Pendulum.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:23cf7a01a91c877f2044ac06ef3c7c6956e70a87b5b5e7b9f2033d7cac098e91"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy\n",
      "\n",
      "import sympy.physics.mechanics as mech\n",
      "import os\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "from sympy.printing.theanocode import theano_function\n",
      "from sympy_utils import rhs_to_scipy_ode, \\\n",
      "    save_sympy_expr, load_sympy_expr, gen_fortran_module\n",
      "from numpy import f2py\n",
      "import numpy as np\n",
      "from sympy.utilities import codegen\n",
      "\n",
      "%matplotlib inline\n",
      "%load_ext autoreload\n",
      "%autoreload 2\n",
      "sympy.init_printing()\n",
      "mech.init_vprinting()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Dynamics"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# symbols\n",
      "m, g, l, t, tau, phi, theta, Q, psi = \\\n",
      "sympy.symbols('m, g, l, t, tau, phi, theta, Q, psi')\n",
      "\n",
      "# state space\n",
      "x = (theta, Q)\n",
      "u = (tau,)\n",
      "no_t_sub = {theta(t).diff(t):Q}\n",
      "no_t_sub.update({v(t): v for v in x+u})\n",
      "\n",
      "# frames    \n",
      "frame_i = mech.ReferenceFrame('i') # inertial\n",
      "frame_b = frame_i.orientnew( # body\n",
      "    newname='b', rot_type='Body',\n",
      "    amounts=(0, theta(t), 0), rot_order='321')\n",
      "\n",
      "# point at center of rotation\n",
      "point_o = mech.Point('o')\n",
      "point_o.set_vel(frame_i, 0)\n",
      "\n",
      "# point at center of mass\n",
      "point_cm = point_o.locatenew('cm', -l*frame_b.z)\n",
      "point_cm.set_vel(frame_b, 0)\n",
      "point_cm.v1pt_theory(otherpoint=point_o,\n",
      "                     outframe=frame_i, interframe=frame_b)\n",
      "\n",
      "# particle\n",
      "ball = mech.Particle(name='ball', point=point_cm, mass=m)\n",
      "ball.set_potential_energy(m*g*l*sympy.cos(theta(t)))\n",
      "\n",
      "# derive eoms\n",
      "L = mech.Lagrangian(frame_i, ball)\n",
      "lm = mech.LagrangesMethod(\n",
      "    Lagrangian=L,\n",
      "    qs=[theta(t)],\n",
      "    forcelist=[(frame_b, tau(t)*frame_b.y)], frame=frame_i)\n",
      "lm.form_lagranges_equations()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}- g l m \\operatorname{sin}\\left(\\theta\\right) + l^{2} m \\ddot{\\theta} - \\tau\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAOIAAAAaBAMAAABY/52QAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n6+HtfwCJc+Q+1ud37QAAAABJRU5ErkJggg==\n",
       "prompt_number": 2,
       "text": [
        "\u23a1                 2         \u23a4\n",
        "\u23a3-g\u22c5l\u22c5m\u22c5sin(\u03b8) + l \u22c5m\u22c5\u03b8\u0308 - \u03c4\u23a6"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sympy.Eq(sympy.Symbol('L'), L)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$L = - g l m \\operatorname{cos}\\left(\\theta\\right) + \\frac{l^{2} m}{2} \\left(\\dot{\\theta}\\right)^{2}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAQoAAAAvBAMAAADp85nLAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZqvNRIkQuyJ2mTLd\nVO9a7b1KAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAFOUlEQVRYCb1XW2gcZRT+Ntmd3c3sTUWwCrpG\nESliVxcFRcmoBB8UsxgDNQoZC+IFbWIfWunTvHmhJEslaArqQLGlorLguxvJS9Vol0IpFmojhNpS\nsZuYmDQxrN8//8zO7G72gunkPPznO5f/nLP/7cwC/lLo+DF/E3QUfTfu6sjPX6eTKBr+Zugk+jwm\ntDZ+wwf1Nh7XwXyhTY6Q0ZW5Dmmah4ieKgA/NLdblpihrrZx2aL5DiBktomR0CJLbVy2aD4K3No+\nRPyf9j5b8biMYC7IXWlNsXxr+xatkXV8e/6s3hAlkBIqJW0bhm3uEwuUcbVSAfrv/eBwvv9jzUnz\nkQRPSRYwHb0/vGtMxs0dyCvXtPicnSV4UYJo2uL9eMY2+MMScsPV0gwiy+DKSNpbsMEDgquPn99v\ny/6wokynKEvgPXBWBjtFtlgamNAJEpWKUx4lH+gzO2a8jJ5p2CsD1bqYoxmgK+1D0oaQ+xSp6skg\nlsOAoVtitym13AyfHwqZZyEkeSKHUQ1HIyVLnDCkluMjVeQjWHpDBmdb5Vv+kF3TV27G2124VaSm\n+ALdANzWEOhITqqeBQ4Dp1+S0mWLvcJZ3q5/Y+VBoWlOVmtsbn6PpqffNtFVaO7jsfBBJQX3n+PI\nrarS31XUBHA5W9DDPGYXwYOWaeHkmuSz8Z2e1HlJ3CnBZddlc8TW2Jyi/D2xFDaASdvp9ebOtPDO\nkr5HsgREywJbFGrb3uVOOv51PGEAPGULwF7b8mudR60YG6McmEMyBcTd75tut6Baf0eSO+lI9ZxH\nDz9C5Vp0l6StdRVJk14xE0V6i1k2JTMO2oSfmTorGoCnKypfDJXw6tQLUD+dEjPZl4NLiHJBQyZF\nUpsq8nQZ0PC5xqvFFbRpICdBKGuR6egFD41F1kQD8HTF8ZJ6ST2JcP41YJou7/CQLfbeX+Yyi6JI\nrasYTdFlV2/vVeF6TQwWjWg22ITxA3qDDcDbFbOIr/M9Vtef0yHq/5nrm4FY0Pi0jNC6iglRxQxg\n3Uz3YvRRaz/4MgrFx2ZJMwX8AX4gFwuerqis0Uns6XJs5RPhPw8kc3KXy3K+U0WyUk/CLuZi2T4S\nIpikFbJbHKGWqwuIToOt0e2KQbGIFzRgRRmsmMSsYrSEb4hUUcVgNvtLNvsoURMqpvgrN9AzJ+zV\nKqywJjUh8ftnZ9OEDgVWETbB1uh2xeparL2PgLjj3JFRzdrg4LSc56yFE6WWix3hB0cyL9TVHQnx\nRY3SshlxCfi4sDV6umKWK5MweS/OAHdyEk9nQgtNE3V4OkX6ebzM0XplLI5YGRjRJa4flVXsMsDW\nOOF2xfEUdqtX0J37Tce7nPA8n8P8uEHUY3IgtV4LHiLgROSS8IxsiJG0p2+xt29R4sbxyUnWzNbo\n6YrKzkkDHw7djf4dN2ucQZNy4piY2i1EUusqEmm6vHlE5wi17bMtvEgHJWs+xgzHNm6DuioiXx4o\nOC7k4YwrdPavTBXnqA25fydetD2fqJ2xBzWdKjTnmr3Y1dajET2crtc1yOJwCFI8P1Jq5HgP8JdH\n9v7+DqJz5ukdX3vmN4HiK0dQ2LBYw/AnH2zPlnh6h9VXG/z/nyKSkvOavHzo02uqwD43TdFwsf/o\nlO7J4fnkHfSofYe1X3N87x363QHbwWNj3izRjCPF5xy0Hfx4bZIrjsjP1e2jaLo2102OWAWOwk9+\nDhHDGz+cl5LsJV6Lj1g1ETW88ZWfpPRWyav1GR8aGr6vNsUhw5L5TbB91Fep/FubLVIQsqJVtf8B\na11ZDlNADKgAAAAASUVORK5CYII=\n",
       "prompt_number": 3,
       "text": [
        "                     2     2\n",
        "                    l \u22c5m\u22c5\u03b8\u0307 \n",
        "L = -g\u22c5l\u22c5m\u22c5cos(\u03b8) + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                       2    "
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f = lm.rhs().subs(no_t_sub)\n",
      "f"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}Q\\\\\\frac{1}{l^{2} m} \\left(g l m \\operatorname{sin}\\left(\\theta\\right) + \\tau\\right)\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAMQAAAAyBAMAAADxQ2lcAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nzAAAAABJRU5ErkJggg==\n",
       "prompt_number": 4,
       "text": [
        "\u23a1       Q        \u23a4\n",
        "\u23a2                \u23a5\n",
        "\u23a2g\u22c5l\u22c5m\u22c5sin(\u03b8) + \u03c4\u23a5\n",
        "\u23a2\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
        "\u23a2       2        \u23a5\n",
        "\u23a3      l \u22c5m      \u23a6"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Measurements"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Accelerometer"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "accel = point_cm.acc(frame_i)  - frame_i.z*g\n",
      "accel"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$-  l \\ddot{\\theta}\\mathbf{\\hat{b}_x} + l \\left(\\dot{\\theta}\\right)^{2}\\mathbf{\\hat{b}_z} -  g\\mathbf{\\hat{i}_z}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAANUAAAAsBAMAAAAA8+BhAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nFZglE1PRAAAAAElFTkSuQmCC\n",
       "prompt_number": 5,
       "text": [
        "- l\u22c5\u03b8\u0308 b_x +     2\n",
        "l\u22c5\u03b8\u0307  b_z - g i_z"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "g_accel = accel.to_matrix(frame_b).subs(\n",
      "    theta(t).diff(t,2), f[1]).subs(no_t_sub).simplify()\n",
      "g_accel"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}- \\frac{\\tau}{l m}\\\\0\\\\Q^{2} l - g \\operatorname{cos}\\left(\\theta\\right)\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJEAAABLCAMAAABHo5VYAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 6,
       "text": [
        "\u23a1      -\u03c4       \u23a4\n",
        "\u23a2      \u2500\u2500\u2500      \u23a5\n",
        "\u23a2      l\u22c5m      \u23a5\n",
        "\u23a2               \u23a5\n",
        "\u23a2       0       \u23a5\n",
        "\u23a2               \u23a5\n",
        "\u23a2 2             \u23a5\n",
        "\u23a3Q \u22c5l - g\u22c5cos(\u03b8)\u23a6"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Gyroscope"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gyro = frame_b.ang_vel_in(frame_i)\n",
      "gyro"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\dot{\\theta}\\mathbf{\\hat{b}_y}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACIAAAAcBAMAAAD2GXAsAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA3asQzWZEu1SZMu92\niSKllWA0AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVQYGWNggAIDGANG84kgCwkBhbMd98Ek\nGRiYvwDxH4bbCBEwy4CBGU2EAJc5lIHr/x9kRekWExhWI4twbWb4zMCCLMIYwPADVSSageErqogk\nAxdIzRWXyVDD2b4x8HxjYPkfwPX7AUSI6ZOS9gcGlp8MDPcdICKMDgz8DmCR/n8QEf4LDOsbwCLr\nf0BE7BsYZjOgiiQwAF0HMif/X/Rvg/XbGLgTeAUgIvcd+D4ycBswcB54/QAo8nsB1+4HDPoJkcDQ\nmwNyGcvkSSUXGBjWO8hBTIeT7J8U4GwIg+v/AzQRhnI0gTcMUmgi99cooIk89AQKAABiPEgg0n3+\nfwAAAABJRU5ErkJggg==\n",
       "prompt_number": 7,
       "text": [
        "\u03b8\u0307 b_y"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "g_gyro = gyro.to_matrix(frame_b).subs(no_t_sub)\n",
      "g_gyro"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}0\\\\Q\\\\0\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACAAAABLCAMAAAAml3VfAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nkZguWtbCDxIJG87BYcdqAAAAAElFTkSuQmCC\n",
       "prompt_number": 8,
       "text": [
        "\u23a10\u23a4\n",
        "\u23a2 \u23a5\n",
        "\u23a2Q\u23a5\n",
        "\u23a2 \u23a5\n",
        "\u23a30\u23a6"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Save"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "save_sympy_expr({\n",
      "    't': t, 'x': x, 'u': u, 'f': f,\n",
      "    'g_dict': {\n",
      "        'g_accel': g_accel,\n",
      "        'g_gyro': g_gyro},\n",
      "    'const': (m, g, l),\n",
      "    }, os.path.join('save','pendulum.sympy'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Generate Code"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy_utils"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pendulum = sympy_utils.create_fortran_module_from_sympy_save(\n",
      "    'pendulum', os.path.join('save','pendulum.sympy'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "pendulum.compute_a(t=0, x=[1,2], u=1, m=1, l=1, g=9.8)\n",
      "pendulum.compute_b(t=0, x=[1,2], u=1, m=1, l=1, g=9.8)\n",
      "pendulum.compute_f(t=0, x=[1,2], u=1, m=1, l=1, g=9.8)\n",
      "pendulum.compute_g_accel(t=0, x=[0,0], u=0, m=1, l=1, g=9.8)\n",
      "pendulum.compute_g_accel_h(t=0, x=[0,0], u=0, m=1, l=1, g=9.8)\n",
      "pendulum.compute_g_gyro(t=0, x=[0,0], u=0, m=1, l=1, g=9.8)\n",
      "pendulum.compute_g_gyro_h(t=0, x=[0,0], u=0, m=1, l=1, g=9.8)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100000 loops, best of 3: 12.7 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The lambdify function which uses numpy is sufficiently fast."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def do_sim():\n",
      "    import scipy.integrate\n",
      "    ode = scipy.integrate.ode(pendulum.compute_f, pendulum.compute_a)\n",
      "    ode.set_initial_value([0.1,0])\n",
      "    dt = 0.001\n",
      "    x = []\n",
      "    t = []\n",
      "    u = 0\n",
      "    m = 1\n",
      "    g = 9.8\n",
      "    l = 1\n",
      "    while ode.t +dt < 100:\n",
      "        ode.set_f_params(u, m, g, l)\n",
      "        ode.set_jac_params(u, m, g, l)\n",
      "        x.append(ode.y)\n",
      "        t.append(ode.t)\n",
      "        ode.integrate(ode.t + dt)\n",
      "    plt.plot(t, x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%time\n",
      "do_sim();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 754 ms, sys: 19.8 ms, total: 774 ms\n",
        "Wall time: 773 ms\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SJP0f1nPNDGiymZWooWyDvkuFxdh5juC4Dn2JVKMIN9Gf9oKly0ywEj4Vk5Rh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\nl1zMFfQUO/P5/OJ72ordo2J047NA+zPqkoKfgmESu27YYyjZ+nyOYQ4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       "text": [
        "<matplotlib.figure.Figure at 0x5246490>"
       ]
      }
     ],
     "prompt_number": 14
    }
   ],
   "metadata": {}
  }
 ]
}