moorepants/chaos_pendulum_pythreejs_manual.ipynb

## chaos_pendulum_pythreejs_manual.ipynb

      
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## mae223-l18-01-complete.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sm\n",
    "import sympy.physics.mechanics as me\n",
    "me.init_vprinting()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Problem Description\n",
    "\n",
    "![](https://objects-us-east-1.dream.io/mae223/2019f/mae223-l17-example-fig.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generalized coordinates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "q1, q2, q3 = me.dynamicsymbols('q1, q2, q3')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generalized speeds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "u1, u2, u3 = me.dynamicsymbols('u1, u2, u3')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Specified Inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "F, T = me.dynamicsymbols('F, T')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( k, \\  c, \\  m_{a}, \\  m_{b}, \\  m_{c}, \\  I_{B_bo}, \\  l, \\  k_{T}, \\  g\\right)$"
      ],
      "text/plain": [
       "(k, c, mₐ, m_b, m_c, I_{B_bo}, l, k_T, g)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k, c, ma, mb, mc, IB_bo, l, kT, g = sm.symbols('k, c, m_a, m_b, m_c, I_{B_bo}, l, k_T, g')\n",
    "k, c, ma, mb, mc, IB_bo, l, kT, g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reference Frames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = me.ReferenceFrame('N')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "B = N.orientnew('B', 'Axis', (q2, N.z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = B.orientnew('C', 'Axis', (q3, N.z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "O = me.Point('O')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "Pab = O.locatenew('P_{ab}', q1 * N.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Bo = Pab.locatenew('B_o', - 2 * l / 3 * B.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "Pbc = Pab.locatenew('P_{bc}', -l * B.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "Pc = Pbc.locatenew('P_c', -l * C.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle -  l\\mathbf{\\hat{c}_y} -  l\\mathbf{\\hat{b}_y} + q_{1}\\mathbf{\\hat{n}_x}$"
      ],
      "text/plain": [
       "-l c_y + -l b_y + q₁ n_x"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pc.pos_from(O)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Velocities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\dot{q}_{1}\\mathbf{\\hat{n}_x}$"
      ],
      "text/plain": [
       "q₁̇ n_x"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pab.set_vel(N, Pab.pos_from(O).dt(N))\n",
    "Pab.vel(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\dot{q}_{1}\\mathbf{\\hat{n}_x} + \\frac{2 l \\dot{q}_{2}}{3}\\mathbf{\\hat{b}_x}$"
      ],
      "text/plain": [
       "          2⋅l⋅q₂̇\n",
       "q₁̇ n_x + ─────── b_x\n",
       "             3"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Bo.v2pt_theory(Pab, N, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHQAAAAaCAYAAABmZHgNAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAE8klEQVRoBe2ai1HcMBCGczdXAKGDQAeQDgIdEFJBoAOYVMCQDiAlQAeQCgh0AKkggQ4u/ye0HluWfbJlM3eT2xkhaaV96N/Vw5dM5vP5uzUtBwKTyWRD8XjJ8WaaI7yWHQ4BBXNL2u5VUzb6al4HtC9yA8opgHsEU4XdSTB/+wCr2Y3WAe2G1+Cz/W68keIzHbe7KttqX6oQ4M40Wd+hnTEbXICghndnjJdieB3QFJRWaM7oR64/UlYIktV2ddSAKphbgif75bbaENe9Fy47KvNSOarP6scZLaBydrCXW7+l5UnJ/xOVRw/6Tp62qrTuywdxdlWyvjmrWn2PR1FYNMTT+VnlPhxL6Xt5frE4sflqn6s8W38VavnLzpGrdYyMp/HeWEmWlyw4HZm+3Dq6Q6WUzPmr8qTSmbz8e9XfTVjtU7U/WH/sWjvrgF2WaYdddNumIxerNt19xmZNQnKU76He5BdakY/xKhOWr3Mol84WuZWL1SL9XcajO7SLgnCuv3Pswuce2lC5UOFx9OzrQe+k0Ich+vKTBx3HaesOHcIWdmTv3GNjj0gww343UnYVd6gkWQR3HXcHxxUKqffK89razFV5VOFuQBe/guwgIzpQoTH6XeptFXd4m8+xMcm33p8aHwIru0Mr96h0k/AOJ+zE/GvilYNJIHgIFQrUvlKRbCXoGLsp88K2ySGr4oLJHBEg0KjwQ/kh+rJB8uQElLVH1yn+Qqw0h2S+QIev+TWowNvjYQG9iIwhD06dHqZTCbzzW5sFnEpx+BDiic0cvp1w8FiFwKTQi/Q5eSYHulN1pNgZYw5BIxgVSsTKBVPrPVbZl4JNlZ8VRdUOj9CQ7jwD3JOxmnkhHCCD+FG4TCzK8TRGYI6lHB4lhX6lTMqZI3/wPeYP18Wmxr9E9D9pPZ8jfMeSDKcQ8teROQuxkgynA8lvxMOKu5HTL9wwNiesy/Pwp9wP5xb9mW/xmqtc/hgXj0XVstTLLEUlgPgcqpH8B1QALD6dapOaGSQIp0sMxFSswM/kbQeWec3WM0amWjhBiwXOZb0WVQl0hq2oKMCr2C8yvI7xhSOeFzF9xhwvqmAcJsekW3fZtm8vxEqYbQe4scOgLicWx7TRg2wn4TQ1CdWWTcbiSCruP2MOXWvh1wAgvZY4H+U8mQy5fx/U+Mtr983+ksx2Mn2LWO2KFcc075OmdcQSlqSCbiXHFZGE09QbIXAGIruDJzuLMpDVHJfkBwsAKICkfBVv9ISSnSZ68jvyj03og5V0EEyC0nb0H2qe7WL3AJUMMSABeIQWtAinmZ/5SfUPKeWbE7IMtCx95Sb8lQ73feKn7vk+O5A7jcUZXWmMhVomwqfNNyzHzZslk2yFBIicUPvyL7yjk7HS+ggKj81KUAJjPDqxwQ8LrJvdSn0ZsS22o2acJFT5NqIvavyo1hg79zEml8uTXhLIffvm2pB81ndo6lpkJ4qV+OB0bnp8v/gmN36fWroacSrfoZpXEBnQdNzFzvtCsG9D2UkgeVm6naH2lnidT4iSfXZ4+BlWGh6sWcNKfnN8chrdqc1jhuRiF9rJp2Y/kq52nGIZIlP8YlRkF3NE3LF8W9nPeiju/UuM2ZUOMhx7GCn0+T487B3Y/GWr5VsMK1sP/hclx3fpScKp8n+KFH2yiqOCDCObuOPazn9N+T9pWbH6B+Lx8jGA8WHOAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\dot{q}_{1}\\mathbf{\\hat{n}_x} + l \\dot{q}_{2}\\mathbf{\\hat{b}_x}$"
      ],
      "text/plain": [
       "q₁̇ n_x + l⋅q₂̇ b_x"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pbc.v2pt_theory(Pab, N, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\dot{q}_{1}\\mathbf{\\hat{n}_x} + l \\dot{q}_{2}\\mathbf{\\hat{b}_x} + l \\left(\\dot{q}_{2} + \\dot{q}_{3}\\right)\\mathbf{\\hat{c}_x}$"
      ],
      "text/plain": [
       "q₁̇ n_x + l⋅q₂̇ b_x + l⋅(q₂̇ + q₃̇) c_x"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pc.v2pt_theory(Pbc, N, C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kinematic Differential Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "u1_eq = sm.Eq(u1, Pab.vel(N).dot(N.x))\n",
    "u2_eq = sm.Eq(u2, Bo.vel(N).dot(B.x))\n",
    "u3_eq = sm.Eq(u3, C.ang_vel_in(B).dot(B.z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ \\dot{q}_{1} : u_{1}, \\  \\dot{q}_{2} : \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right)}{2 l}, \\  \\dot{q}_{3} : u_{3}\\right\\}$"
      ],
      "text/plain": [
       "⎧              3⋅(-u₁⋅cos(q₂) + u₂)         ⎫\n",
       "⎨q₁̇: u₁, q₂̇: ────────────────────, q₃̇: u₃⎬\n",
       "⎩                      2⋅l                  ⎭"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qdots = sm.solve([u1_eq, u2_eq, u3_eq], q1.diff(), q2.diff(), q3.diff())\n",
    "qdots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Substitute expressions for the $\\dot{q}$'s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle u_{1}\\mathbf{\\hat{n}_x}$"
      ],
      "text/plain": [
       "u₁ n_x"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pab.set_vel(N, Pab.vel(N).subs(qdots).simplify())\n",
    "Pab.vel(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle u_{2}\\mathbf{\\hat{b}_x} -  u_{1} \\operatorname{sin}\\left(q_{2}\\right)\\mathbf{\\hat{b}_y}$"
      ],
      "text/plain": [
       "u₂ b_x + -u₁⋅sin(q₂) b_y"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Bo.set_vel(N, Bo.vel(N).subs(qdots).express(B).simplify())\n",
    "Bo.vel(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle u_{1}\\mathbf{\\hat{n}_x} + (- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2})\\mathbf{\\hat{b}_x} + (l u_{3} - \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2})\\mathbf{\\hat{c}_x}$"
      ],
      "text/plain": [
       "         ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞       ⎛       3⋅u₁⋅cos(q₂)   3⋅u₂⎞\n",
       "u₁ n_x + ⎜- ──────────── + ────⎟ b_x + ⎜l⋅u₃ - ──────────── + ────⎟ c_x\n",
       "         ⎝       2          2  ⎠       ⎝            2          2  ⎠"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pc.set_vel(N, Pc.vel(N).subs(qdots).simplify())\n",
    "Pc.vel(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Angular Velocities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right)}{2 l}\\mathbf{\\hat{n}_z}$"
      ],
      "text/plain": [
       "3⋅(-u₁⋅cos(q₂) + u₂)\n",
       "──────────────────── n_z\n",
       "        2⋅l"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.set_ang_vel(N, B.ang_vel_in(N).subs(qdots).simplify())\n",
    "B.ang_vel_in(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "C.set_ang_vel(B, u3 * N.z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mass and Inertia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( m_{a}, \\  m_{c}\\right)$"
      ],
      "text/plain": [
       "(mₐ, m_c)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ma, mc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle I_{B_bo}\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_z}$"
      ],
      "text/plain": [
       "I_{B_bo} b_z⊗b_z"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IB = me.inertia(B, 0, 0, IB_bo)\n",
    "IB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loads (forces and torques)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle (- c u_{1} - k q_{1} + F)\\mathbf{\\hat{n}_x}$"
      ],
      "text/plain": [
       "(-c⋅u₁ - k⋅q₁ + F) n_x"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rab = (F - k*q1 - c*qdots[q1.diff()]) * N.x\n",
    "Rab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle -  g m_{b}\\mathbf{\\hat{n}_y}$"
      ],
      "text/plain": [
       "-g⋅m_b n_y"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rbo = -(mb*g)*N.y\n",
    "Rbo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle -  g m_{c}\\mathbf{\\hat{n}_y}$"
      ],
      "text/plain": [
       "-g⋅m_c n_y"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rc = -(mc*g)*N.y\n",
    "Rc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle (k_{T} q_{3} + T)\\mathbf{\\hat{n}_z}$"
      ],
      "text/plain": [
       "(k_T⋅q₃ + T) n_z"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "TB = (T + kT*q3)*N.z\n",
    "TB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kane's Equations (the short way)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "kdes = [u1_eq.rhs - u1_eq.lhs,\n",
    "        u2_eq.rhs - u2_eq.lhs,\n",
    "        u3_eq.rhs - u3_eq.lhs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "block = me.Particle('block', Pab, ma)\n",
    "pendulum = me.RigidBody('pendulum', Bo, B, mb, (IB, Bo))\n",
    "bob = me.Particle('bob', Pc, mc)\n",
    "\n",
    "bodies = [block, pendulum, bob]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loads are a list of (force, point) or reference (frame, torque) 2-tuples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "loads = [(Pab, Rab),\n",
    "         (Bo, Rbo),\n",
    "         (Pc, Rc),\n",
    "         (B, TB)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "kane = me.KanesMethod(N, (q1, q2, q3), (u1, u2, u3), kd_eqs=kdes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "fr, frstar = kane.kanes_equations(bodies, loads=loads)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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S/J2uh3XiFXB50x/eKurKlpevxTdvFelMpLHYNysZ+XEfyr9CbuVjAv6FPDgRz5vVC8ug4ge5SI+64eUdebBmC/oHSoMXFjSkY5HEGobFCx6weJH+o7zl0e0bXgl0OGTr5DvWz9tk8IIvtnjTDtgm1VlWedocZZChWlZ1Ug/t0NoSYQac9FY95nmmeGur78Y8iW7EqBVX5e1yW+PSi0kXs2unxTbAQtraHvhgSe6zeI9hjV0P36ouHuzmGgegqj76Hm8bUjuwjEteB9aDlTy1tVg/vNMf6R84+rONIyFC/IMdfXVzN0UulcEqj17sucB491HO/J4y5XzU7q9V7gFyLdpG99bzAHlpAqNl3luuWrttixevjC+7j8VtvC0VN0DPo3UMb3vqeYBMsHg6uWC6cMy30nMxYs6cFtlotzwTg4ttecm5pZFe+8rcm/mPzU9pW/RLZA9zFqWtOkeZK+DA9litRvIyH0Dex9yLXmOeUy1YtHEwVPnO+UUHrcWSxMNu8zKEGKCPXcYGGjpmjmRVE6OL736AvjwLzPRmUfdM9INlS9fwVym60uAab74Uxmojti75Ujz8z7ZUiQaNY9bOB5WnwyRedI/MYGuy0YkUDHIje6pP9yyASUTW9OZe9/BV4gFGLER6rYLKYwvrhk4V37AeR3psFb/Ip7SSV5Ors83EctW/11R60LWuiY7u2S6edK17MGUxBQ9cO629Sr+w4OUyKR3eeauet0PaEHGBD10J01YTX5negs6UNgjXvG67V1lk2QwX6pLvbSvGX3lV2dl9o6SZh0UfndCe4ZP236vnvPyS96qbNlnVzVJ1ddUT5WcsAJPBuz+UlzYZxpql+BxLR/VX8YM3+VFyKf8omZS/0WfH8j81v+rdVe6pfPeVq8ml+NG6pC65Vn3W4vv4WzpdfBxaj+LvZsbipXWb06vpWfGLtuu8zrXvazJR75nlMtwkA2MHwtjfbzNXYO5AnyU+PbdjXJrTRQwac8sYt8j6IdKa3TczWRrPccXD+y7PNsN/7DXKknQytvzY/KpvUt8t61kaZ9FrfeaV9a4druljKm5T5FIZ+ohEDWNSWGhxt2rDFn0Wc2HxbSArTIeCGQaQ0Eh1pQE1FkoKs1hLi/rIOIMGefGNhbTRH3MVjVkDRywPjo3FscLEQRt+bdAEi1JGMCBviRELMolyYRQIi/IyvgyrLAMzg3DJVzJ8UEYOjNuMD8Q3jB8xP4U6BxalN4xNOW9Ko0PCV4OGwrSJgI2uyJjaZZ6W08rvlQesq+1BaRdGm1gGXsJCj/LyDT1EmdEhcnMdhGvOm92r7Ka4qL5OTIyv2jWWb7SXWt5riI/ypna3lkxL1yN6TMYa/Xwt3rvoLinXUWTqktfSrlXuLeQ6kp63kNfazNhr5O1mxuKx+IzJf2Q9j5Ejz7ukTNCVO8QzJfLCPAammDsmvmI4zSNjuG9uuej6IeNvVt8U78x5kZF5Kmsb5sPIcjEHz/V+1Hvxjc5Wn0sdVf7YLlJb3ZvPJfUhWqPlivULhn/e4hQxOiEN3f7LXbdNpy0jdPZfm7G9oS9VQdg2rfJ0IhbRbyvuriwJfYvXPR3tO4Xzzy4u4oyG8rMIxEo46O/vlJ/OTZnSIeM78mnbVpaBLVBhS3gW17iNfPOvDnxWEZziDNu3iVAaW4CoB3k+UbjcPsZA08BI+YkDn0RXYbZhoTNw6t1+pbwsdjFuUB/GhJ9VriGn8hB/p/iGnDH+HcWzLSc5xTNAfqv4pKeUGG+UBznz/9hNWZQW2oTKh5PsLCGW+UHxbJWCb3AKvCpseHa11ZCnpAt9lTfsoR8ODrR67ZrVAd8X2CodufnHBOOvE1ejm19FY1NcTKY2TAq+1uobYObOEXAEHAFHQAj4WOzN4MwIdLVfzTeYZ01eL9RwEV3mjJ/L/6j6W+dvlI35MEZU55bkwynvqPVDLLPKPCnSZl7PHDatAyKeLyRPY25O/pqLZdbQgc/laqB7/JDnGsYoXnI/eDQEL2W8U77G4nNIuSwPAwZnO0Dnwll8HAgYuNK32IqjIxKXFuoXBEZEqK7Wb4dUj1noqovpWjUZjxgKcsfA1vh2S+Fg+BAfpTwYF8q80CL/d9wUDlyGfhOP7p7JQ4uBk9PRqwtwpZfurzJigXBoEzkd8cRCHl1jCDFHnBlKrP3kcZZvyJVyOIwaNWd5rK62fGCPm4vrPZXm7x64BA7W6BsQFt3GJKAproccAUfAEXAEcgR8LM7R8PszIaC2y9xpznqhJi7zV+bNf2iuyByR3dBt8/Whc6haPZ3xa/XNWClzy7Z1wH86mSoS19KB6PpcrsDag9MQeDSt2PBSGiRYTOKHLJTbFuAMOLyRH1J+OGPL5nwaybUZFNri2mRBzsabdmFHHNiFeLBkUNHVFr/85zdVc0gbO00Y9BtO6Sym/1JaMroojl0oz3XFAlXy1yg/M4DRAv4bTvUSh8+NDORBXhargSddy90sJvdv5Ku4dxRvxooyi8WXdPN8lueC7yzTnzNx3RqXLkwysfzWEbg+BNRXMbjSn81oyY6tu+uT1CVyBByBKQj4GDEFte3KxDkj4zeHt/N3zMyJMUI0DiaP+XrnlttxPrwm8R7mvyrRWAfEZ1UjbjhVz7kkAtJRdS4R294L1cfn9W6k6QH+YU/67ORsktf6tlkKY8eBORaX5cIcg0RYbCrvV1HBlv8oVxaTLJpt4Wp8MZiUC+w2q6xNjMu8bLNicLXFrg1OXKmL3QtYfl/J0ynaHAM2xobkVIadJQxmpK3p4JGFb82VeAV5a5kVj4x9Cwdkal1YSG7iaV9mLNLtG0dbVB7Sydf4zIVcSqd94tjhMgfXrXGpYhKk8R9H4EoRUJ9lzOCzvPCPQ7pnPBq7HfVK0XGxHAFHwMeIU7QB5s3pxZRuw5xbV+bOzM3K+e/YuSVk9nY25yzXAXvz5fULgb5xIq4v+DSobHuOXwsCD1vi1ohisWsdK9CXIvkLlVJRDaUpnUU2C0WL51v/1oVlILrfT3hTL35Z5AWne/sEI+0siOkMluXgEowKki3ljWSQ3eKYPJv1EyyZUBsWXFsX1JHOM9VNvbkjbLQtvsxj8VOvLOQvtt9FvknL8cJAAg4lT4pKHZ9Pd9q22YU88Yf6WmnEdAwc7wmPhkFGYR5e8ITjr/4+V5wZG0Kkfl7Ic96D0R+Kq5W369a49GFifPnVEbg2BD4tBOITtifq22nsKdI96Ag4AreFgI8Rx9c3c16bd2GEYM6Ls7VBCEyZW4aCx/gJ7TCbXx6DK+fCEBgyTjTaqRX06yUCjy6jlo9RZ/qaxV1c4NkOCD4hKA+N4dOAF8r3TeSCgYWFE2WJ+0+MP9SFAU/80ejgk10I78rDe/ntFhNe4tIgqjCO+HTORYi5/2Gi/Ilohs8ksvinus8tvWDUGISzvNxCm8U0xgUGbT474N8c2FHBAtvOg8C6h9HkS3l4KuPhh3jTG4vvD0WHBX2bw8iCganNscAvdU2+0jADT8jf1l7IXzqwgf9WF2X+lxKpG9xoj+gLY07AUNfXMY1DJe0hB3bsush1V8VVebvc1rh0YtLFqKc5AleAQBh3oxzWn/O4KxDRRXAEHIEZCOTjgY8RM4BcqSjzr3IuyXqBtQVzOOam5gbPLa3AXlfxjlzM5Zmj0QZtDv6XbsMcnTh3h0Ggb5xgPWUvng/D9BEZ4bsUwOr8t4sjMm48qfPytnzwv11YufIqOp8qjr+E6XuzXhZtDYseC0wMDbZQb803JVK0OXE2Pw2Xf0/gzAfbGTGF7CplxCsPhvSPFbVKlC8YWCRD41spxaNfyoczK2KYMyxsl0IiqTQGcv6mE+PKoZ143QSXJTARjUX7xqEV48xdNQKxLTM5SOPnVQvswl0VAj4Wr69OHyPWx3jLGqTP1rklPChtkfVDpOXzpC0Vu3NdbeOE4libVf+Nb2eWd6/eMGOdt8nOh5UlZsG5hMvfaI+iJ0Cf5IthheEpLJpHERqeOe1yUF0MrPzF5+EMD1EcrLrBQt0jHjtHGgYFcFUc5b/TPQM7DmNObacFOzVK6zhljui2wmUJTCb3jSMC7zzdNAKh32m8vLtpFFz4syLgY/H6mvMxYn2Mt6zhYm6ZVb7U+gGS3jczYG/gtjFOxPUKf46Q1mc3gMFkEU9rfJCi2f7CopZFPt/w8zbrlRQ/aefC1Mmo6qUBfqNr/iYNXjgMcq3BiMU3nw3YZwIMrod0wuAH8flSnl0lXZ0SPZafnvyqOB4OjW1MbboS/WDwURqfUhzebYHLUpi04X14gJ1BR6BAQP2BsXrIuTFFSQ86AsdAwMfidfXgY8S6+O5E/WJuKT0vun5ALu+bO2l3h2or4wTt7Lcd2DlllY9OybWYVkdnIbv4Jw0T8ODzCgYyO1OBLf98BrLaTgTRZodA7e2/kg7n4BUDwoWRJHZiOi3GA/46NJ3tIDnfVtxQB/0zYYJca+NyRkyG6tvzOQKDEdC4MubcmMF0PaMj4AhcBwI+RlyHHk2KnrnlUdYPxq5fT4JAxzjB+ubizLqTiLU5m6c/82FzxLzCSQiow2Kg+VgGhXJ3wyR6eaE4GPBGs2tnRV7kMPdr4XJmTA6jHGfkKhBQX8C4OejcmKsQ2IVwBByBUQj4GDEKLs/sCNwkAl3jhNI4e4/DTnk53viE/CbBahFaGPH5/E/C54EbH1oA8ihHwBFwBByB8yOghx3nxryQz09DD+fG6AF4d34JXQJHwBGYg4CPEXPQ87KOwG0g0DdOKF1TCi2q9c+Muk76/P/akRQ2bny4diW7fI6AI+AIzEVAD4u+s1rmVpHKL1WX6KQDgHXP2wg+6Wo4JgmNiBUDa8i1IruLkb5GuZeSCZBFK7XTHPRafJ7H75dDQHiPGiOWagPXoOelsFhOm9tRugb9bYfW+WuSvjvHCaVz2D0vNF5qfrHWeX+nBlIYJePDw1NL4sw7Ao6AI3BCBDQI/1ueg2qfy/8kf7FA3lss8TT4f8aV9yt5/j52khtT14AKOICYTy3Y/shBwLySaPgBNBbJspZcizDXQUR8H1KfHSyvnrSwLuE3tdOC+Vp8kW3bIPLLH3rM6kKk1qbHjBELt4FT67nEIraNv7l26eGoaeKbMQ/+eR7zXOagdF5lW5grYc4Pwh1Sf/es+e/SCPSNE0r/Wv5beTc8DADfjQ8DQPIsjoAj4AgshYAmL1jI/9BD6nseWLr/S77xjy5L1TWVDhMulR3zt7WctzLpO8cJdXWKJUw57Pcz0eWcmd3cyeVyfWYtZ2ldQrrWTmvxGTub30r+w49ZA0CZ3KahvXQbOLOe27CQPGw151k26TkAxjs7Dgz8l+T4TJ7ncngmW5ir4ogPZ4spfIjnjPhx5wicDgE3PpxOZc6wI+AIXAEC/CuOud91E97UW8SeV00sOSfhT02uwiRrCC/Ky4Gvo/9tZkpdQ/hRHv6Gmb/W3MUdQa64QJgkv+vzDWwr6pJKau20Fv+Gse3vDjtmDYFiapuG9opt4HR6rmGheHbvYfA95N8Nir+qgT/y/kpthG3z5vjb9vItNsaV/Ll4RP0Z/351BA6LgBsfDqsaZ8wRcASuEQFNcML2vEy2tklOlrz57TPV+J8xtTJ5k5+y02B0XUP4ipNItsVO4WlIFX15jiDX5E95XJ8N9a6iS2qotdNafIOrDQMnGLN60ZjRpqG9Shs4qZ5rWDwVThit8wV8r142zNA1HvKcKP+JjRcC5S6OO8mXjA9H09+GWHpVjsAsBB7NKu2FHQFHwBFwBCYjwIRYhT+XD3/RlBNSGt+W8rbxfzH+Q012wu6CmIbRgl0TvGmynRPvK8/XSrfvbj9U2neKKydRiq662kF4RpPJZeBLdL+PMvBWCR7CQY6KYzJHHFdkM/6SDIrDtdZFQqTL7gU7SwIZHqtOtrsOcRhQqLecVKayqiPfHYEu0jkXSjN5yf+uPDgiO7xZWgML0qJrlWsBmSDfK5cx0XWtyRB5XFSfW8itOjbVJdiuLNcieu0ajowAACAASURBVO5qA1PSosyfq+yRxqwginhr7ZeR56ltGtqH788BgAV/OvTcioWq5rOFsFNAZdk9x9hbjveKGu4iD/Trqc+AQZWVz8dYL8+ulzkB5St3QpB8yH6a8+33jsAREWCQ+EeeU82xxLt3DLwNeBvwNrByG9CYy0QZ4wF/zdTAO6bxf8ghXmEmQc+zMIYJJnecwPxVFk+YSTaLdF1CHYmO5atdlZ8JF+dRlPxQFwtz44d8iW/ds3BX8ptyCpMHJj61eN0jbwjr2loXeeWgx4STiS7hxnMqhpmU4sHm4vmlODtZuSFLxgs45TKlcKSZ8x34ibz0YdEql2gOkQm90i6eywfZjV+7Kr5Triwfp27XZO+TYTF9it/V5VYdSXfInId1T/tYVJexjiFydbbRSKdVn/CMHDUd7hEvfg43ZhkO4m3xNh31M6c/T9a/ybXHtaZnxbdiEXFibGf8ot2iizCGcI3ppJHHMKGjMs4RDvG5rIob0r96x0ujKXrV8dDy2FV54R/+Au8W33ZVnsP10zY+Pa79Wei4bIdL7CuCPDyjm5M6V8R2inCsHWtvA/dtQIMSk5q0iF4SlzjgXSxOl6xjDi3xxwQsTYx0DxaMzoln0uXzRTsTMxYCDUOBwpT72PjRfZjcWbjvSln5xIvlV5zxBD0mW9SfJmYxrOxv+rTFFflYJAajha6tdUFDjnpyYwvGh7+Nvu4Tj7onrYFDpNFF3+RJMmS0g6HDwnalTnkwt7I1LFrrVblemZQn6E5XMP7d6s6v5JFP8udp+X1XHqX1yRAWDgW9EKeyCTPd9+pTeVaVO5Ml8WV8K20VXUJ/iFwFHxdtNNJp1afot8YbzT2vUfbUBhW29rT5mGU4ZDzU+uXoNt2jn952nfHWOkZ10beye15b9Fxtk8pLp2A8qBlNu8ZzdJOM2RGXXnxVpne8NPyUN7VXi6tdlReDSGt/LcvAwxjaZXkPv5kzOBbXjYX6CfMaqfmftx7qxp0j4Ag4AlUEtAWRb+f5CyreMizu4hZHJibV7fFzKhVdtunzN3FMkI/omOh8LP4YmHFMZsoDH4kLWz4lj31XyycVTNCCU3kmuHdKz7eGUu7VfY7Bv3dlTupUHNtqwZAJJjssnsr3OpW9oJcVqqV9rjws9s0l+WPEO5agK7y16ZbDwfJ8WZH7/BXekKuNL+L4rGUIFm3l+2TilHXTHbq1+5xv7i/kku75G7jfc698T/NwvA99eKAMZb0hXMHM8m4qd6w06L7C11q6pOo+feZtr9ZGoXOhTyLlavH3qfv+Hm3MYkY7pF+2olZpO3neKe16rv7z+ve6L/UMHxdYaGx5EuN51vCstWcZ+c3l4zn9shzfynBf/6qOl6p/1HhoDGZX5Hmdhbtuj9xPu/j2NEdgNwQe7VazV+wIOAJnQeCxGMXznf8a7lcRDWcZrEE80vxSV+rhnITdnCZF4Phf+Y804S0nNzZZBeeUZhO7lgkyC/Lv5M0RTieNqxyLMt5E/gyNvD6FmRySzkTyA6XxF2I4JlLw2HCRB4weGCD41p3yGD7mtIlaXdSPTxjonnrT5FV85HpEbhYepQPPtnjyhXjJAT5lHjC8wCDGvRqAxYVcKjNEprtI+wvVhb4C1rov3YVcynvRf0SLN32tNAbIUNY5JLy53JGpTXVJnQP1OaSNQu5Cn0TK1eLvUzf6jbIeecwKSKzUpqE9tV3P1f9GGr6vZqCeL7CITIZnj8YbzgDCiMCzludOGl+Vlp/Vw7iUjOJKu1P4tXxwkZe+Z0B1vBS9UeOh1ZtdkceeiVl06+0h+mkrZx7pCBwUgYcH5cvZcgQcgYMgoAf5a/kH8vyt1KJOkwzexP4m2uUCcNF6RJ/JzS+q75tFCY8kFvlgAgc/5pjoEP4xRqRJWQw/07XxVohJneLYZp4mbArztjwt0HUPXSvHgjY4lcVw8IXKfi/PbpOcF/QA7dIRl/Svckwk+3TGpKzLtdYl2vCTeBK/TxTOZUk0lfZYAfBpW2TDcyuPqoN4ZEgyQUuerb9gSlsBp+B0D62n8uDVh8WFXENlom55eOLtId9Bt7mqXG2ZK3F9MrQVG63PLeRWHZvqEmCGykVe6bGrjZKlps9aPGU2c1HWI49ZhsUabRrak/szhWfon+KDnOr4VH7Ws22gni+wiAwy/ubPHtoLLo2h98H0y5huz6YUaTdD+5fyDRkvjeygq3CENxxG6CHuEP10CKOexxE4CgKPjsKI8+EIOAI3iQALrbaF4xpgsEuAN3jfr0F8BE3eyvCPFP/T9V15Ji/sPggLbl15Y/RJnExaevq8QnlxlMnfJFlcWkwrgskddNg6m++QYLH+pXxwqi+VgQflDxNm48fy6UqaTXDhK7wZUhyLqxfk0z2fzyAbcYFn3XNo3me6YmjCiPBE9+yiQM5aXWDEAhxDDHWx4MsNLTapp152kQTsyJe5D3T/UxZu3EaeqAM+OdySOkLb0DXgpjQMOjjkCTqCZ7lWLEiAF/LIYxzK+eqUSfkxfFj9GD/AKb05hHZ0nXJZpgHXVhngW2WX1Ofqcgs32teWugTeTrnIkGFZa6Nkq+mzFk+ZrR2yHnLMKoBYvE1P7c/wNVP/hWibBPv0XBvbMEyG55Hwei258TwrLgwMERPGtcZ43iJdZ/+CvmgMGS9bSF9GiR7PJurkinumOJ5T6fl4H33xe6R+esGcRzgCR0UAKx8HxTAYMHFy7xh4G/A2kNoAY4M840TrQVJTx4xId9ChTlPrKMupTt4mpwMZy/QjhsUv5ysshn3EII33Cqd75Jdj0pj+HWBNTIbUpTwYLRqHLyrMAhmjAVd8+tcK41dxjTIWv8VVdXdiqPSGTAojQ36gJv0thXOeFT9ILuUbfMBaTn/OvercXe45/LeV7ZOJMnINfca43jYa87XqUzRb49t4PFqceN90zFpbfskzql1Hvc7S/xiZxB87DBoHNo4pPyZvHxZ9tFSexf2otq38jf6l8ODx0vhRmVXGw7GyGD9+9bXmrbUB9RXGKYn9z1uPdMM2Kqx9tk1Kt+4cAUdgaQRkRafj8ZY/vGXVlb73tTpiePMfLe/cs9g3a7ttW/xQca+Ul28qWZh8Ic+bc+J523zxhkHxg1ykx4QAft6R58HOtvwPlAYvLPJI580GYwVvdOCBt6Ok/yhveXQbeAq8EuhwyNbJd6yfN+xgBl9se2ciwnbLzrLK0+YogwxTyrbRWzQuystC2nAGI96+9L0lGsMHux6+VV35tv502Kfqoo29VJ5yZ8WYOgblHVgXb5ZKfcE7bY+2gKPtWp+hfYIbbXIXN0CuhkzKzxtFdMIuFevXH5XM7y1XyU8Zvka5B8gEDA19Rlw62yh5avqsxUe6h7qIV/rhrmPW2oAMaAOL6n9teebQH4BFlbzaSjjAUhkecy9aacyuFrpPaOCrcoPGyx6as5PP1E9nC+sEHIH5CDCPDXNbSLGIYGLfePulzp3efPq9Y+FtYF4bUP/ioZss7/Q3eV6Z5X8/Fd7eki/69CZDYRbe5OcNTHpzr3sWWa1vSIfoTGWhm/iyMopr7EhQmIn0xX/Ok08efnNeTbbOMSWWq/69ptIxePAGLdHRPdvoxeY0fahs4w3KVDprlUNWebCGT3Qd3u6vVV+NruoF+6puauWmxHfVFeWn3YPJoN0fykebTv1qCk9LlBEPrRjCm/womeBHbpRcyp/6zRLyDKWheneVeyifY/LVZIKG3KL6FL1Reh4jxxp5xe8hxqw1ZMtpSs7DtmvxxjwgPYNzvte4r2GxUl2T+lfJi3hedDwUvVP10xIPD0+bQzpu03FTn2GcCmuLR7rB8fBw5wg4AisgEK3jLCTfNvIawP5UPEEW7raTwA4apD/yl4nhe0bS5diRgHtX8flbYNupcJ+qX9FlkoSxg1U6bwy63FMl8pd85ffpPPBzV9sZxRvnp6on7N6ggO5NNvhIb9RJKxxyttKFH6VhaPgWekW5tAtA+ZCTvNAKb7+V/67Inwepj/yHdFHWPp2tzrv4CAcuCl8mbCX+i9bfVZfS2PUSzpYYUSmGm6Fv1EaQHZe1JtdEmah8lFyqZ1W91dDYW+4aX3PiazJBcwV9jtLzHLmWKBvb2e5j1hKydNGotYEV9N/FxiHSaliswdwMfBvsiM7S4+Gp+mkDDA84AvshEOwNrH7Y+cBbJfv/8v1Y8podgYMhEBfBv45k60s96PIFMm/v+UeHtEAXXet3byueLYRh8R/rI/8nik9GBsVjMWQxHvLrGpziiaNsok2C4sOiXPG9CzflDTufVIz6wnZ7lWs8qJWHeAwiacuUwtRD/DuKb0w+Fc8rQQwHuQGFIskpD3Lm/9Wdp2H84M17sNBYQizzg+JtizpvuAOvSgMLFssNXqwsV+UJuJd08zwxHwaKWXovaXrYEXAEHIG1ENDY5mPWWuAehK50zHMdo37p0D0vIhrP7ZiJz/Yaz+2ysIcdAUfAEVgbAY1fYR3D/Nt2Pqxdp9N3BE6JgDrJnRivLmb7hIqLXSYGLIxzxwSCSQH0eXsWrroNEwuFk+GBdDmMCyl/iLn/If93Wdhua/GWnl+R75k8ZZjccGo8C/xew4Xy4lp3L9wnTf79XCUbGIgnLKZgGXaL6MpAlu/QAIffySfe2yZhSh7moj4m671Wi3gL+7Rr6R7vCDgCjkAbAhqTGobYMo+PWSUi5wx36VlprTu69FzhWchzr2rs70PDn019CA1P79LhcCqe0xG4XgQeXa9oLpkjcAgEnkYuGgtpxWFMKOPISnzaNUFEdBgGGgcAarJAHIvxEK9w/ukEb/jb6Cj6jVOZ8OlDPqlRHNsJn+vKGQ9tPL4hMO8OowX8NxxyKCI3Mlg68mKoyXmyzy1IuuNHLo+7j3nzW3s79CbHinc+KVkRXCftCDgCiyPgY9bikB6SoOv5kGpxphyBq0TAjQ9XqVYX6kAIhF0BerCXb+JZSLdtheSNf+OchLgYZ0Ftb/xNPMrzrw+csUA6Boefdc8V96nuuX4oz6cgtjgnzhzleGuS3pgo3w8qhxGEtDUdmGAMqLkSsyCvZRaf79t9vJrcvxXxeRCZ2nDI8/i9I7AZAuprY88t2Yw3r8gROBMC3pfOpK1uXrt0qTReTryQ5y+hO3cEddfiqY6AI7AHAg/3qNTrdARuCIHwll4Py7SQ1719gpG/wec8AvLwUC2NDG1v/IGQXRVGg7/stJ0R5GfhzqcTGBVeybPAqbln8WGep8OH0bZ44pZ07My4+LRBPN8pnrQcM3ZjIFfJk6KSQ0bOmaB8zVFfF41aOY93BBZHQP2ONsu5JfaXuxjjxp41sjhfTtAROBsC3pfOprE6v326jM94PrksX1DUiXqKI+AIHAYBNz4cRhXOyDUiEB+S7CLgHIVv4kOVB2bb+Q0stokvF8fEN3ZDKIzjjAP+Lzt8JhFi7n+ojwWNLcK52ucfWbZ0C+3PI39fRR752092VDyRx1jCwv9j7uWpsy2eOHZbmPEEo4YZWlJl2Q35gmEli7Pbj3TzocqDGf8UEnaQ6Gq0LV+4Kg+LuF/Ec9rB0cjwJgAO/3kT9DtHYFcE2HWUO/o0/SgZ3vJEv3cEHIEqAt6XqtCcLmGILpnnlHOl0wnqDDsCt4jAo1sU2mV2BLZEIBoT0kNSCwsW0ClsvMR85acEnHHQuqBWPDsdbLeDkeHKApvFuDne9re+ISh5swJ2VTo7ENo+D+mKb+PJSKYrdQuLsOND9w3+FMZgkupVPgws5XkPgVZM47yLzgMyle+xCpAP3t05AkdBIBgdIzNmMMzjjsKn8+EIHB2BvN94Xzq6trr569Mln1l2vdzopu6pjoAjsBsCbnzYDXqv+BYQ0IL3Sb7YjQtg3vZjtV/Lscj+LSPOORJfZuEj3WIk4QTvTsOB0sHrwmggPMGSvwkO5WP4rxxzpZvjHz3yf8eweL86ArsgoHZaGhuHnFuyC69eqSNwZARuvC9dvMw4sq76eBuoS579ffOGvqo83RFwBHZA4OEOdXqVjsBNIKCFMAtr/voRY4A5LPWcxbDmZCHtIlDd7Bj4TfUN2o1gTG51FV988vGe+OQtR5djotHATGVYqIHxK93zuQdbNTFkJPl1H5zS0MHHqq91F0nM5hdHYG8EgjFO7dTe2u7Nj9fvCJwVgZvpS4wXVz5mNHQZn/3IfPGsP2tjdb4dgVtC4NEtCeuyOgIbI8DnFSyqOU+BxS9vOTmLYW1DAJ8rvFCd4cGs+tbcZaGqZjv4xShzwadkYNKB4QH8MDDkn1dwMB/xja2XlUkYedJnHLp35wgcCoHY1oecW3Iovp0ZR+BoCHhfOppGpvNT0SVzgnx35/QKvKQj4AhsjgB/UcPbw9/l2brsVsTNVeAVOgKOgCYYGGnYmdB2sOYsgESb3R8s6nx8m4WkF14LgdhGP1Ab9W3Ea4HsdG8CAe9L16Pmmi4Vz4udlxovfSfj9ajbJblyBNRv2Z38k/rtA//s4sqV7eI5AmdAAMOA/OKGB2SHLvTPgIPzeHsI6IHMW7zGuSWKs7Mfbg8Ql9gRmIiA96WJwB2wWI8uOVSbA6t9nDyg7pwlR6APATc+9CHk6Y6AI+AIOAKOwAoIxMkznxb1nluyQvVO0hG4GgS8L12NKvkHrL7znOxfqzDcunMEHIGTIeCfXZxMYc6uI+AIOAKOwHUgoEn235KEc0saTjt1eDa7cwQcgYEIeF8aCNQJsvXpUun8a9WdPJ9eNA6iPoF4zqIjcJMIqN+mzy4e3SQCLrQj4Ag4Ao6AI7AzApo4v70zC169I3AVCHhfugo1BiH6dKl0PxvnetTtktwgAv7ZxQ0q3UV2BBwBR8ARcAQcAUfAEXAEHAFHwBFwBLZEwI0PW6LtdTkCjoAjcIMIaLvde/L868hh3Jo8sb0Q+ocRdgQja+FyZkxGwDcoq2N8CdNamFBTX9vrS7/k1mMcAUfAEXAEpiLgxoepyHk5R8ARcAQOgoAmz9/I/yH/j/yhTgAXP5xp8FxbZQf/m4nKYKz4W34Vg8UUnsaoWrL+rPz/Ro4x5fbOuyYuZ8EEncmfsu2dBeOyna/Z7qirD5e+9JJfDzsCjoAj4AhMR8CND9Ox85KOgCPgCBwCAU2e+b9z/jWBifbrQzD1holfdTv2G10MFvj335BZ9G4KT2MZ+FIFfhpbaOf8a+NyBkzO3vbOgHHZzNdud9TXh0tfesmzhx0BR8ARcAQmIODGhwmgeRFHwBFwBA6IwAfi6VAnf+uNJjsXfpNB5M8xeGFAkX8g/+2YckPyTuVpCO08j3i/U5j/ov8mjz/q/Ra4LIWJeOWzllVwFY+nbntLYbxVO92i3SFLHy596Vvh4fU4Ao6AI3DtCPhfbV67hl0+R8ARuAkENInnbxu/0ySaXRCHcOLpDzHyiXgaZXxYk/kteVJdvEX/r+Q//L9abIXLEpiIBn/Z9d6R2vqQNnsmjIfIs0SerTCB176215e+hLxOwxFwBByBW0RA42v6q03f+XCLLcBldgQcgatCQIM6Zwuw0D3MzofIE28cRxseKCv/BL+koubwNIUPyc7uhz9V78dTym9VZktcjo4JWMifuu0dHWNr11u2O+rsw6Uv3fj2qyPgCDgCjsB0BB5NL+olHQFHwBFwBLZAQJN0LMafyLOTAMeC/mtNlonDhcWtwo3zHlSOePJgnLBPGKCF+1D+lcp8z2JL91/I/y/Gc0DkXEMG9bTSiPXBG3K8I4/h5AvV+YHS4PW5POkc3PiZPG8t4fGFPOk/ylse3b6RhUCHq/JkZWL9nFEB1vDFQZl8PsJ2/FZ5lNblKIMM1bKqk3o4swNjBY7wS9WH/MHFPM8UQEe4d+XJk+hGjFpxDSXqP1vj0otJndV5KV0YKe2a2t4gjGO72qvtbd3uaDx9uPSlz2uAXtoRcAQcgRtH4NGNy+/iOwKOgCNwaAS0OGBh8ESLzGBoiAskFsb5v0eQxqS5dHzy8K3KvFQCi3UWq+GzjLjo4FR/yrCwDsYJhVkQcFDi3E8F4OniwMVY779NHuUJTvHhUErFY5D4ROHfY1K4KB7DCsYJZGeR+LHiTBbC/NvHz7G8gq2ulSfLqfIs3OH5A6OjOMKfKhyAUhh9YBygTnj9VmlmNFDwwsFv9cBN0YMOsn4pOsHYoDgMLb/qil7YOUEYPhqfsCj+JWnKgwEJnqq4Kq3LLYULhhEOCcWghDw1XDox6WJ0TlofRmAt+kdve4thLDz2bntLtbvF+qP0v0vbnNOuvawj4Ag4AmdC4OGZmHVeHQFHwBG4JQS0OMAQwMF64e0/sscFErcYFMyxaM7DtlPgVczAIuMdFqlWgHC8f1fxueGCeCbzcx11/tVC5KninsaFYJ6McSR3bWVJZ4H4NJclwwQculyNJ/senAU+xgTqyF3YUSKeMTywK8R2nYDVr3nGlnvk6MKTOv8UzbTLQWH4xFk58rQZVjAY8ZeeT3QdiquyXri5uKC7PyTD92Cje2SG55rrw6RWbm78UIzgr83t2fbWwHjvtje33a3RH/dqm23tzeMcAUfAEbg6BHznw9Wp1AVyBByBIyAQF9d9C9OSVd4Wv84i+czgF8XdWVxcaBIMBoMYZpGaL15JZ0H7OvLBJJ+3jLljwYr77v6SfsmXGyNSwsgbFuaJbysrnvgHCCb47LqgHowmLKxzw4hlr11L44Dls8W6hctrK08xU9jRID7yHSUkYdCwOIxBuZEE7H6XHBx+WOOJeDMm6PaNi7pBD0Y/JIoWusx3QVD+VUjMfpQP/RLDJyvscJmK61xc4CH/W1R2cvCpSs1VMckLSB500mZQQs/vKJ1PhUpHu0/GujxR8Wdue4iyGMbCDgz3bntz292i/TG2lUFtM+b1iyPgCDgCjsBIBNz4MBIwz+4IOAKOwBAEtNBh4c3fX05yWhywMGCBUL5BZjHGAgv6OMJ3CjcWv0U6OyZKgwJGhpwOtHDQKw0SIWHBH3B5Jk9dLDB5e/+DeOSt+RDHIntp97kINjASTyz60UG+q4Q4w9p0kMcpebCjHI6t3jVneayutny0FdxcXO+pNH97cWnRG3w0sGySHBYS3fApUJlbemHROfXfLuZitEvbWwFja1dHbXu97S62i7zvWR/J48rm42FHwBFwBByBHRF4tGPdXrUj4Ag4Ao5AHQG2iOPKRVy5MyGFtSh7rEWKTcDvS9/veHhtgezKwr+xW0LliXts8SU9hTEU8M15cKqra7cCizRoNZxosDD4K19YKo635M91/UnxpbyN8jMDNZ7gE58bGagKPJLhRrzlb55JskX/bwQqjre7Zqwos1h8STfPZ3kusMwycS7EHFxn4ZLxYZ+vsHD8KI8v7rswKbIuF5yJ0VxGjoaxtas9294sTFboj+h4l7Y5t3F5eUfAEXAEzoLAw7Mw6nw6Ao6AI3BjCDAxz894MPFZEOeL5DzMboLStb1BZCHLYjWnQzm2q9shh6SHxTcJWrjxhtQOrMRA0FYXWc2xuGEiXzroNrbkaxHBZwcYQkhb09V4sjptQWbhgIcFWq4YY/oOnESmu5ay6Jb41/JmaGpkE+YcdEk6+TAyNZzSn8QIdsfMwXURXMTPN+KDT42+i3xH9i4uVUwuci4bMQejuZwcCuODtL1FMMkUM6s/Rjp7tc1MDL91BBwBR+B6EXh4vaK5ZI6AI+AInBqBsANACzomw8Hp3j7BKHcH8OYbg0LalUCBWJb40sjQeKNP3uhYBBttDlW0cwc454BPNEJaXFh2vdmGHItmtri3uWeR3zwNPq1uiyduSdfKU7YQy7HGQAJOJU+BH/HPQofzOLp2f5C37xMEDBzviV7DIBPpwy8OrD9XnBkbQqR+XshzyKPxOBRXK2/XRXABC3nkfV+8lm3O6uLah0med+n7oRgdsu0tjPHebW+RdkcDif1lif64Z9tcuq07PUfAEXAEDofAo8Nx5Aw5Ao6AI+AIhLfimlDztpvzEDhs8F153hSW5zRwTgKLCP6GsfxGnsV0Mhro3hzxjUMOYwJnPfBXg+EzCMusK7snvszC8GcL4zw6v2fxidGizVE3i2kWeHfybP3mbyLtbyXZVREMJMqDwYW64bmMh1/i7awIFpYfig54tLkunljgv1B53t7jwBp3sYhWHvDhExerN2Ss/GDQaWCX54sy/0tx1M3Chx0m6Jp/1Qg86MrBkqRxqCR44cCOXRdmeCCuiiuJHW4RXDL6GGb461N2bjQ+7Yl5OjHJ6KxxW8VI/GLcKdvYodpeBshsjGlfknnPtrdIu5MMi/VH4btn28zU67eOgCPgCFwnAhyTzcOWk6nf50F0nWK6VI6AI+AInB8BTbKZrGNMGLLoXUxg1fuPiI1+RqgcC2mMIod5tgzlSfmCAUa8h7+TMDAVj1EkGXpimDMsLowxSsNA8LvSMK4c2onXQbpSvgYuUcb/SriPDAPFYRCCHrtnGkaumH8WJqLxqWhPPXBSRfdx4vs0GG+F0FRMjD+VX6w/itZp+qvJ71dHwBFwBM6AgMZXntuc6/Xg4RkYdh4dAUfAEbg1BDRQN7bYx4kxE2379GJLSFhYs6BMTvzUdjWkPLoJ32DnEQe4H8rTJ+K1YVCIOqH8K91/itc9u01qxhXeog/BSdl2d5Nw0USCnRh/yXM1Rzsl/KNFZNclMGG3R8OokdE/8u2ZMN4Kx0mYwNwK/XGJtrkVbl6PI+AIOAKnRODRKbl2ph0BR8ARuGIENKlmQv6Nrm/HxR3SYnTg7yjzbfbEb+H4jIEt/xhEWFQ+Jizf6cTrDyrzUp631LUFeieNpRNH8MQCulzg/qo4ZG8YgEQTTBpOMpPvY6XxucTh3UxcaB9fS2bOHOGTEQxVH5S4LIVJSVd1ncKdCeOtAJ2JyWL9cam2uRVuXo8j4Ag4AmdFIP/sok2Gn/VgqH0725bf4xwBR8ARcARmIqCJMAtfPq3gMwsW9nJH1gAAAMtJREFUsWzb558m2r6fV9JxXZzUs9WOnQSHcF08KQ3DD/hjaMFgwiF2oz9zER10x2cHhzC6iJdetzYuZ8SkF7SRGRzjS8DWxoQa+9peX/ol1x7jCDgCjoAj0IaAxlM+MWzslrV8mhM9wPjAxJZvONscf7m2x1u2Nl48zhFwBBwBR+CECOhBxEOIXQDlToLdpFmTJ9HmmYrR4jSGB1PEWricGRPDZqmrY3yJ5FqYUFNf2+tLv+TWYxwBR8ARcARqCMQxFfvChdO86Pv/AwefqU0hoq+nAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- c u_{1} + g m_{b} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{2}\\right) + \\frac{3 g m_{c} \\left(\\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) + \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 g m_{c} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2} - k q_{1} + F - \\frac{3 \\left(k_{T} q_{3} + T\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2 l}\\\\- g m_{b} \\operatorname{sin}\\left(q_{2}\\right) - \\frac{3 g m_{c} \\left(\\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) + \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)\\right)}{2} - \\frac{3 g m_{c} \\operatorname{sin}\\left(q_{2}\\right)}{2} + \\frac{3 \\left(k_{T} q_{3} + T\\right)}{2 l}\\\\- g l m_{c} \\left(\\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) + \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)\\right)\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                3⋅g⋅m_c⋅(sin(q₂)⋅cos(q₃) + sin(q₃)⋅cos(q₂))⋅c\n",
       "⎢-c⋅u₁ + g⋅m_b⋅sin(q₂)⋅cos(q₂) + ─────────────────────────────────────────────\n",
       "⎢                                                         2                   \n",
       "⎢                                                                             \n",
       "⎢                                          3⋅g⋅m_c⋅(sin(q₂)⋅cos(q₃) + sin(q₃)⋅\n",
       "⎢                         -g⋅m_b⋅sin(q₂) - ───────────────────────────────────\n",
       "⎢                                                               2             \n",
       "⎢                                                                             \n",
       "⎣                                                  -g⋅l⋅m_c⋅(sin(q₂)⋅cos(q₃) +\n",
       "\n",
       "os(q₂)   3⋅g⋅m_c⋅sin(q₂)⋅cos(q₂)              3⋅(k_T⋅q₃ + T)⋅cos(q₂)⎤\n",
       "────── + ─────────────────────── - k⋅q₁ + F - ──────────────────────⎥\n",
       "                    2                                  2⋅l          ⎥\n",
       "                                                                    ⎥\n",
       "cos(q₂))   3⋅g⋅m_c⋅sin(q₂)   3⋅(k_T⋅q₃ + T)                         ⎥\n",
       "──────── - ─────────────── + ──────────────                         ⎥\n",
       "                  2               2⋅l                               ⎥\n",
       "                                                                    ⎥\n",
       " sin(q₃)⋅cos(q₂))                                                   ⎦"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{9 I_{B_bo} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{2}\\right)}{4 l^{2}} + m_{b} \\left(- \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{cos}\\left(q_{2}\\right) + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{2}}{2 l}\\right) \\operatorname{sin}\\left(q_{2}\\right) - \\frac{3 m_{c} \\left(- \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)\\right) \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2} - m_{c} \\left(- \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) - \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)\\right) \\left(u_{3} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right)}{2 l}\\right) \\left(l u_{3} - \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) + \\frac{9 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} + 3 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{2}\\right) - \\frac{3 m_{c} \\left(u_{3} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right)}{2 l}\\right) \\left(l u_{3} - \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2} - m_{c} \\left(l \\left(- \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)\\right) - \\frac{3 l \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} - \\frac{3 l \\operatorname{cos}\\left(q_{2}\\right)}{2}\\right) \\dot{u}_{3} - \\left(- \\frac{9 I_{B_bo} \\operatorname{cos}\\left(q_{2}\\right)}{4 l^{2}} + m_{c} \\left(- \\frac{3 \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right)}{2} - 3 \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) - 3 \\operatorname{cos}\\left(q_{2}\\right)\\right)\\right) \\dot{u}_{2} - \\left(\\frac{9 I_{B_bo} \\operatorname{cos}^{2}\\left(q_{2}\\right)}{4 l^{2}} + m_{a} + m_{b} \\operatorname{sin}^{2}\\left(q_{2}\\right) + m_{c} \\left(- 3 \\left(- \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)\\right) \\operatorname{cos}\\left(q_{2}\\right) + \\frac{9 \\operatorname{cos}^{2}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} + \\frac{3 \\operatorname{cos}^{2}\\left(q_{2}\\right)}{2} + 1\\right)\\right) \\dot{u}_{1} + \\frac{3 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) \\operatorname{sin}\\left(q_{2}\\right)}{2 l} + \\frac{9 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)}{4 l}\\\\- \\frac{9 I_{B_bo} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l^{2}} - m_{c} \\left(\\frac{3 l \\operatorname{cos}\\left(q_{3}\\right)}{2} + \\frac{3 l}{2}\\right) \\dot{u}_{3} - \\frac{9 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} - \\frac{9 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2} + \\frac{3 m_{c} \\left(u_{3} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right)}{2 l}\\right) \\left(l u_{3} - \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\operatorname{sin}\\left(q_{3}\\right)}{2} - \\left(- \\frac{9 I_{B_bo} \\operatorname{cos}\\left(q_{2}\\right)}{4 l^{2}} + m_{c} \\left(- \\frac{3 \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right)}{2} - 3 \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) - 3 \\operatorname{cos}\\left(q_{2}\\right)\\right)\\right) \\dot{u}_{1} - \\left(\\frac{9 I_{B_bo}}{4 l^{2}} + m_{b} + m_{c} \\left(\\frac{9 \\operatorname{cos}\\left(q_{3}\\right)}{2} + \\frac{9}{2}\\right)\\right) \\dot{u}_{2} - \\frac{3 m_{b} \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2 l} - \\frac{9 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right)}{4 l}\\\\- l^{2} m_{c} \\dot{u}_{3} - \\frac{3 l m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} - \\frac{3 l m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2} - m_{c} \\left(\\frac{3 l \\operatorname{cos}\\left(q_{3}\\right)}{2} + \\frac{3 l}{2}\\right) \\dot{u}_{2} - \\frac{3 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right)}{2} - m_{c} \\left(l \\left(- \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)\\right) - \\frac{3 l \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} - \\frac{3 l \\operatorname{cos}\\left(q_{2}\\right)}{2}\\right) \\dot{u}_{1}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡           ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                                           \n",
       "⎢9⋅I_{B_bo}⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)⋅cos(q₂)                        \n",
       "⎢           ⎝      2⋅l        2⋅l ⎠                          ⎛  ⎛  3⋅u₁⋅cos(q₂\n",
       "⎢───────────────────────────────────────────────────── + m_b⋅⎜- ⎜- ───────────\n",
       "⎢                            2                               ⎝  ⎝      2⋅l    \n",
       "⎢                         4⋅l                                                 \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎣                                                                             \n",
       "\n",
       "                                                                              \n",
       "                                                          3⋅m_c⋅(-sin(q₂)⋅sin(\n",
       ")   3⋅u₂⎞              3⋅(-u₁⋅cos(q₂) + u₂)⋅u₂⎞                               \n",
       "─ + ────⎟⋅u₁⋅cos(q₂) + ───────────────────────⎟⋅sin(q₂) - ────────────────────\n",
       "    2⋅l ⎠                        2⋅l          ⎠                               \n",
       "                                                                              \n",
       "                                                                              \n",
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       "                                                                              \n",
       "\n",
       "                       ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                                \n",
       "q₃) + cos(q₂)⋅cos(q₃))⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)                     \n",
       "                       ⎝      2⋅l        2⋅l ⎠                                \n",
       "───────────────────────────────────────────────────────── - m_c⋅(-sin(q₂)⋅cos(\n",
       "                  2                                                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
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       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                       ⎛     3⋅(-u₁⋅cos(q₂) + u₂)⎞ ⎛       3⋅u₁⋅cos(q₂)   3⋅u₂\n",
       "q₃) - sin(q₃)⋅cos(q₂))⋅⎜u₃ + ────────────────────⎟⋅⎜l⋅u₃ - ──────────── + ────\n",
       "                       ⎝             2⋅l         ⎠ ⎝            2          2  \n",
       "                                                                              \n",
       "                                                                              \n",
       "               ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                                        \n",
       "    9⋅I_{B_bo}⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)                             \n",
       "               ⎝      2⋅l        2⋅l ⎠                  ⎛3⋅l⋅cos(q₃)   3⋅l⎞   \n",
       "  - ───────────────────────────────────────────── - m_c⋅⎜─────────── + ───⎟⋅u₃\n",
       "                            2                           ⎝     2         2 ⎠   \n",
       "                         4⋅l                                                  \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "          ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                                             \n",
       "    9⋅m_c⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)⋅cos(q₂)⋅cos(q₃)                  \n",
       "⎞         ⎝      2⋅l        2⋅l ⎠                                    ⎛  3⋅u₁⋅c\n",
