{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Triple Pendulum CHAOS!" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "*This notebook originally appeared as a [post](http://jakevdp.github.io/blog/2017/03/08/triple-pendulum-chaos/) on the blog [Pythonic Perambulations](http://jakevdp.github.io). The content is MIT licensed.*" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "\n", "\n", "Earlier this week a tweet made the rounds which features a video that nicely demonstrates chaotic dynamical systems in action:\n", "\n", "

A visualization of chaos: 41 triple pendulums with very slightly different initial conditions pic.twitter.com/CTiABFVWHW

— Fermat's Library (@fermatslibrary) March 5, 2017
\n", "\n", "\n", "*Edit: a reader pointed out that the original creator of this animation [posted it on reddit](https://www.reddit.com/r/mathpics/comments/4nd5h1/41_triple_pendulums_with_very_slightly_different/) in 2016.*\n", "\n", "Naturally, I immediately wondered whether I could reproduce this simlulation in Python.\n", "This post is the result.\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This should have been pretty easy. After all, a while back I wrote a [Matplotlib Animation Tutorial](https://jakevdp.github.io/blog/2012/08/18/matplotlib-animation-tutorial/) containing a double pendulum example, simulated in Python using SciPy's [``odeint`` solver](https://docs.scipy.org/doc/scipy-0.17.0/reference/generated/scipy.integrate.odeint.html) and animated using matplotlib's [animation module](http://matplotlib.org/api/animation_api.html).\n", "All we need to do is to extend that to a three-segment pendulum, and we're good to go, right?" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Unfortunately, things are not so simple.\n", "While the double pendulum equations of motion can be solved [relatively straightforwardly](http://scienceworld.wolfram.com/physics/DoublePendulum.html), the equations for a triple pendulum are much more involved.\n", "For example, the appendix of [this document](https://www.nickeyre.com/images/triplependulum.pdf) lists the three coupled second-order differential equations that govern the motion of the a triple pendulum;\n", "here's a screenshot of just the first of those three:" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "![Equation Screenshot](http://jakevdp.github.io/images/eqn-screenshot.png)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Yikes." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Fortunately, there are easier approaches than brute-force algebra, that rely on higher abstractions: one such approach is known as [Kane's Method](http://docs.sympy.org/dev/modules/physics/mechanics/kane.html).\n", "This method still involves a significant amount of book-keeping for any but the most trivial problems, but the [Sympy package](http://sympy.org) has a nice implementation that handles the details for you.\n", "This is the approach I took to simulate the triple pendulum, borrowing heavily from [Gede et al. 2013](https://www.researchgate.net/publication/267490975_Constrained_Multibody_Dynamics_With_Python_From_Symbolic_Equation_Generation_to_Publication) who present a nice example of Sympy's API for applying Kane's Method." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## The Code\n", "\n", "The following function defines and solves the equations of motion for a system of *n* pendulums, with arbitrary masses and lengths.\n", "It's a bit long, but hopefully commented well enough that you can follow along." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "from sympy import symbols\n", "from sympy.physics import mechanics\n", "\n", "from sympy import Dummy, lambdify\n", "from scipy.integrate import odeint\n", "\n", "\n", "def integrate_pendulum(n, times,\n", " initial_positions=135,\n", " initial_velocities=0,\n", " lengths=None, masses=1):\n", " \"\"\"Integrate a multi-pendulum with `n` sections\"\"\"\n", " #-------------------------------------------------\n", " # Step 1: construct the pendulum model\n", " \n", " # Generalized coordinates and velocities\n", " # (in this case, angular positions & velocities of each mass) \n", " q = mechanics.dynamicsymbols('q:{0}'.format(n))\n", " u = mechanics.dynamicsymbols('u:{0}'.format(n))\n", "\n", " # mass and length\n", " m = symbols('m:{0}'.format(n))\n", " l = symbols('l:{0}'.format(n))\n", "\n", " # gravity and time symbols\n", " g, t = symbols('g,t')\n", " \n", " #--------------------------------------------------\n", " # Step 2: build the model using Kane's Method\n", "\n", " # Create pivot point reference frame\n", " A = mechanics.ReferenceFrame('A')\n", " P = mechanics.Point('P')\n", " P.set_vel(A, 0)\n", "\n", " # lists to hold particles, forces, and kinetic ODEs\n", " # for each pendulum in the chain\n", " particles = []\n", " forces = []\n", " kinetic_odes = []\n", "\n", " for i in range(n):\n", " # Create a reference frame following the i^th mass\n", " Ai = A.orientnew('A' + str(i), 'Axis', [q[i], A.z])\n", " Ai.set_ang_vel(A, u[i] * A.z)\n", "\n", " # Create a point in this reference frame\n", " Pi = P.locatenew('P' + str(i), l[i] * Ai.x)\n", " Pi.v2pt_theory(P, A, Ai)\n", "\n", " # Create a new particle of mass m[i] at this point\n", " Pai = mechanics.Particle('Pa' + str(i), Pi, m[i])\n", " particles.append(Pai)\n", "\n", " # Set forces & compute kinematic ODE\n", " forces.append((Pi, m[i] * g * A.x))\n", " kinetic_odes.append(q[i].diff(t) - u[i])\n", "\n", " P = Pi\n", "\n", " # Generate equations of motion\n", " KM = mechanics.KanesMethod(A, q_ind=q, u_ind=u,\n", " kd_eqs=kinetic_odes)\n", " fr, fr_star = KM.kanes_equations(forces, particles)\n", " \n", " #-----------------------------------------------------\n", " # Step 3: numerically evaluate equations and integrate\n", "\n", " # initial positions and velocities – assumed to be given in degrees\n", " y0 = np.deg2rad(np.concatenate([np.broadcast_to(initial_positions, n),\n", " np.broadcast_to(initial_velocities, n)]))\n", " \n", " # lengths and masses\n", " if lengths is None:\n", " lengths = np.ones(n) / n\n", " lengths = np.broadcast_to(lengths, n)\n", " masses = np.broadcast_to(masses, n)\n", "\n", " # Fixed parameters: gravitational constant, lengths, and masses\n", " parameters = [g] + list(l) + list(m)\n", " parameter_vals = [9.81] + list(lengths) + list(masses)\n", "\n", " # define symbols for unknown parameters\n", " unknowns = [Dummy() for i in q + u]\n", " unknown_dict = dict(zip(q + u, unknowns))\n", " kds = KM.kindiffdict()\n", "\n", " # substitute unknown symbols for qdot terms\n", " mm_sym = KM.mass_matrix_full.subs(kds).subs(unknown_dict)\n", " fo_sym = KM.forcing_full.subs(kds).subs(unknown_dict)\n", "\n", " # create functions for numerical calculation \n", " mm_func = lambdify(unknowns + parameters, mm_sym)\n", " fo_func = lambdify(unknowns + parameters, fo_sym)\n", "\n", " # function which computes the derivatives of parameters\n", " def gradient(y, t, args):\n", " vals = np.concatenate((y, args))\n", " sol = np.linalg.solve(mm_func(*vals), fo_func(*vals))\n", " return np.array(sol).T[0]\n", "\n", " # ODE integration\n", " return odeint(gradient, y0, times, args=(parameter_vals,))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Extracting Positions\n", "\n", "The function above returns generalized coordinates, which in this case are the angular position and velocity of each pendulum segment, relative to vertical.\n", "To visualize the pendulum, we need a quick utility to extract *x* and *y* coordinates from these angular coordinates:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "def get_xy_coords(p, lengths=None):\n", " \"\"\"Get (x, y) coordinates from generalized coordinates p\"\"\"\n", " p = np.atleast_2d(p)\n", " n = p.shape[1] // 2\n", " if lengths is None:\n", " lengths = np.ones(n) / n\n", " zeros = np.zeros(p.shape[0])[:, None]\n", " x = np.hstack([zeros, lengths * np.sin(p[:, :n])])\n", " y = np.hstack([zeros, -lengths * np.cos(p[:, :n])])\n", " return np.cumsum(x, 1), np.cumsum(y, 1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Finally, we can call this function to simulate a pendulum at a set of times *t*.\n", "Here are the paths of a double pendulum over time:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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5BVxZy0JeydBbsbfKdXxpMdUz5beev9HapjWzfGeVr/jLYldYnm8hud+P6puS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YtMdUmtOOqpq62+L3CrDjn5OXJt5FrZb1M/4wK1w3GHSy260eq1ctf1XdJvq5/0Wecjn9j9hAyJ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\nQUFBQUGhBP8P7CRyYOdNlWMAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, 10, 1000)\n", "p = integrate_pendulum(n=2, times=t)\n", "x, y = get_xy_coords(p)\n", "plt.plot(x, y);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "And here are the positions of a triple pendulum over time:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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NSyMvLMzYohgEQyiHaOD+kzG++WUFCCEyhBBZ+b/vBswkSXItTtv7+lgohKgrhKjr5uZm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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p = integrate_pendulum(n=3, times=t)\n", "x, y = get_xy_coords(p)\n", "plt.plot(x, y);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Pendulum Animations\n", "\n", "The static plots above provide a bit of insight into the situation, but it's much more intuitive to see the results as an animation.\n", "Drawing from the double pendulum code in my [Animation Tutorial](https://jakevdp.github.io/blog/2012/08/18/matplotlib-animation-tutorial/), here is a function to animate the pendulum's motion over time:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "from matplotlib import animation\n", "\n", "\n", "def animate_pendulum(n):\n", " t = np.linspace(0, 10, 200)\n", " p = integrate_pendulum(n, t)\n", " x, y = get_xy_coords(p)\n", " \n", " fig, ax = plt.subplots(figsize=(6, 6))\n", " fig.subplots_adjust(left=0, right=1, bottom=0, top=1)\n", " ax.axis('off')\n", " ax.set(xlim=(-1, 1), ylim=(-1, 1))\n", "\n", " line, = ax.plot([], [], 'o-', lw=2)\n", "\n", " def init():\n", " line.set_data([], [])\n", " return line,\n", "\n", " def animate(i):\n", " line.set_data(x[i], y[i])\n", " return line,\n", "\n", " anim = animation.FuncAnimation(fig, animate, frames=len(t),\n", " interval=1000 * t.max() / len(t),\n", " blit=True, init_func=init)\n", " plt.close(fig)\n", " return anim" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "anim = animate_pendulum(3)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "In the notebook, you can embed the resulting animation using the following snippet:\n", "\n", "```python\n", "from IPython.display import HTML\n", "HTML(anim.to_html5_video())\n", "```\n", "\n", "Embedding videos directly like this can lead to very large file sizes for notebooks (and blog posts!), so instead I've saved the animation and will load it with an HTML5 video tag.\n", "This is less portable (because the video file is separate from the notebook) but avoids embedding the entire content of the video into the single notebook file." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "