{
 "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": [
    "# 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": "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\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": [
    "# Partial Velocities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each partial velocity can be calculated manually like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\mathbf{\\hat{n}_x}$"
      ],
      "text/plain": [
       "n_x"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pab.vel(N).diff(u1, N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or you can use this convenience function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\mathbf{\\hat{n}_x}$"
      ],
      "text/plain": [
       "n_x"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pab.partial_velocity(N, u1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All partial velocities can be calculated at once with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\mathbf{\\hat{n}_x}, \\  0, \\  0\\right)$"
      ],
      "text/plain": [
       "(n_x, 0, 0)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pab.partial_velocity(N, u1, u2, u3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( -  \\operatorname{sin}\\left(q_{2}\\right)\\mathbf{\\hat{b}_y}, \\  \\mathbf{\\hat{b}_x}, \\  0\\right)$"
      ],
      "text/plain": [
       "(-sin(q₂) b_y, b_x, 0)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Bo.partial_velocity(N, u1, u2, u3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4hqOfVbU9S8i1K+nTh6gezEyyRnxzFbPnWA7DXXfnRQBD+rkERK+u5PrCS7Qeth8EXC96ZKnOpx3n6KGYFOz43n7NrZq2ZyG5ThL+ykRh3w2DpHsxI3bVhQ9bKPD9ypk7+x4EhH3fzIJ1hHxU24PdnoNdL9aVruOreU5ve9ZSMvYnhW9M2MjWvnFMhLuKENAoF5nQO/pZL4R3hCqSzTmL4nqxLvqObxh8edtzhJpJh2i3mY0MH9gIa7bwUwRz9myzHvxoNbTuToeA5MJ6On9N5nI5HezV5+R6sa6IHN9gE7ztOULNpEOs1bJmG/ba5MaWHY9sNpj7Ty5HFMeTDiEgYSETpnieDtF53GUh4Hqxrrwd32Bove05Us2kR4xoOf8cNrzaNDJs2fHKCNenkgHizE5yoFfkhvbMcqgte9eLdSXi+AYb4G3PMmqGLQ2dFtglYyvryyIuG3B8uhJkzuj0wtsxnzSiVRg7BVkDcHehCLherCt4xzcYWm97FlAz6VLosIhV2i2fjG3kz/zyExH6EZMFAD+EhbBn5/HXhaljXgJ3F4qA68W6gnd8g6H1tmc5NXsuVvyLVdrUmtZsLQ8pHRulfhFR8Y+Kjc7vyyMg7Bm5Ms//MuNOx+daF/+g0/jYRUbj3h0j4HqxrnAd32Bove1ZSM2kTwyMWJZtfISoZGyN8JPcKi9UDmczgICExHlnO1PbpvQ/bmgjciHPrhfrCtrxDcbW256F1Czq0x+yn2kZENYdYxsCbxv9DvFCZXE2joAj4Ag4Ao7A7hCQoWWw+quuz9qD1T5jy5QCPZ0HSvBGd3eOgCPgCDgCjoAj0IOADC1Lfv/o+kZ2M3w1KictGlsIooXmL458nTBHzP2OgCPgCDgCjkALAdlM1mn5I5nG9LGRtXcjWzjnO9mk8zoySOHucQQcAUfAEXAEHIGPCMhO8neh/Kdw0dBC2WtsibSEYmRnhgh25wg4Ao6AI+AIOAJCQPaRj1c8lb18NATIoLEloRjwkYubyHCIl8c5Ao6AI+AIOAIXg4DsIuu0jGYfjFX6//qkJhfyo/MYAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\left( \\mathbf{\\hat{n}_x} -  \\frac{3 \\operatorname{cos}\\left(q_{2}\\right)}{2}\\mathbf{\\hat{b}_x} -  \\frac{3 \\operatorname{cos}\\left(q_{2}\\right)}{2}\\mathbf{\\hat{c}_x}, \\  \\frac{3}{2}\\mathbf{\\hat{b}_x} + \\frac{3}{2}\\mathbf{\\hat{c}_x}, \\  l\\mathbf{\\hat{c}_x}\\right)$"
      ],
      "text/plain": [
       "⎛         -3⋅cos(q₂)        -3⋅cos(q₂)  , 3/2 b_x + 3/2 c_x, l c_x⎞\n",
       "⎜n_x + ─────────── b_x + ─────────── c_x                          ⎟\n",
       "⎝                2                 2                              ⎠"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pc.partial_velocity(N, u1, u2, u3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This also works for angular partial velocities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( -  \\frac{3 \\operatorname{cos}\\left(q_{2}\\right)}{2 l}\\mathbf{\\hat{n}_z}, \\  \\frac{3}{2 l}\\mathbf{\\hat{n}_z}, \\  0\\right)$"
      ],
      "text/plain": [
       "⎛   -3⋅cos(q₂)  ,     3  , 0⎞\n",
       "⎜─────────── n_z  ─── n_z   ⎟\n",
       "⎝        2⋅l        2⋅l     ⎠"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.partial_velocity(N, u1, u2, u3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The convenience function is doing this behind the scenes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ -  \\frac{3 \\operatorname{cos}\\left(q_{2}\\right)}{2 l}\\mathbf{\\hat{n}_z}, \\  \\frac{3}{2 l}\\mathbf{\\hat{n}_z}, \\  0\\right]$"
      ],
      "text/plain": [
       "⎡   -3⋅cos(q₂)  ,     3  , 0⎤\n",
       "⎢─────────── n_z  ─── n_z   ⎥\n",