       "⎟ + ──────────────────────────────────────────────────────── + 3⋅m_c⋅⎜- ──────\n",
       "⎠                              2                                     ⎝      2⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "          ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                            ⎛  3⋅u₁⋅cos(q₂)  \n",
       "    9⋅m_c⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)⋅cos(q₃)   9⋅m_c⋅⎜- ──────────── +\n",
       "          ⎝      2⋅l        2⋅l ⎠                            ⎝      2⋅l       \n",
       "̇ - ──────────────────────────────────────────────── - ───────────────────────\n",
       "                           2                                              2   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                          ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞             \n",
       "                                  3⋅l⋅m_c⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)⋅c\n",
       "                      2                   ⎝      2⋅l        2⋅l ⎠             \n",
       "                   - l ⋅m_c⋅u₃̇ - ────────────────────────────────────────────\n",
       "                                                          2                   \n",
       "\n",
       "                                          ⎛     3⋅(-u₁⋅cos(q₂) + u₂)⎞ ⎛       \n",
       "                                    3⋅m_c⋅⎜u₃ + ────────────────────⎟⋅⎜l⋅u₃ - \n",
       "os(q₂)   3⋅u₂⎞                            ⎝             2⋅l         ⎠ ⎝       \n",
       "────── + ────⎟⋅u₁⋅sin(q₂)⋅cos(q₂) - ──────────────────────────────────────────\n",
       "l        2⋅l ⎠                                                            2   \n",
       "                                                                              \n",
       "                                                                              \n",
       " 3⋅u₂⎞                    ⎛     3⋅(-u₁⋅cos(q₂) + u₂)⎞ ⎛       3⋅u₁⋅cos(q₂)   3\n",
       " ────⎟⋅u₁⋅sin(q₂)   3⋅m_c⋅⎜u₃ + ────────────────────⎟⋅⎜l⋅u₃ - ──────────── + ─\n",
       " 2⋅l ⎠                    ⎝             2⋅l         ⎠ ⎝            2          \n",
       "───────────────── + ──────────────────────────────────────────────────────────\n",
       "                                                      2                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                 ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                                      \n",
       "os(q₃)   3⋅l⋅m_c⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)                           \n",
       "                 ⎝      2⋅l        2⋅l ⎠                  ⎛3⋅l⋅cos(q₃)   3⋅l⎞ \n",
       "────── - ────────────────────────────────────────── - m_c⋅⎜─────────── + ───⎟⋅\n",
       "                             2                            ⎝     2         2 ⎠ \n",
       "\n",
       "3⋅u₁⋅cos(q₂)   3⋅u₂⎞                                                          \n",
       "──────────── + ────⎟⋅sin(q₃)⋅cos(q₂)                                          \n",
       "     2          2  ⎠                       ⎛                                  \n",
       "──────────────────────────────────── - m_c⋅⎜l⋅(-sin(q₂)⋅sin(q₃) + cos(q₂)⋅cos(\n",
       "                                           ⎝                                  \n",
       "                                                                              \n",
       "                                                                              \n",
       "⋅u₂⎞                                                                          \n",
       "───⎟⋅sin(q₃)                                                                  \n",
       "2  ⎠           ⎛  9⋅I_{B_bo}⋅cos(q₂)       ⎛  3⋅sin(q₂)⋅sin(q₃)               \n",
       "──────────── - ⎜- ────────────────── + m_c⋅⎜- ───────────────── - 3⋅cos(q₂)⋅co\n",
       "               ⎜            2              ⎝          2                       \n",
       "               ⎝         4⋅l                                                  \n",
       "                                                                              \n",
       "            ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                                           \n",
       "      3⋅m_c⋅⎜- ──────────── + ────⎟⋅(-u₁⋅cos(q₂) + u₂)⋅sin(q₃)                \n",
       "            ⎝       2          2  ⎠                                  ⎛        \n",
       "u₂̇ - ──────────────────────────────────────────────────────── - m_c⋅⎜l⋅(-sin(\n",
       "                                 2                                   ⎝        \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "       3⋅l⋅cos(q₂)⋅cos(q₃)   3⋅l⋅cos(q₂)⎞       ⎛  9⋅I_{B_bo}⋅cos(q₂)       ⎛ \n",
       "q₃)) - ─────────────────── - ───────────⎟⋅u₃̇ - ⎜- ────────────────── + m_c⋅⎜-\n",
       "                2                 2     ⎠       ⎜            2              ⎝ \n",
       "                                                ⎝         4⋅l                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                 ⎞⎞       ⎛9⋅I_{B_bo}             ⎛9⋅cos(q₃)   9⎞⎞       3⋅m_b\n",
       "s(q₃) - 3⋅cos(q₂)⎟⎟⋅u₁̇ - ⎜────────── + m_b + m_c⋅⎜───────── + ─⎟⎟⋅u₂̇ - ─────\n",
       "                 ⎠⎟       ⎜      2                ⎝    2       2⎠⎟            \n",
       "                  ⎠       ⎝   4⋅l                                ⎠            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                 3⋅l⋅cos(q₂)⋅cos(q₃)   3⋅l⋅cos(q₂)⎞           \n",
       "q₂)⋅sin(q₃) + cos(q₂)⋅cos(q₃)) - ─────────────────── - ───────────⎟⋅u₁̇       \n",
       "                                          2                 2     ⎠           \n",
       "\n",
       "                                                                              \n",
       "                                                           ⎛              2   \n",
       " 3⋅sin(q₂)⋅sin(q₃)                                ⎞⎞       ⎜9⋅I_{B_bo}⋅cos (q₂\n",
       " ───────────────── - 3⋅cos(q₂)⋅cos(q₃) - 3⋅cos(q₂)⎟⎟⋅u₂̇ - ⎜──────────────────\n",
       "         2                                        ⎠⎟       ⎜           2      \n",
       "                                                   ⎠       ⎝        4⋅l       \n",
       "                                                                              \n",
       "                                       ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                \n",
       "                                 9⋅m_c⋅⎜- ──────────── + ────⎟⋅(-u₁⋅cos(q₂) + \n",
       "⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)         ⎝       2          2  ⎠                \n",
       "────────────────────────────── - ─────────────────────────────────────────────\n",
       "           2⋅l                                             4⋅l                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                            ⎛                                                 \n",
       ")               2           ⎜                                                 \n",
       "─ + mₐ + m_b⋅sin (q₂) + m_c⋅⎜-3⋅(-sin(q₂)⋅sin(q₃) + cos(q₂)⋅cos(q₃))⋅cos(q₂) +\n",
       "                            ⎝                                                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "u₂)⋅sin(q₃)                                                                   \n",
       "                                                                              \n",
       "───────────                                                                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                   ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞    \n",
       "      2                    2        ⎞⎞       3⋅m_c⋅⎜- ──────────── + ────⎟⋅(-u\n",
       " 9⋅cos (q₂)⋅cos(q₃)   3⋅cos (q₂)    ⎟⎟             ⎝       2          2  ⎠    \n",
       " ────────────────── + ────────── + 1⎟⎟⋅u₁̇ + ─────────────────────────────────\n",
       "         2                2         ⎠⎟                                 2⋅l    \n",
       "                                     ⎠                                        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
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       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                       \n",
       "₁⋅cos(q₂) + u₂)⋅sin(q₂)   9⋅m_c⋅⎜- ──────────── + ────⎟⋅(-u₁⋅cos(q₂) + u₂)⋅sin\n",
       "                                ⎝       2          2  ⎠                       \n",
       "─────────────────────── + ────────────────────────────────────────────────────\n",
       "                                                        4⋅l                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
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       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "            ⎤\n",
       "(q₃)⋅cos(q₂)⎥\n",
       "            ⎥\n",
       "────────────⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎥\n",
       "            ⎦"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frstar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{9 I_{B_bo} \\operatorname{cos}^{2}\\left(q_{2}\\right)}{4 l^{2}} + m_{a} + m_{b} \\operatorname{sin}^{2}\\left(q_{2}\\right) + m_{c} \\left(- 3 \\left(- \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)\\right) \\operatorname{cos}\\left(q_{2}\\right) + \\frac{9 \\operatorname{cos}^{2}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} + \\frac{3 \\operatorname{cos}^{2}\\left(q_{2}\\right)}{2} + 1\\right) & - \\frac{9 I_{B_bo} \\operatorname{cos}\\left(q_{2}\\right)}{4 l^{2}} + m_{c} \\left(- \\frac{3 \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right)}{2} - 3 \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) - 3 \\operatorname{cos}\\left(q_{2}\\right)\\right) & m_{c} \\left(l \\left(- \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)\\right) - \\frac{3 l \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} - \\frac{3 l \\operatorname{cos}\\left(q_{2}\\right)}{2}\\right)\\\\- \\frac{9 I_{B_bo} \\operatorname{cos}\\left(q_{2}\\right)}{4 l^{2}} + m_{c} \\left(- \\frac{3 \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right)}{2} - 3 \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) - 3 \\operatorname{cos}\\left(q_{2}\\right)\\right) & \\frac{9 I_{B_bo}}{4 l^{2}} + m_{b} + m_{c} \\left(\\frac{9 \\operatorname{cos}\\left(q_{3}\\right)}{2} + \\frac{9}{2}\\right) & m_{c} \\left(\\frac{3 l \\operatorname{cos}\\left(q_{3}\\right)}{2} + \\frac{3 l}{2}\\right)\\\\m_{c} \\left(l \\left(- \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)\\right) - \\frac{3 l \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} - \\frac{3 l \\operatorname{cos}\\left(q_{2}\\right)}{2}\\right) & m_{c} \\left(\\frac{3 l \\operatorname{cos}\\left(q_{3}\\right)}{2} + \\frac{3 l}{2}\\right) & l^{2} m_{c}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡              2                               ⎛                              \n",
       "⎢9⋅I_{B_bo}⋅cos (q₂)               2           ⎜                              \n",
       "⎢─────────────────── + mₐ + m_b⋅sin (q₂) + m_c⋅⎜-3⋅(-sin(q₂)⋅sin(q₃) + cos(q₂)\n",
       "⎢           2                                  ⎝                              \n",
       "⎢        4⋅l                                                                  \n",
       "⎢                                                                             \n",
       "⎢                            9⋅I_{B_bo}⋅cos(q₂)       ⎛  3⋅sin(q₂)⋅sin(q₃)    \n",
       "⎢                          - ────────────────── + m_c⋅⎜- ───────────────── - 3\n",
       "⎢                                      2              ⎝          2            \n",
       "⎢                                   4⋅l                                       \n",
       "⎢                                                                             \n",
       "⎢                              ⎛                                         3⋅l⋅c\n",
       "⎢                          m_c⋅⎜l⋅(-sin(q₂)⋅sin(q₃) + cos(q₂)⋅cos(q₃)) - ─────\n",
       "⎣                              ⎝                                              \n",
       "\n",
       "                         2                    2        ⎞                      \n",
       "                    9⋅cos (q₂)⋅cos(q₃)   3⋅cos (q₂)    ⎟    9⋅I_{B_bo}⋅cos(q₂)\n",
       "⋅cos(q₃))⋅cos(q₂) + ────────────────── + ────────── + 1⎟  - ──────────────────\n",
       "                            2                2         ⎠              2       \n",
       "                                                                   4⋅l        \n",
       "                                                                              \n",
       "                            ⎞                                                 \n",
       "⋅cos(q₂)⋅cos(q₃) - 3⋅cos(q₂)⎟                                                 \n",
       "                            ⎠                                                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "os(q₂)⋅cos(q₃)   3⋅l⋅cos(q₂)⎞                                                 \n",
       "────────────── - ───────────⎟                                                 \n",
       "    2                 2     ⎠                                                 \n",
       "\n",
       "                                                                              \n",
       "       ⎛  3⋅sin(q₂)⋅sin(q₃)                                ⎞      ⎛           \n",
       " + m_c⋅⎜- ───────────────── - 3⋅cos(q₂)⋅cos(q₃) - 3⋅cos(q₂)⎟  m_c⋅⎜l⋅(-sin(q₂)\n",
       "       ⎝          2                                        ⎠      ⎝           \n",
       "                                                                              \n",
       "                                                                              \n",
       " 9⋅I_{B_bo}             ⎛9⋅cos(q₃)   9⎞                                       \n",
       " ────────── + m_b + m_c⋅⎜───────── + ─⎟                                       \n",
       "       2                ⎝    2       2⎠                                       \n",
       "    4⋅l                                                                       \n",
       "                                                                              \n",
       "            ⎛3⋅l⋅cos(q₃)   3⋅l⎞                                               \n",
       "        m_c⋅⎜─────────── + ───⎟                                               \n",
       "            ⎝     2         2 ⎠                                               \n",
       "\n",
       "                                                                ⎤\n",
       "                              3⋅l⋅cos(q₂)⋅cos(q₃)   3⋅l⋅cos(q₂)⎞⎥\n",
       "⋅sin(q₃) + cos(q₂)⋅cos(q₃)) - ─────────────────── - ───────────⎟⎥\n",
       "                                       2                 2     ⎠⎥\n",
       "                                                                ⎥\n",
       "                                                                ⎥\n",
       "                ⎛3⋅l⋅cos(q₃)   3⋅l⎞                             ⎥\n",
       "            m_c⋅⎜─────────── + ───⎟                             ⎥\n",
       "                ⎝     2         2 ⎠                             ⎥\n",
       "                                                                ⎥\n",
       "                                                                ⎥\n",
       "                      2                                         ⎥\n",
       "                     l ⋅m_c                                     ⎥\n",
       "                                                                ⎦"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kane.mass_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{9 I_{B_bo} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{2}\\right)}{4 l^{2}} - c u_{1} + g m_{b} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{2}\\right) + \\frac{3 g m_{c} \\left(\\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) + \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 g m_{c} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2} - k q_{1} + m_{b} \\left(- \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{cos}\\left(q_{2}\\right) + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{2}}{2 l}\\right) \\operatorname{sin}\\left(q_{2}\\right) - \\frac{3 m_{c} \\left(- \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)\\right) \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2} - m_{c} \\left(- \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) - \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)\\right) \\left(u_{3} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right)}{2 l}\\right) \\left(l u_{3} - \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) + \\frac{9 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} + 3 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{2}\\right) - \\frac{3 m_{c} \\left(u_{3} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right)}{2 l}\\right) \\left(l u_{3} - \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2} + F + \\frac{3 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) \\operatorname{sin}\\left(q_{2}\\right)}{2 l} + \\frac{9 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)}{4 l} - \\frac{3 \\left(k_{T} q_{3} + T\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2 l}\\\\- \\frac{9 I_{B_bo} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l^{2}} - g m_{b} \\operatorname{sin}\\left(q_{2}\\right) - \\frac{3 g m_{c} \\left(\\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) + \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)\\right)}{2} - \\frac{3 g m_{c} \\operatorname{sin}\\left(q_{2}\\right)}{2} - \\frac{9 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} - \\frac{9 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2} + \\frac{3 m_{c} \\left(u_{3} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right)}{2 l}\\right) \\left(l u_{3} - \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\operatorname{sin}\\left(q_{3}\\right)}{2} - \\frac{3 m_{b} \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2 l} - \\frac{9 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right)}{4 l} + \\frac{3 \\left(k_{T} q_{3} + T\\right)}{2 l}\\\\- g l m_{c} \\left(\\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) + \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)\\right) - \\frac{3 l m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} - \\frac{3 l m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 u_{2}}{2 l}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2} - \\frac{3 m_{c} \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right)}{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡           ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                                           \n",
       "⎢9⋅I_{B_bo}⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)⋅cos(q₂)                        \n",
       "⎢           ⎝      2⋅l        2⋅l ⎠                                           \n",
       "⎢───────────────────────────────────────────────────── - c⋅u₁ + g⋅m_b⋅sin(q₂)⋅\n",
       "⎢                            2                                                \n",
       "⎢                         4⋅l                                                 \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎣                                                                             \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "          3⋅g⋅m_c⋅(sin(q₂)⋅cos(q₃) + sin(q₃)⋅cos(q₂))⋅cos(q₂)   3⋅g⋅m_c⋅sin(q₂\n",
       "cos(q₂) + ─────────────────────────────────────────────────── + ──────────────\n",
       "                                   2                                       2  \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       ")⋅cos(q₂)              ⎛  ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞              3⋅(-u₁⋅cos(q₂) \n",
       "───────── - k⋅q₁ + m_b⋅⎜- ⎜- ──────────── + ────⎟⋅u₁⋅cos(q₂) + ───────────────\n",
       "                       ⎝  ⎝      2⋅l        2⋅l ⎠                        2⋅l  \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                          ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞             \n",
       "                               9⋅I_{B_bo}⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)  \n",
       "                                          ⎝      2⋅l        2⋅l ⎠             \n",
       "                             - ───────────────────────────────────────────── -\n",
       "                                                       2                      \n",
       "                                                    4⋅l                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                               ⎛  3⋅u₁⋅cos(q₂)\n",
       "                    3⋅m_c⋅(-sin(q₂)⋅sin(q₃) + cos(q₂)⋅cos(q₃))⋅⎜- ────────────\n",
       "+ u₂)⋅u₂⎞                                                      ⎝      2⋅l     \n",
       "────────⎟⋅sin(q₂) - ──────────────────────────────────────────────────────────\n",
       "        ⎠                                                 2                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                 3⋅g⋅m_c⋅(sin(q₂)⋅cos(q₃) + sin(q₃)⋅cos(q₂))   3⋅g⋅m_c⋅sin(q₂)\n",
       " g⋅m_b⋅sin(q₂) - ─────────────────────────────────────────── - ───────────────\n",
       "                                      2                               2       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                      -g⋅l⋅m_c⋅(sin(q₂)⋅cos(q₃\n",
       "                                                                              \n",
       "\n",
       "   3⋅u₂⎞                                                                      \n",
       " + ────⎟⋅u₁⋅sin(q₂)                                                           \n",
       "   2⋅l ⎠                                                       ⎛     3⋅(-u₁⋅co\n",
       "─────────────────── - m_c⋅(-sin(q₂)⋅cos(q₃) - sin(q₃)⋅cos(q₂))⋅⎜u₃ + ─────────\n",
       "                                                               ⎝             2\n",
       "                                                                              \n",
       "                                                                              \n",
       "         ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                            ⎛  3⋅u₁⋅cos(q₂)   \n",
       "   9⋅m_c⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)⋅cos(q₃)   9⋅m_c⋅⎜- ──────────── + \n",
       "         ⎝      2⋅l        2⋅l ⎠                            ⎝      2⋅l        \n",
       " - ──────────────────────────────────────────────── - ────────────────────────\n",
       "                          2                                              2    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                               ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                        \n",
       "                       3⋅l⋅m_c⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)⋅cos(q₃)   3⋅\n",
       "                               ⎝      2⋅l        2⋅l ⎠                        \n",
       ") + sin(q₃)⋅cos(q₂)) - ────────────────────────────────────────────────── - ──\n",
       "                                               2                              \n",
       "\n",
       "                                                  ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞     \n",
       "                                            9⋅m_c⋅⎜- ──────────── + ────⎟⋅u₁⋅s\n",
       "s(q₂) + u₂)⎞ ⎛       3⋅u₁⋅cos(q₂)   3⋅u₂⎞         ⎝      2⋅l        2⋅l ⎠     \n",
       "───────────⎟⋅⎜l⋅u₃ - ──────────── + ────⎟ + ──────────────────────────────────\n",
       "⋅l         ⎠ ⎝            2          2  ⎠                              2      \n",
       "                                                                              \n",
       "                                                                              \n",
       "3⋅u₂⎞                    ⎛     3⋅(-u₁⋅cos(q₂) + u₂)⎞ ⎛       3⋅u₁⋅cos(q₂)   3⋅\n",
       "────⎟⋅u₁⋅sin(q₂)   3⋅m_c⋅⎜u₃ + ────────────────────⎟⋅⎜l⋅u₃ - ──────────── + ──\n",
       "2⋅l ⎠                    ⎝             2⋅l         ⎠ ⎝            2          2\n",
       "──────────────── + ───────────────────────────────────────────────────────────\n",
       "                                                     2                        \n",
       "                                                                              \n",
       "                                                                              \n",
       "      ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                    ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞      \n",
       "l⋅m_c⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)   3⋅m_c⋅⎜- ──────────── + ────⎟⋅(-u₁⋅\n",
       "      ⎝      2⋅l        2⋅l ⎠                    ⎝       2          2  ⎠      \n",
       "──────────────────────────────────────── - ───────────────────────────────────\n",
       "                  2                                                   2       \n",
       "\n",
       "                                                                              \n",
       "in(q₂)⋅cos(q₂)⋅cos(q₃)                                                      3⋅\n",
       "                               ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                        \n",
       "────────────────────── + 3⋅m_c⋅⎜- ──────────── + ────⎟⋅u₁⋅sin(q₂)⋅cos(q₂) - ──\n",
       "                               ⎝      2⋅l        2⋅l ⎠                        \n",
       "                                                                              \n",
       "                                                                              \n",
       "u₂⎞                                                       ⎛  3⋅u₁⋅cos(q₂)   3⋅\n",
       "──⎟⋅sin(q₃)                                         9⋅m_c⋅⎜- ──────────── + ──\n",
       "  ⎠           3⋅m_b⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)         ⎝       2          2\n",
       "─────────── - ─────────────────────────────────── - ──────────────────────────\n",
       "                              2⋅l                                             \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "cos(q₂) + u₂)⋅sin(q₃)                                                         \n",
       "                                                                              \n",
       "─────────────────────                                                         \n",
       "                                                                              \n",
       "\n",
       "    ⎛     3⋅(-u₁⋅cos(q₂) + u₂)⎞ ⎛       3⋅u₁⋅cos(q₂)   3⋅u₂⎞                  \n",
       "m_c⋅⎜u₃ + ────────────────────⎟⋅⎜l⋅u₃ - ──────────── + ────⎟⋅sin(q₃)⋅cos(q₂)  \n",
       "    ⎝             2⋅l         ⎠ ⎝            2          2  ⎠                  \n",
       "──────────────────────────────────────────────────────────────────────────── +\n",
       "                                    2                                         \n",
       "                                                                              \n",
       "                                                                              \n",
       "u₂⎞                                                                           \n",
       "──⎟⋅(-u₁⋅cos(q₂) + u₂)⋅sin(q₃)                                                \n",
       "  ⎠                              3⋅(k_T⋅q₃ + T)                               \n",
       "────────────────────────────── + ──────────────                               \n",
       "4⋅l                                   2⋅l                                     \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "           ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                                    ⎛  3⋅u₁⋅\n",
       "     3⋅m_c⋅⎜- ──────────── + ────⎟⋅(-u₁⋅cos(q₂) + u₂)⋅sin(q₂)   9⋅m_c⋅⎜- ─────\n",
       "           ⎝       2          2  ⎠                                    ⎝       \n",
       " F + ──────────────────────────────────────────────────────── + ──────────────\n",
       "                               2⋅l                                            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "cos(q₂)   3⋅u₂⎞                                                            ⎤\n",
       "─────── + ────⎟⋅(-u₁⋅cos(q₂) + u₂)⋅sin(q₃)⋅cos(q₂)                         ⎥\n",
       "2          2  ⎠                                      3⋅(k_T⋅q₃ + T)⋅cos(q₂)⎥\n",
       "────────────────────────────────────────────────── - ──────────────────────⎥\n",
       "                4⋅l                                           2⋅l          ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎥\n",
       "                                                                           ⎦"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kane.forcing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pydy.system import System"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # provides basic array types and some linear algebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt  # used for plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys = System(kane)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys.constants = {ma: 1.0,\n",
    "                 mb: 2.0,\n",
    "                 mc: 1.0,\n",
    "                 g: 9.81,\n",
    "                 l: 2.0,\n",
    "                 IB_bo: 2.0,\n",
    "                 c: 10.0,\n",
    "                 k: 60.0,\n",
    "                 kT: 10.0}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys.times = np.linspace(0.0, 20.0, num=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys.initial_conditions = {q1: 1.0,\n",
    "                          q2: 0.0,\n",
    "                          q3: 0.0,\n",
    "                          u1: 0.0,\n",
    "                          u2: 0.0,\n",
    "                          u3: 0.0}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = sys.integrate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "axes = plt.plot(sys.times, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Angle [deg]')"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2, 1, sharex=True)\n",
    "axes[0].plot(sys.times, x[:, 0])\n",
    "axes[0].set_ylabel('{} [m]'.format(sm.latex(q1, mode='inline')))\n",
    "axes[1].plot(sys.times, np.rad2deg(x[:, 1:3]))\n",
    "axes[1].legend([sm.latex(q, mode='inline') for q in (q2, q3)])\n",
    "axes[1].set_xlabel('Time [s]')\n",
    "axes[1].set_ylabel('Angle [deg]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Animate with PyDy and pythreejs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pydy.viz.shapes import Cube, Cylinder, Sphere, Plane\n",
    "from pydy.viz.visualization_frame import VisualizationFrame\n",
    "from pydy.viz import Scene\n",
    "import pythreejs as pjs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define some PyDy shapes for each moving object you want visible in the scene."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "block_shape = Cube(0.25, color='red')\n",
    "cpendulum_shape = Plane(l, l/4, color='blue')\n",
    "spendulum_shape = Cylinder(l, 0.02, color='green')\n",
    "bob_shape = Sphere(0.2, color='black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a visualization frame that attaches a shape to a reference frame and point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "v1 = VisualizationFrame('block', N, Pab, block_shape)\n",
    "\n",
    "v2 = VisualizationFrame('cpendulum',\n",
    "                        B,\n",
    "                        Pab.locatenew('Bc', -l/2*B.y),\n",
    "                        cpendulum_shape)\n",
    "\n",
    "v3 = VisualizationFrame('spendulum', \n",
    "                        C,\n",
    "                        Pbc.locatenew('Cc', -l/2*C.y),\n",
    "                        spendulum_shape)\n",
    "\n",
    "v4 = VisualizationFrame('bob', C, Pc, bob_shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a scene with the origin point O and base reference frame N, then setup the scene with `create_static_html()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "scene = Scene(N, O, v1, v2, v3, v4, system=sys)\n",
    "scene.create_static_html(overwrite=True, silent=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create PyThreeJS mesh objects that mirror the shapes already created above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "block_mesh = pjs.Mesh(\n",
    "    pjs.BoxBufferGeometry(0.25, 0.25, 0.25),\n",
    "    pjs.MeshStandardMaterial(color='red'),\n",
    "    name=\"block\"\n",
    ")\n",
    "\n",
    "cpendulum_mesh = pjs.Mesh(\n",
    "    pjs.BoxBufferGeometry(height=sys.constants[l], width=sys.constants[l]/4.0, depth=0.01),\n",
    "    pjs.MeshStandardMaterial(color='blue'),\n",
    "    name='cpendulum'\n",
    ")\n",
    "\n",
    "spendulum_mesh = pjs.Mesh(\n",
    "    pjs.CylinderBufferGeometry(radiusTop=0.02, radiusBottom=0.02, height=sys.constants[l]),\n",
    "    pjs.MeshStandardMaterial(color='green'),\n",
    "    name='spendulum'\n",
    ")\n",
    "\n",
    "bob_mesh = pjs.Mesh(\n",
    "    pjs.SphereBufferGeometry(radius=0.2),\n",
    "    pjs.MeshStandardMaterial(color='black'),\n",
    "    name='bob'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the transformation matrices over time to define animation tracks for the meshes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "block_matrices = v1.evaluate_transformation_matrix(x, list(sys.constants.values()))\n",
    "cpendulum_matrices = v2.evaluate_transformation_matrix(x, list(sys.constants.values()))\n",
    "spendulum_matrices = v3.evaluate_transformation_matrix(x, list(sys.constants.values()))\n",
    "bob_matrices = v4.evaluate_transformation_matrix(x, list(sys.constants.values()))\n",
    "\n",
    "block_track = pjs.VectorKeyframeTrack(\n",
    "    name='scene/block.matrix',\n",
    "    times=list(sys.times),\n",
    "    values=block_matrices)\n",
    "\n",
    "cpendulum_track = pjs.VectorKeyframeTrack(\n",
    "    name='scene/cpendulum.matrix',\n",
    "    times=list(sys.times),\n",
    "    values=cpendulum_matrices)\n",
    "\n",
    "spendulum_track = pjs.VectorKeyframeTrack(\n",
    "    name='scene/spendulum.matrix',\n",
    "    times=list(sys.times),\n",
    "    values=spendulum_matrices)\n",
    "\n",
    "bob_track = pjs.VectorKeyframeTrack(\n",
    "    name='scene/bob.matrix',\n",
    "    times=list(sys.times),\n",
    "    values=bob_matrices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`matrixAutoUpdate` should be set to false so that we can directly manipulate the transformation matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "block_mesh.matrixAutoUpdate = False\n",
    "cpendulum_mesh.matrixAutoUpdate = False\n",
    "spendulum_mesh.matrixAutoUpdate = False\n",
    "bob_mesh.matrixAutoUpdate = False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the initial orientation and position of the objects in the scene."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "block_mesh.matrix = block_matrices[0]\n",
    "cpendulum_mesh.matrix = cpendulum_matrices[0]\n",
    "spendulum_mesh.matrix = spendulum_matrices[0]\n",
    "bob_mesh.matrix = bob_matrices[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create some axes indicators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_arrow = pjs.ArrowHelper(dir=[1, 0, 0], length=1.0, color='blue')\n",
    "y_arrow = pjs.ArrowHelper(dir=[0, 1, 0], length=1.0, color='red')\n",
    "z_arrow = pjs.ArrowHelper(dir=[0, 0, 1], length=1.0,color='green')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Setup the scene."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "view_width = 800\n",
    "view_height = 600\n",
    "\n",
    "camera = pjs.PerspectiveCamera(position=[1, 1, 1],\n",
    "                               aspect=view_width/view_height)\n",
    "key_light = pjs.DirectionalLight(position=[0, 10, 10])\n",
    "ambient_light = pjs.AmbientLight()\n",
    "\n",
    "scene_pjs = pjs.Scene(children=[block_mesh, cpendulum_mesh, spendulum_mesh, bob_mesh,\n",
    "                                x_arrow, y_arrow, z_arrow, \n",
    "                                camera, key_light, ambient_light])\n",
    "\n",
    "controller = pjs.OrbitControls(controlling=camera)\n",
    "renderer = pjs.Renderer(camera=camera, scene=scene_pjs, controls=[controller], width=view_width, height=view_height)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show the scene:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "215bdf2d79a545cd975a8607444797f4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Renderer(camera=PerspectiveCamera(aspect=1.3333333333333333, position=(1.0, 1.0, 1.0), quaternion=(0.0, 0.0, 0…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "renderer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Setup and show the animation controls:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cdca8dbfbab343498dd1e976061ffe4c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "AnimationAction(clip=AnimationClip(duration=20.0, tracks=(VectorKeyframeTrack(name='scene/block.matrix', times…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "clip = pjs.AnimationClip(tracks=[block_track, cpendulum_track, spendulum_track, bob_track], duration=sys.times[-1])\n",
    "action = pjs.AnimationAction(pjs.AnimationMixer(scene_pjs), clip, scene_pjs)\n",
    "action"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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 },
 "nbformat": 4,
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}

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