{ "metadata": { "language": "Julia", "name": "", "signature": "sha256:9919ef874333610b1ee4df0fbdfab4fa9d44fc8244c838c9d47bd2f5a9e8ce60" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "3 Body Problem in Julia" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a test of the animation capabilities of Julia. I'm going to simulate the 3-body problem in 2D. This is largely based on \n", "\n", "http://nbviewer.ipython.org/github/pjpmarques/Julia-Modeling-the-World/blob/master/Three-Body%20Problem.ipynb\n", "\n", "but I've done the animation in Julia.\n", "\n", "We start by calling the relevant packages." ] }, { "cell_type": "code", "collapsed": false, "input": [ "using PyPlot\n", "using ODE\n", "using PyCall\n", "@pyimport matplotlib.animation as anim" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "INFO: Loading help data...\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The system of ODEs we are gong to solve will be of the form:\n", "\n", "$$\\frac{d^2\\mathbf{r}_i}{dt^2} = \\sum_j G\\frac{m_j}{||\\mathbf{r}_i-\\mathbf{r}_j||^3}(\\mathbf{r}_i-\\mathbf{r}_j)$$\n", "\n", "where of course each of the $\\mathbf{r}_i$ are position vectors for each planet.\n", "\n", "We'll turn this into a first order system by considering the equivalent set of equations:\n", "\n", "$$\\frac{d\\mathbf{r}_i}{dt} = \\mathbf{v}_i$$\n", "with \n", "$$\\frac{d\\mathbf{v}_i}{dt} = \\sum_j G\\frac{m_j}{||\\mathbf{r}_i-\\mathbf{r}_j||^3}(\\mathbf{r}_i-\\mathbf{r}_j)$$\n", "\n", "We'll encode all of the position and velocity vectors in one vector $y$, in the format:\n", "\n", "$$y = [\\text{First Planet's Position}, \\text{First Planet's Velocity}, \\text{Second Planet's Position}, \\text{Second Planet's Velocity},\\ldots]$$\n", "\n", "To start, we must define the right hand side of the sytem above, as this is what the ODE solver requires." ] }, { "cell_type": "code", "collapsed": false, "input": [ "function F(t,y)\n", " \n", " #Extract current position and velocity\n", " r1, v1 = y[1:2], y[3:4]\n", " r2, v2 = y[5:6], y[7:8]\n", " r3, v3 = y[9:10], y[11:12]\n", " \n", " \n", " #Give spatial derivatives\n", " dr1dt = v1\n", " dr2dt = v2\n", " dr3dt = v3\n", " \n", " \n", " #Work out velocity derivatives (ie accelerations)\n", " dv1dt = -(G*m2*(r1-r2)/(norm(r1-r2)^3) + G*m3*(r1-r3)/(norm(r1-r3)^3))\n", " dv2dt = -(G*m1*(r2-r1)/(norm(r2-r1)^3) + G*m3*(r2-r3)/(norm(r2-r3)^3))\n", " dv3dt = -(G*m1*(r3-r1)/(norm(r3-r1)^3) + G*m2*(r3-r2)/(norm(r3-r2)^3))\n", " \n", " #Combine back together into dydt vector\n", " dydt = [dr1dt,dv1dt,dr2dt,dv2dt,dr3dt,dv3dt]\n", " \n", " return dydt\n", "end" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 2, "text": [ "F (generic function with 1 method)" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now set the simulation parameters and integrate the equations of motion." ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Set the planetary masses\n", "m1 = 5\n", "m2 = 4\n", "m3 = 3\n", "\n", "#Set the gravitational field strength\n", "G = 1\n", "\n", "#Set initial positions and velocities \n", "r10 = [1.01,-1]; v10 = [0.0,0.0]\n", "r20 = [1.0,3.0]; v20 = [0.0,0.0]\n", "r30 = [-2.0,-1.0]; v30 = [0.0,0.0]\n", "\n", "#Specify simulation time and steps per second ('steps per second' is only for animation purposes, as ode23s is an adaptive solver.)\n", "tf = 50\n", "stepsPerUnitTime = 500\n", "\n", "#Solve the system\n", "y0 = [r10,v10,r20,v20,r30,v30]\n", "tspan = linspace(0,tf,tf*stepsPerUnitTime)\n", "t,y = ode23s(F, y0, tspan; points=:specified);\n", "\n", "#Extract the data into a useful form\n", "ymat= hcat(y...)\n", "r1x = ymat[1,:]\n", "r1y = ymat[2,:]\n", "r2x = ymat[5,:]\n", "r2y = ymat[6,:]\n", "r3x = ymat[9,:]\n", "r3y = ymat[10,:]\n", "r1x = reshape(r1x, length(r1x))\n", "r1y = reshape(r1y, length(r1y))\n", "r2x = reshape(r2x, length(r2x))\n", "r2y = reshape(r2y, length(r2y))\n", "r3x = reshape(r3x, length(r3x))\n", "r3y = reshape(r3y, length(r3y));" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting in Julia using PyPlot is quite straightforward, especially if you're a Matplotlib user. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Find Axis Limits\n", "xmin = minimum([r1x,r2x,r3x])\n", "xmax = maximum([r1x,r2x,r3x])\n", "xmin, xmax = xmin - 0.1(xmax-xmin), xmax+ 0.1*(xmax-xmin)\n", "ymin = minimum([r1y,r2y,r3y])\n", "ymax = maximum([r1y,r2y,r3y])\n", "ymin, ymax = ymin - 0.1(ymax-ymin), ymax+ 0.1*(ymax-ymin)\n", "\n", "#Construct Figure and Plot Data\n", "fig = figure()\n", "ax = plt.axes(xlim = (xmin,xmax),ylim=(ymin,ymax))\n", "ax[:plot](r1x,r1y, \"r-\")\n", "ax[:plot](r2x,r2y, \"g-\")\n", "ax[:plot](r3x,r3y, \"b-\")\n", " \n", "#Plot start and end points\n", "ax[:plot](r1x[1],r1y[1], \"ro\")\n", "ax[:plot](r1x[end],r1y[end], \"rs\")\n", "ax[:plot](r2x[1],r2y[1], \"go\")\n", "ax[:plot](r2x[end],r2y[end], \"gs\")\n", "ax[:plot](r3x[1],r3y[1], \"bo\")\n", "ax[:plot](r3x[end],r3y[end], \"bs\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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", "text": [ "Figure(PyObject )" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "1-element Array{Any,1}:\n", " PyObject " ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Animation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PyPlot's animation syntax is very similar to matplotlib, but there are some idiosyncrasies:\n", "\n", "1. We write ax[:plot] rather than ax.plot\n", "2. The animate function takes an input i, which increases by $1$ each frame. However, on the first frame $i = 0$, rather than $1$, because this is Python, not Julia. The simplest way to avoid confusion is to define $k = i+1$ as I have done.\n", "3. Rather than writing \n", "\n", "line, = ax.plot([], []) \n", "\n", "we write \n", "\n", "line = ax[:plot]([],[])[1].\n", "\n", "I find Matplotlib's animation tools very intuitive and powerful, and it's fantastic that they're so easy to use in Julia. I haven't explained all the details of the animation below, because it's so similar to standard matplotlib. A great tutorial on making animations with Matplotlib is here:\n", "\n", "https://jakevdp.github.io/blog/2012/08/18/matplotlib-animation-tutorial/" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Use External Viewer for Animation\n", "pygui(true)\n", "\n", "#Find Axis Limits\n", "xmin = minimum([r1x,r2x,r3x])\n", "xmax = maximum([r1x,r2x,r3x])\n", "xmin, xmax = xmin - 0.1(xmax-xmin), xmax+ 0.1*(xmax-xmin)\n", "ymin = minimum([r1y,r2y,r3y])\n", "ymax = maximum([r1y,r2y,r3y])\n", "ymin, ymax = ymin - 0.1(ymax-ymin), ymax+ 0.1*(ymax-ymin)\n", "\n", "#Construct Figure and Plot Data\n", "fig = figure()\n", "ax = plt.axes(xlim = (xmin,xmax),ylim=(ymin,ymax))\n", "global line1 = ax[:plot]([],[],\"r-\")[1]\n", "global line2 = ax[:plot]([],[],\"g-\")[1]\n", "global line3 = ax[:plot]([],[],\"b-\")[1]\n", "global p1 = ax[:plot]([],[],\"or\")[1]\n", "global p2 = ax[:plot]([],[],\"og\")[1]\n", "global p3 = ax[:plot]([],[],\"ob\")[1]\n", "\n", "function init()\n", " global line1\n", " global line2\n", " global line3\n", " global p1\n", " global p2\n", " global p3\n", " line1[:set_data]([],[])\n", " line2[:set_data]([],[])\n", " line3[:set_data]([],[])\n", " p1[:set_data]([],[])\n", " p2[:set_data]([],[])\n", " p3[:set_data]([],[])\n", " return (line1,line2,line3,p1,p2,p3,None)\n", "end\n", "\n", "step = 15\n", "function animate(i)\n", " k = i + 1\n", " global line1\n", " global line2\n", " global line3\n", " global p1\n", " global p2\n", " global p3 \n", " line1[:set_data](r1x[max(1,step*(k-50)):(step*k)],r1y[max(1,step*(k-50)):(step*k)])\n", " line2[:set_data](r2x[max(1,step*(k-50)):(step*k)],r2y[max(1,step*(k-50)):(step*k)])\n", " line3[:set_data](r3x[max(1,step*(k-50)):(step*k)],r3y[max(1,step*(k-50)):(step*k)])\n", " p1[:set_data]([r1x[step*k]],r1y[step*k])\n", " p2[:set_data]([r2x[step*k]],r2y[step*k])\n", " p3[:set_data]([r3x[step*k]],r3y[step*k])\n", " return (line1,line2,line3,None)\n", "end\n", "\n", "#Call the animator.\n", "myanim = anim.FuncAnimation(fig, animate, init_func=init, frames=ifloor(length(t)/step), interval=20)\n", "\n", "#This will require ffmpeg or equivalent.\n", "#myanim[:save](\"3Body2D.mp4\", bitrate=-1, extra_args=[\"-vcodec\", \"libx264\", \"-pix_fmt\", \"yuv420p\"])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "PyObject " ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Animation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Function for creating an embedded video given a filename\n", "function html_video(filename)\n", "\tbase64_video = base64(open(readbytes, filename))\n", "\t\"\"\"