       "⎣        2⋅l        2⋅l     ⎦"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[B.ang_vel_in(N).diff(ur, N) for ur in [u1, u2, u3]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Angular Accelerations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{3 \\left(- \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1} + \\dot{u}_{2} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2 l}\\right)}{2 l}\\mathbf{\\hat{n}_z}$"
      ],
      "text/plain": [
       "  ⎛                     3⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎞\n",
       "3⋅⎜-cos(q₂)⋅u₁̇ + u₂̇ + ───────────────────────────────⎟\n",
       "  ⎝                                   2⋅l              ⎠\n",
       "──────────────────────────────────────────────────────── n_z\n",
       "                          2⋅l"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_B_N = B.ang_acc_in(N).subs(qdots)\n",
    "alpha_B_N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\dot{u}_{1}\\mathbf{\\hat{n}_x}$"
      ],
      "text/plain": [
       "u₁̇ n_x"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_Pab_N = Pab.acc(N).subs(qdots)\n",
    "a_Pab_N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle (\\dot{u}_{2} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2 l})\\mathbf{\\hat{b}_x} + (- \\operatorname{sin}\\left(q_{2}\\right) \\dot{u}_{1} - \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{2}}{2 l})\\mathbf{\\hat{b}_y}$"
      ],
      "text/plain": [
       "⎛      3⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎞       ⎛               3⋅(-u₁⋅cos(q₂) +\n",
       "⎜u₂̇ + ───────────────────────────────⎟ b_x + ⎜-sin(q₂)⋅u₁̇ - ────────────────\n",
       "⎝                    2⋅l              ⎠       ⎝                             2⋅\n",
       "\n",
       " u₂)⋅u₁⋅cos(q₂)   3⋅(-u₁⋅cos(q₂) + u₂)⋅u₂⎞\n",
       "─────────────── + ───────────────────────⎟ b_y\n",
       "l                           2⋅l          ⎠"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_Bo_N = Bo.acc(N).express(B).subs(qdots)\n",
    "a_Bo_N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle (l \\dot{u}_{3} + \\left(- \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\operatorname{cos}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)\\right) \\dot{u}_{1} + \\left(- \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{cos}\\left(q_{3}\\right) - \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{3 \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) \\operatorname{sin}\\left(q_{3}\\right)}{2 l} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l})\\mathbf{\\hat{c}_x} + (\\left(- \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) - \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)\\right) \\dot{u}_{1} + \\left(u_{3} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right)}{2 l}\\right) \\left(l u_{3} - \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) - \\left(- \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\frac{3 \\left(- \\frac{3 u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 u_{2}}{2}\\right) \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2 l})\\mathbf{\\hat{c}_y}$"
      ],
      "text/plain": [
       "⎛\n",
       "⎜\n",
       "⎜                                                   ⎛  3⋅cos(q₂)⋅u₁̇   3⋅u₂̇\n",
       "⎜l⋅u₃̇ + (-sin(q₂)⋅sin(q₃) + cos(q₂)⋅cos(q₃))⋅u₁̇ + ⎜- ───────────── + ───── +\n",
       "⎝                                                   ⎝        2           2\n",
       "\n",
       "                                                                      ⎛  3⋅u₁⋅\n",
       "                                                                    3⋅⎜- ─────\n",
       " 9⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎞           3⋅cos(q₂)⋅u₁̇   3⋅u₂̇     ⎝\n",
       " ───────────────────────────────⎟⋅cos(q₃) - ───────────── + ───── + ──────────\n",
       "               4⋅l              ⎠                 2           2\n",
       "\n",
       "cos(q₂)   3⋅u₂⎞                                                             ⎞\n",
       "─────── + ────⎟⋅(-u₁⋅cos(q₂) + u₂)⋅sin(q₃)                                  ⎟\n",
       "2          2  ⎠                              9⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎟\n",
       "────────────────────────────────────────── + ───────────────────────────────⎟\n",
       "              2⋅l                                          4⋅l              ⎠\n",
       "\n",
       "      ⎛\n",
       "      ⎜\n",
       "      ⎜                                           ⎛     3⋅(-u₁⋅cos(q₂) + u₂)⎞\n",
       "c_x + ⎜(-sin(q₂)⋅cos(q₃) - sin(q₃)⋅cos(q₂))⋅u₁̇ + ⎜u₃ + ────────────────────⎟⋅\n",
       "      ⎝                                           ⎝             2⋅l         ⎠\n",
       "\n",
       "\n",
       "\n",
       "⎛       3⋅u₁⋅cos(q₂)   3⋅u₂⎞   ⎛  3⋅cos(q₂)⋅u₁̇   3⋅u₂̇   9⋅(-u₁⋅cos(q₂) + u₂)\n",
       "⎜l⋅u₃ - ──────────── + ────⎟ - ⎜- ───────────── + ───── + ────────────────────\n",
       "⎝            2          2  ⎠   ⎝        2           2                   4⋅l\n",
       "\n",
       "                         ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                           ⎞\n",
       "                       3⋅⎜- ──────────── + ────⎟⋅(-u₁⋅cos(q₂) + u₂)⋅cos(q₃)⎟\n",
       "⋅u₁⋅sin(q₂)⎞             ⎝       2          2  ⎠                           ⎟\n",
       "───────────⎟⋅sin(q₃) + ────────────────────────────────────────────────────⎟ c\n",
       "           ⎠                                   2⋅l                         ⎠\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "_y\n"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_Pc_N = Pc.acc(N).express(C).subs(qdots)\n",
    "a_Pc_N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mass and Inertia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFMAAAAUCAYAAADx7wHUAAAACXBIWXMAAA7EAAAOxAGVKw4bAAADPklEQVRYCe2Y7XEaMRCGDeMC8tGBS3DiCmJ3YDsVxOnATCrI4A7sDjJOB5AKHNyBSQWJ6YA8j6K9EXAwIcCRH7czQqvdPd17r1arOzrT6fQgpNPpHKGfYrsLW9vXMwBX53ge4WocEZ0gE+cLjPeMz8LZ9qsZgLN7InpBaEnmCMdFOFZP03plICfgNzh747ibjVf031siZePvBb4mRA8h9dqrUmYyeEI/a8mUkvUkZ+cPuHvZZeChc9ASuR6JEQ1vZucYHk8PUTyVhuEsewMYeyBJeC/7jFdOaA9MdkPcMfp72s9sv8VeOyf+ncke8fqsFz7YgHbFw5udMw17X1uOMe46YtA9/XVaL3ydSteiS/ZzjJvsue9e8HJfz5yRmWnW/aLNSM62h2w0ZgIxN0XQq6y/xl5moXaJblT2jFf+0jM/o1SZFZmkUz0HqczEMDYDtae44jrfvQYxbqoPHPa0RvFyP8vctMtPrUDCJDusm27hMvs0WUvHRZw2xXhLQqNS4NgbXrd5laJLnl7SHmt8gv5a2vMBYGYkO2OzNi2KOvY+zdcwDy9Lxwf8dXPj+mfZCl7vDmbxeqgmAWtZ5sJsb2lLn5VLDyAuNtAykAq742yTmLqtdIt9lGMk67yIl8TjPE7bgvFMidC3aWPOjfFmjOJNpU3czrsMG750ALnNzYz0OUQ/I6yMhEjc/LZdtpXeEhvl4CM3j8x1hYeMyyxcKBFmL21K89N2bdkWXuYxKcSXniXjfrcCkPwNJVOiEjk1wZJZTVr4tdf9s/QZu4S4UgIKuUQpF8T7lcSmOEBbEtwuzuEirivbxFvid8cs4C3AmURfYtua0kdcsPE2m5+DeaMkVPNjS6Ul+xa2OnbfFBbs83Pvasy9LWEV3lX3ESftyRgzU3EbxhdOMmzrh5uYbbYkZJz1x8w0Ay+zP/mKn5Ml9iJkp6pZaJZXkrd+NS6UT+gpiw81AvyO4AHN1aj+7Cwu2FT1U6vP/H4EOL8Lp22hNhLjSlcnKPo+RGw9sLjwJoKYFpItY/WQ+nPmoMRW94LGX7bj/tGDofbTNvz/Uy9ftKocVH8OY/S9ytSW6brDxZBWMgNw5SHrG0q1k38DmUMFu5cXyU8AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left( m_{a}, \\  m_{c}\\right)$"
      ],
      "text/plain": [
       "(mₐ, m_c)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ma, mc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "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": 38,
     "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": 39,
   "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": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rab = (F - k*q1 - c*qdots[q1.diff()]) * N.x\n",
    "Rab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rbo = -(mb*g)*N.y\n",
    "Rbo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rc = -(mc*g)*N.y\n",
    "Rc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "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": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "TB = (T + kT*q3)*N.z\n",
    "TB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generalizd Active Forces"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - c u_{1} - k q_{1} + F$"
      ],
      "text/plain": [
       "-c⋅u₁ - k⋅q₁ + F"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pab.partial_velocity(N, u1).dot(Rab)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOCAYAAAAWo42rAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVQoFW1SiRGCMBAkGQtgtAPswKcCKYEa7MESLMWhBGkBOtAOEDuA3XDL3Cg3c9lkby+bEMI4jpkihHDHvEd+kXvkA/UOmGUUmrjFsnLrHOsXskh1E11BDBIJwdGh9cIniFoCIbgKybPlEQOjnOFv5FkZZcQFeBbGZ4bVseCOWyup2yuXZlmzqJ29UPMdhUuXWIdy6yNuKEuRTre4vGXdoLpmreZGwhrCk9/K5nzGLrm6j8vn+n3CAdyBmo11Eo7IG75rYdwZeIEo/RQTNRRqzYwqZmYAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pab.partial_velocity(N, u2).dot(Rab)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - g m_{b} \\operatorname{sin}\\left(q_{2}\\right) + \\frac{3 \\left(k_{T} q_{3} + T\\right)}{2 l}$"
      ],
      "text/plain": [
       "                 3⋅(k_T⋅q₃ + T)\n",
       "-g⋅m_b⋅sin(q₂) + ──────────────\n",
       "                      2⋅l      "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Bo.partial_velocity(N, u2).dot(Rbo) + B.partial_velocity(N, u2).dot(TB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = [u1, u2, u3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[ - c u_{1} + g m_{b} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{2}\\right) + \\frac{3 g m_{c} \\left(\\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) + \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2} + \\frac{3 g m_{c} \\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2} - k q_{1} + F - \\frac{3 \\left(k_{T} q_{3} + T\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2 l}, \\  - g m_{b} \\operatorname{sin}\\left(q_{2}\\right) - \\frac{3 g m_{c} \\left(\\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) + \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)\\right)}{2} - \\frac{3 g m_{c} \\operatorname{sin}\\left(q_{2}\\right)}{2} + \\frac{3 \\left(k_{T} q_{3} + T\\right)}{2 l}, \\  - g l m_{c} \\left(\\operatorname{sin}\\left(q_{2}\\right) \\operatorname{cos}\\left(q_{3}\\right) + \\operatorname{sin}\\left(q_{3}\\right) \\operatorname{cos}\\left(q_{2}\\right)\\right)\\right]$"
      ],
      "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",
       "os(q₂)   3⋅g⋅m_c⋅sin(q₂)⋅cos(q₂)              3⋅(k_T⋅q₃ + T)⋅cos(q₂)          \n",
       "────── + ─────────────────────── - k⋅q₁ + F - ──────────────────────, -g⋅m_b⋅s\n",
       "                    2                                  2⋅l                    \n",
       "\n",
       "         3⋅g⋅m_c⋅(sin(q₂)⋅cos(q₃) + sin(q₃)⋅cos(q₂))   3⋅g⋅m_c⋅sin(q₂)   3⋅(k_\n",
       "in(q₂) - ─────────────────────────────────────────── - ─────────────── + ─────\n",
       "                              2                               2               \n",
       "\n",
       "T⋅q₃ + T)                                              ⎤\n",
       "─────────, -g⋅l⋅m_c⋅(sin(q₂)⋅cos(q₃) + sin(q₃)⋅cos(q₂))⎥\n",
       "2⋅l                                                    ⎦"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fr = []\n",
    "\n",
    "for ur in u:\n",
    "    Fr.append(Pab.partial_velocity(N, ur).dot(Rab) + # particle\n",
    "              Pc.partial_velocity(N, ur).dot(Rc) + # particle\n",
    "              Bo.partial_velocity(N, ur).dot(Rbo) + B.partial_velocity(N, ur).dot(TB)) # rigid body\n",
    "    \n",
    "Fr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\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": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fr = sm.Matrix(Fr)\n",
    "Fr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generalized Inertia Forces"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "Frstar = []\n",
    "\n",
    "for ur in u:\n",
    "    Frstar.append(Pab.partial_velocity(N, ur).dot(-ma*a_Pab_N) +\n",
    "                  Pc.partial_velocity(N, ur).dot(-mc*a_Pc_N) +\n",
    "                  Bo.partial_velocity(N, ur).dot(-mb*a_Bo_N) +\n",
    "                  B.partial_velocity(N, ur).dot(-alpha_B_N.dot(IB) +\n",
    "                                                B.ang_vel_in(N).cross(IB.dot(B.ang_vel_in(N)))))\n",
    "    \n",
    "Frstar = sm.Matrix(Frstar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "Frstar = Frstar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{9 I_{B_bo} \\left(- \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1} + \\dot{u}_{2} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2 l}\\right) \\operatorname{cos}\\left(q_{2}\\right)}{4 l^{2}} - m_{a} \\dot{u}_{1} + m_{b} \\left(- \\operatorname{sin}\\left(q_{2}\\right) \\dot{u}_{1} - \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{cos}\\left(q_{2}\\right)}{2 l} + \\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) - 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(l \\dot{u}_{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) \\dot{u}_{1} + \\left(- \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{cos}\\left(q_{3}\\right) - \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{3 \\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 l} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) - 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(\\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) \\dot{u}_{1} + \\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) - \\left(- \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\frac{3 \\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{cos}\\left(q_{3}\\right)}{2 l}\\right) + \\frac{3 m_{c} \\left(l \\dot{u}_{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) \\dot{u}_{1} + \\left(- \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{cos}\\left(q_{3}\\right) - \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{3 \\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 l} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2} - \\frac{3 \\left(m_{c} \\left(\\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) \\dot{u}_{1} + \\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) - \\left(- \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\frac{3 \\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{cos}\\left(q_{3}\\right)}{2 l}\\right) \\operatorname{sin}\\left(q_{3}\\right) - m_{c} \\left(l \\dot{u}_{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) \\dot{u}_{1} + \\left(- \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{cos}\\left(q_{3}\\right) - \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{3 \\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 l} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{cos}\\left(q_{3}\\right)\\right) \\operatorname{cos}\\left(q_{2}\\right)}{2}\\\\- \\frac{9 I_{B_bo} \\left(- \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1} + \\dot{u}_{2} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2 l}\\right)}{4 l^{2}} - m_{b} \\left(\\dot{u}_{2} + \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{2 l}\\right) + \\frac{3 m_{c} \\left(\\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) \\dot{u}_{1} + \\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) - \\left(- \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{sin}\\left(q_{3}\\right) + \\frac{3 \\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{cos}\\left(q_{3}\\right)}{2 l}\\right) \\operatorname{sin}\\left(q_{3}\\right)}{2} - \\frac{3 m_{c} \\left(l \\dot{u}_{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) \\dot{u}_{1} + \\left(- \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{cos}\\left(q_{3}\\right) - \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{3 \\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 l} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{cos}\\left(q_{3}\\right)}{2} - \\frac{3 m_{c} \\left(l \\dot{u}_{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) \\dot{u}_{1} + \\left(- \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{cos}\\left(q_{3}\\right) - \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{3 \\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 l} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right)}{2}\\\\- l m_{c} \\left(l \\dot{u}_{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) \\dot{u}_{1} + \\left(- \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right) \\operatorname{cos}\\left(q_{3}\\right) - \\frac{3 \\operatorname{cos}\\left(q_{2}\\right) \\dot{u}_{1}}{2} + \\frac{3 \\dot{u}_{2}}{2} + \\frac{3 \\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 l} + \\frac{9 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right) u_{1} \\operatorname{sin}\\left(q_{2}\\right)}{4 l}\\right)\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                                                                             \n",
       "⎢           ⎛                     3⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎞            \n",
       "⎢9⋅I_{B_bo}⋅⎜-cos(q₂)⋅u₁̇ + u₂̇ + ───────────────────────────────⎟⋅cos(q₂)    \n",
       "⎢           ⎝                                   2⋅l              ⎠            \n",
       "⎢───────────────────────────────────────────────────────────────────────── - m\n",
       "⎢                                      2                                      \n",
       "⎢                                   4⋅l                                       \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎣                                                                             \n",
       "\n",
       "                                                                              \n",
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       "                                                                              \n",
       "                                                                              \n",
       "            ⎛               3⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅cos(q₂)   3⋅(-u₁⋅cos(q₂) +\n",
       "ₐ⋅u₁̇ + m_b⋅⎜-sin(q₂)⋅u₁̇ - ─────────────────────────────── + ────────────────\n",
       "            ⎝                             2⋅l                           2⋅l   \n",
       "                                                                              \n",
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       "\n",
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       "                                                            ⎛                 \n",
       "                                                            ⎜                 \n",
       " u₂)⋅u₂⎞                                                    ⎜                 \n",
       "───────⎟⋅sin(q₂) - m_c⋅(-sin(q₂)⋅sin(q₃) + cos(q₂)⋅cos(q₃))⋅⎜l⋅u₃̇ + (-sin(q₂)\n",
       "       ⎠                                                    ⎝                 \n",
       "                                                                              \n",
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       "\n",
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       "                                                                              \n",
       "                                  ⎛  3⋅cos(q₂)⋅u₁̇   3⋅u₂̇   9⋅(-u₁⋅cos(q₂) + \n",
       "⋅sin(q₃) + cos(q₂)⋅cos(q₃))⋅u₁̇ + ⎜- ───────────── + ───── + ─────────────────\n",
       "                                  ⎝        2           2                   4⋅l\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
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       "                                                                             -\n",
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       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                    ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞   \n",
       "                                                  3⋅⎜- ──────────── + ────⎟⋅(-\n",
       "u₂)⋅u₁⋅sin(q₂)⎞           3⋅cos(q₂)⋅u₁̇   3⋅u₂̇     ⎝       2          2  ⎠   \n",
       "──────────────⎟⋅cos(q₃) - ───────────── + ───── + ────────────────────────────\n",
       "              ⎠                 2           2                             2⋅l \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "            ⎛                     3⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎞            \n",
       " 9⋅I_{B_bo}⋅⎜-cos(q₂)⋅u₁̇ + u₂̇ + ───────────────────────────────⎟            \n",
       "            ⎝                                   2⋅l              ⎠       ⎛    \n",
       " ───────────────────────────────────────────────────────────────── - m_b⋅⎜u₂̇ \n",
       "                                   2                                     ⎝    \n",
       "                                4⋅l                                           \n",
       "                                                                              \n",
       "                                                                              \n",
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       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                          ⎞                   \n",
       "u₁⋅cos(q₂) + u₂)⋅sin(q₃)                                  ⎟                   \n",
       "                           9⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎟                   \n",
       "──────────────────────── + ───────────────────────────────⎟ - m_c⋅(-sin(q₂)⋅co\n",
       "                                         4⋅l              ⎠                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                           ⎛                                  \n",
