{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Classical motion of mercury\n", "## Modeling\n", "Let $m$ be the mass of mercury, $M$ the mass of the sun and $G$ the gravitational constant. We will use heliocentric coordinates so that the position of the sun is always $(0,0)$ and the position of Mercury will be denoted $(q_1,q_2)$. \n", "* The Kinetic energy of the system is $K(\\dot{q})=\\frac{1}{2}m||\\dot{q}||^2$.\n", "* The Potential energy of the system is $U(q)=\\frac{-GmM}{||q||}$.\n", "* The total energy of the system is $H=K+U=\\frac{1}{2}m||\\dot{q}||^2 -\\frac{GmM}{||q||}$.\n", "\n", "## Nondimensionalization\n", "We introduce the following dimensionless quantities: dimensionless time $\\bar{t}=t/T$ with $\\frac{1}{T}=\\sqrt{\\frac{GM}{D^3}}$ (where $D$ is the perihelion of Mercury); dimensionless coordinates $\\bar{q}=q/D$; and dimensionless energy $\\bar{H} = \\frac{H}{E_0}$, where $E_0=\\frac{mMG}{D}$. \n", "\n", "The dimensionless mechanical system is then seen to have a Hamiltonian which reads (omitting the bars)\n", "$$H(q,p)= \\frac{1}{2}(p_1^2+p_2^2) - \\frac{1}{\\sqrt{q_1^2+q_2^2}}.$$\n", "Since in these rescaled units the mass is unity, the momenta and the velocities coincide: $p=\\dot{q}$.\n", "Note that one unit of rescaled time corresponds roughly to 10 earth days. \n", "\n", "## Equations of motion\n", "\\begin{equation}\n", "\\left\\lbrace\n", "\\begin{array}{ccc}\n", "\\dot{q}&=&p \\\\\n", "\\dot{p}&=&-\\frac{1}{||q||^3}q\n", "\\end{array}\n", "\\right.\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "26.7626114716\n", "3685.21916683\n", "1.05362948631\n" ] } ], "source": [ "# Constantes physiques\n", "G=6.67408e-11 #m^3 kg^-1 s^-2\n", "m = 3.285e+23 #mass of mercury in kg\n", "M = 1.989e30 #mass of the sun kg\n", "D = 46001200*1000 #perihelion of mercury in m\n", "T = np.sqrt(D**3/(M*G)) #time scale\n", "print 265.25*24*3600/T #One earth year corresponds to 26 units of rescaled time\n", "e = 0.205630 #eccentricity as measured by nasa in nov 2007\n", "# Temps pendant lequel on veut simuler le systeme\n", "years = 100.\n", "tbarf = years*365.25*24*3600./T#final rescaled time, corresponding to N earth years \n", "print tbarf\n", "#Initial conditions:\n", "q1init, q2init = 1., 0.\n", "p1init, p2init = 0., T/D*56.6e3\n", "print p2init\n", "x0 = np.array([q1init,q2init,p1init,p2init])\n", "#Dynamics right hand side x=(q1,q2,p1,p2), t=time (all rescaled)\n", "def f(x,t):\n", " return np.concatenate((x[2:4],-np.linalg.norm(x[0:2])**(-3) * x[0:2]))\n", " #-mu*np.linalg.norm(x[0:2])**(-5) * x[0:2]))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Integration avec odeint de scipy, c'est une methode de Adams-Bashforth\n", "times = np.linspace(0,tbarf,10000)\n", "states = odeint(f, x0, times)\n", "plt.plot(states[:,0],states[:,1],'b-',label='odeint')\n", "plt.legend()\n", "plt.grid()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "H = lambda x: 0.5*(x[2:4].dot(x[2:4])) - 1./np.linalg.norm(x[0:2])\n", "Harray = np.array([H(xs) for xs in states])" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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C2AQWwt3TsmVw0EHlVOQ4DQ+f/OCkJu+cBJ1Dh1ZvAGsWHkL42GM790mCzrrg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\ns43RV78KQ4bsvM2R07goNDC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(times, Harray, label='odeint')\n", "plt.title('Total Energy')\n", "plt.grid()\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#Methode a pas separes du TD, changer les valeurs des coeffs alpha, \n", "# beta et gamma pour observer le comportement (consistence, ordre, stabilite)\n", "def phi_mps(x,t,h):\n", " alpha=0\n", " gamma,beta =0.5,0.5\n", " return beta*f(x,t) +gamma*f(x +alpha*h*f(x,t), t+alpha*h) \n", "# Euler Explicite\n", "def phi_explicit_euler(x,t,h):\n", " return f(x,t)\n", "# RK2 avec coefficients classiques\n", "def phi_rk2(x,t,h): #beta=0,gamma =1 , alpha=1/2 \n", " return f(x +h/2.*f(x,t), t+h/2.) \n", "# Integrateur\n", "def integ(phi, tf, h):\n", " t, sol = 0., [x0]\n", " times=[0.]\n", " while t +h/2. < tf:\n", " x=sol[-1]\n", " sol.append(x + h*phi(x,t,h))\n", " t+=h\n", " times.append(t)\n", " return np.array(sol), times" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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IMDq80cvLGDmadIai2FgWEUOCSSrL6Ph0HRmjTWvtH5hZwfxlS0xMFNu/mLjt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Integration\n", "h=0.01\n", "TF = tbarf\n", "euler_states, euler_times = integ(phi_explicit_euler,TF,h) #euler\n", "rk2_states, rk2_times = integ(phi_rk2,TF,h) #rk2 classique\n", "#mps_states, mps_times = integ(phi_mps,TF,h) #methode du TD\n", "\n", "#Affichage\n", "plt.plot(states[:,0],states[:,1],label='odeint') #solution avec LSODA\n", "plt.plot(euler_states[:,0],euler_states[:,1],'r-',label='euler') #solution euler\n", "#plt.plot(mps_states[:,0], mps_states[:,1],label='mps') #solution methode TD2\n", "plt.legend()\n", "plt.grid()\n", "plt.show()\n", "plt.plot(rk2_states[:,0],rk2_states[:,1],'g-',label='rk2') #solution rk2\n", "plt.plot(states[:,0],states[:,1],label='odeint') #solution avec LSODA\n", "plt.legend()\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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qY5qtcyxOl9kU93lot1vY9mG63V7E6bp7132+EKhQ1V+2kCsOKFPV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\n3P8Hy5H9FI6Nk1MAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Comportement energetique des differents integrateurs\n", "Hrk2 = np.array([H(xs) for xs in rk2_states])\n", "plt.plot(rk2_times,Hrk2,label='rk2')\n", "plt.plot(times, Harray,label='odeint')\n", "plt.legend()\n", "plt.grid()\n", "plt.title('Total Energy')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }