3]\n", "\n", "x,y,z = h*np.sin(theta)*np.cos(phi),h*np.sin(theta)*np.sin(phi),h*np.cos(theta)\n", "\n", "# Create cubic bounding box to simulate equal aspect ratio\n", "max_range = np.array([x.max()-x.min(), y.max()-y.min(), z.max()-z.min()]).max()\n", "Xb = 0.5*max_range*np.array((-1.,1.)) + 0.5*(x.max()+x.min())\n", "Yb = 0.5*max_range*np.array((-1.,1.)) + 0.5*(y.max()+y.min())\n", "Zb = 0.5*max_range*np.array((-1.,1.)) + 0.5*(z.max()+z.min())\n", "\n", "fig2 = plt.figure(figsize = (18,8));\n", "fig2.suptitle('Resultant Motion of Gyroscope', fontsize = 15);\n", "ax2 = fig2.add_subplot(121, projection='3d');\n", "ax2.set_aspect('equal');\n", "ax2.set_xlim3d((Xb[0],Xb[-1]));\n", "ax2.set_ylim3d((Yb[0],Yb[-1]));\n", "ax2.set_zlim3d((Zb[0],Zb[-1]));\n", "\n", "ax2.plot(x,y,z,'r');\n", "\n", "ax3 = fig2.add_subplot(122);\n", "ax3.plot(t,x,'r');\n", "ax3.plot(t,y,'b');\n", "ax3.plot(t,z,'k');\n", "ax3.legend(('x','y','z'));\n", "ax3.set_xlabel('t');\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Animating this behaviour" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "class Arrow3D(FancyArrowPatch):\n", " def __init__(self, xs, ys, zs, *args, **kwargs):\n", " FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)\n", " self._verts3d = xs, ys, zs\n", "\n", " def draw(self, renderer):\n", " xs3d, ys3d, zs3d = self._verts3d\n", " xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n", " self.set_positions((xs[0],ys[0]),(xs[1],ys[1]))\n", " FancyArrowPatch.draw(self, renderer)\n", "\n", "fig = plt.figure(figsize = (12,12));\n", "ax = fig.add_subplot(111, projection='3d');\n", "ax.set_aspect('equal');\n", "\n", "qx = 0.5*x+0.1*h*(np.cos(theta)*np.cos(phi)*np.cos(chi)-np.sin(phi)*np.sin(chi))\n", "qy = 0.5*y+0.1*h*(np.cos(theta)*np.sin(phi)*np.cos(chi)+np.cos(phi)*np.sin(chi))\n", "qz = 0.5*z+0.1*h*(-np.sin(theta)*np.cos(chi))\n", "\n", "def nextframe(arg):\n", " n = arg*2\n", " ax.clear()\n", " ax.plot([0.5*x[n],qx[n]],[0.5*y[n],qy[n]],[0.5*z[n],qz[n]],'k-',lw = 3)\n", " a = Arrow3D([0., x[n]], [0., y[n]], \n", " [0., z[n]], mutation_scale=20, \n", " lw=3, arrowstyle=\"-|>\", color=\"r\")\n", " ax.add_artist(a)\n", " ax.plot(x[:n],y[:n],z[:n],'r')\n", " ax.set_xlim3d((Xb[0],Xb[-1]))\n", " ax.set_ylim3d((Yb[0],Yb[-1]))\n", " ax.set_zlim3d((Zb[0],Zb[-1]))\n", "\n", "animate = FuncAnimation(fig,nextframe, interval = 75, frames = int(len(t)/2), repeat = False)\n", "animate = display.create_animation(animate, temp = True)\n", "display.display_animation(animate)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }