{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from tempfile import NamedTemporaryFile\n",
"#import base64\n",
"\n",
"VIDEO_TAG = \"\"\"\"\"\"\n",
"\n",
"def anim_to_html(anim):\n",
" if not hasattr(anim, '_encoded_video'):\n",
" with NamedTemporaryFile(suffix='.mp4') as f:\n",
" anim.save(f.name, writer='mencoder', fps=20) #extra_args=['-vcodec', 'libx264'])\n",
" video = open(f.name, \"rb\").read()\n",
" anim._encoded_video = video.encode(\"base64\")\n",
" \n",
" return VIDEO_TAG.format(anim._encoded_video)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from IPython.display import HTML\n",
"\n",
"def display_animation(anim):\n",
" plt.close(anim._fig)\n",
" return HTML(anim_to_html(anim))"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from matplotlib import animation\n",
"\n",
"# First set up the figure, the axis, and the plot element we want to animate\n",
"fig = plt.figure()\n",
"ax = plt.axes(xlim=(0, 2), ylim=(-2, 2))\n",
"line, = ax.plot([], [], lw=2)\n",
"\n",
"# initialization function: plot the background of each frame\n",
"def init():\n",
" line.set_data([], [])\n",
" return line,\n",
"\n",
"# animation function. This is called sequentially\n",
"def animate(i):\n",
" x = np.linspace(0, 2, 1000)\n",
" y = np.sin(2 * np.pi * (x - 0.01 * i))\n",
" line.set_data(x, y)\n",
" return line,\n",
"\n",
"# call the animator. blit=True means only re-draw the parts that have changed.\n",
"anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
" frames=100, interval=20, blit=True)\n",
"\n",
"# call our new function to display the animation\n",
"display_animation(anim)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
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"source": [
"#! /usr/bin/env python2.7\n",
"# Double pendulum formula translated from the C code at\n",
"# http://www.physics.usyd.edu.au/~wheat/dpend_html/solve_dpend.c\n",
"\n",
"from numpy import sin, cos, pi, array\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import scipy.integrate as integrate\n",
"import matplotlib.animation as animation\n",
"\n",
"G = 9.8 # acceleration due to gravity, in m/s^2\n",
"L1 = 1.0 # length of pendulum 1 in m\n",
"L2 = 1.0 # length of pendulum 2 in m\n",
"M1 = 1.0 # mass of pendulum 1 in kg\n",
"M2 = 1.0 # mass of pendulum 2 in kg\n",
"\n",
"\n",
"def derivs(state, t):\n",
"\n",
" dydx = np.zeros_like(state)\n",
" dydx[0] = state[1]\n",
"\n",
" del_ = state[2]-state[0]\n",
" den1 = (M1+M2)*L1 - M2*L1*cos(del_)*cos(del_)\n",
" dydx[1] = (M2*L1*state[1]*state[1]*sin(del_)*cos(del_)\n",
" + M2*G*sin(state[2])*cos(del_) + M2*L2*state[3]*state[3]*sin(del_)\n",
" - (M1+M2)*G*sin(state[0]))/den1\n",
"\n",
" dydx[2] = state[3]\n",
"\n",
" den2 = (L2/L1)*den1\n",
" dydx[3] = (-M2*L2*state[3]*state[3]*sin(del_)*cos(del_)\n",
" + (M1+M2)*G*sin(state[0])*cos(del_)\n",
" - (M1+M2)*L1*state[1]*state[1]*sin(del_)\n",
" - (M1+M2)*G*sin(state[2]))/den2\n",
"\n",
" return dydx\n",
"\n",
"# create a time array from 0..100 sampled at 0.1 second steps\n",
"dt = 0.05\n",
"t = np.arange(0.0, 20, dt)\n",
"\n",
"# th1 and th2 are the initial angles (degrees)\n",
"# w10 and w20 are the initial angular velocities (degrees per second)\n",
"th1 = 120.0\n",
"w1 = 0.0\n",
"th2 = -10.0\n",
"w2 = 0.0\n",
"\n",
"rad = pi/180\n",
"\n",
"# initial state\n",
"state = np.array([th1, w1, th2, w2])*pi/180.\n",
"\n",
"# integrate your ODE using scipy.integrate.\n",
"y = integrate.odeint(derivs, state, t)\n",
"\n",
"x1 = L1*sin(y[:,0])\n",
"y1 = -L1*cos(y[:,0])\n",
"\n",
"x2 = L2*sin(y[:,2]) + x1\n",
"y2 = -L2*cos(y[:,2]) + y1\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, autoscale_on=False, xlim=(-2, 2), ylim=(-2, 2))\n",
"ax.grid()\n",
"\n",
"line, = ax.plot([], [], 'o-', lw=2)\n",
"time_template = 'time = %.1fs'\n",
"time_text = ax.text(0.05, 0.9, '', transform=ax.transAxes)\n",
"\n",
"def init():\n",
" line.set_data([], [])\n",
" time_text.set_text('')\n",
" return line, time_text\n",
"\n",
"def animate(i):\n",
" thisx = [0, x1[i], x2[i]]\n",
" thisy = [0, y1[i], y2[i]]\n",
"\n",
" line.set_data(thisx, thisy)\n",
" time_text.set_text(time_template%(i*dt))\n",
" return line, time_text\n",
"\n",
"ani = animation.FuncAnimation(fig, animate, np.arange(1, len(y)),\n",
" interval=25, blit=True, init_func=init)\n",
"\n",
"ani.save('double_pendulum.mp4', writer='mencoder', fps=15)\n",
"# ani.save('double_pendulum.mp4', fps=15, clear_temp=True)"
]
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