       "                                           ⎜                                  \n",
       "                                           ⎜                                  \n",
       "                                     3⋅m_c⋅⎜(-sin(q₂)⋅cos(q₃) - sin(q₃)⋅cos(q₂\n",
       "  3⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎞         ⎝                                  \n",
       "+ ───────────────────────────────⎟ + ─────────────────────────────────────────\n",
       "                2⋅l              ⎠                                            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
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       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                         ⎛                                                    \n",
       "                         ⎜                                                    \n",
       "                         ⎜                                           ⎛     3⋅(\n",
       "s(q₃) - sin(q₃)⋅cos(q₂))⋅⎜(-sin(q₂)⋅cos(q₃) - sin(q₃)⋅cos(q₂))⋅u₁̇ + ⎜u₃ + ───\n",
       "                         ⎝                                           ⎝        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "         ⎛     3⋅(-u₁⋅cos(q₂) + u₂)⎞ ⎛       3⋅u₁⋅cos(q₂)   3⋅u₂⎞   ⎛  3⋅cos(q\n",
       "))⋅u₁̇ + ⎜u₃ + ────────────────────⎟⋅⎜l⋅u₃ - ──────────── + ────⎟ - ⎜- ───────\n",
       "         ⎝             2⋅l         ⎠ ⎝            2          2  ⎠   ⎝        2\n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
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       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "-u₁⋅cos(q₂) + u₂)⎞ ⎛       3⋅u₁⋅cos(q₂)   3⋅u₂⎞   ⎛  3⋅cos(q₂)⋅u₁̇   3⋅u₂̇   9\n",
       "─────────────────⎟⋅⎜l⋅u₃ - ──────────── + ────⎟ - ⎜- ───────────── + ───── + ─\n",
       "     2⋅l         ⎠ ⎝            2          2  ⎠   ⎝        2           2      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                              ⎛  3⋅u₁⋅cos(q₂) \n",
       "                                                            3⋅⎜- ──────────── \n",
       "₂)⋅u₁̇   3⋅u₂̇   9⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎞             ⎝       2       \n",
       "────── + ───── + ───────────────────────────────⎟⋅sin(q₃) + ──────────────────\n",
       "           2                   4⋅l              ⎠                             \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "2                                                                             \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                            ⎛ \n",
       "                                                                            ⎜ \n",
       "                                                                            ⎜ \n",
       "                                                                     -l⋅m_c⋅⎜l\n",
       "                                                                            ⎝ \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                            ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞           \n",
       "                                          3⋅⎜- ──────────── + ────⎟⋅(-u₁⋅cos(q\n",
       "⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎞             ⎝       2          2  ⎠           \n",
       "──────────────────────────────⎟⋅sin(q₃) + ────────────────────────────────────\n",
       "             4⋅l              ⎠                                   2⋅l         \n",
       "                                                                              \n",
       "                                                                              \n",
       "  3⋅u₂⎞                           ⎞                 ⎛                         \n",
       "+ ────⎟⋅(-u₁⋅cos(q₂) + u₂)⋅cos(q₃)⎟                 ⎜                         \n",
       "   2  ⎠                           ⎟                 ⎜                         \n",
       "──────────────────────────────────⎟⋅sin(q₃)   3⋅m_c⋅⎜l⋅u₃̇ + (-sin(q₂)⋅sin(q₃)\n",
       "      2⋅l                         ⎠                 ⎝                         \n",
       "─────────────────────────────────────────── - ────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                  ⎛  3⋅cos(q₂)⋅u₁̇   3⋅u₂̇   9\n",
       "⋅u₃̇ + (-sin(q₂)⋅sin(q₃) + cos(q₂)⋅cos(q₃))⋅u₁̇ + ⎜- ───────────── + ───── + ─\n",
       "                                                  ⎝        2           2      \n",
       "\n",
       "                          ⎛                                                   \n",
       "                          ⎜                                                   \n",
       "                ⎞         ⎜                                                   \n",
       "₂) + u₂)⋅cos(q₃)⎟   3⋅m_c⋅⎜l⋅u₃̇ + (-sin(q₂)⋅sin(q₃) + cos(q₂)⋅cos(q₃))⋅u₁̇ + \n",
       "                ⎟         ⎝                                                   \n",
       "────────────────⎟ + ──────────────────────────────────────────────────────────\n",
       "                ⎠                                                             \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                          ⎛  3⋅cos(q₂)⋅u₁̇   3⋅u₂̇   9⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅s\n",
       " + cos(q₂)⋅cos(q₃))⋅u₁̇ + ⎜- ───────────── + ───── + ─────────────────────────\n",
       "                          ⎝        2           2                   4⋅l        \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                    ⎛  3⋅u₁⋅co\n",
       "                                                                  3⋅⎜- ───────\n",
       "⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎞           3⋅cos(q₂)⋅u₁̇   3⋅u₂̇     ⎝       2 \n",
       "──────────────────────────────⎟⋅cos(q₃) - ───────────── + ───── + ────────────\n",
       "             4⋅l              ⎠                 2           2                 \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "⎛  3⋅cos(q₂)⋅u₁̇   3⋅u₂̇   9⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎞           3⋅cos(q₂\n",
       "⎜- ───────────── + ───── + ───────────────────────────────⎟⋅cos(q₃) - ────────\n",
       "⎝        2           2                   4⋅l              ⎠                 2 \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                 2            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                            ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞           \n",
       "                                          3⋅⎜- ──────────── + ────⎟⋅(-u₁⋅cos(q\n",
       "in(q₂)⎞           3⋅cos(q₂)⋅u₁̇   3⋅u₂̇     ⎝       2          2  ⎠           \n",
       "──────⎟⋅cos(q₃) - ───────────── + ───── + ────────────────────────────────────\n",
       "      ⎠                 2           2                             2⋅l         \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "             2                                                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "s(q₂)   3⋅u₂⎞                                                             ⎞   \n",
       "───── + ────⎟⋅(-u₁⋅cos(q₂) + u₂)⋅sin(q₃)                                  ⎟   \n",
       "         2  ⎠                              9⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎟   \n",
       "──────────────────────────────────────── + ───────────────────────────────⎟   \n",
       "            2⋅l                                          4⋅l              ⎠   \n",
       "\n",
       "                  ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞                                     \n",
       "                3⋅⎜- ──────────── + ────⎟⋅(-u₁⋅cos(q₂) + u₂)⋅sin(q₃)          \n",
       ")⋅u₁̇   3⋅u₂̇     ⎝       2          2  ⎠                              9⋅(-u₁⋅\n",
       "───── + ───── + ──────────────────────────────────────────────────── + ───────\n",
       "          2                             2⋅l                                   \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                  ⎞                 ⎛         \n",
       "₂) + u₂)⋅sin(q₃)                                  ⎟                 ⎜         \n",
       "                   9⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎟                 ⎜         \n",
       "──────────────── + ───────────────────────────────⎟⋅cos(q₃)   3⋅m_c⋅⎜l⋅u₃̇ + (\n",
       "                                 4⋅l              ⎠                 ⎝         \n",
       "─────────────────────────────────────────────────────────── - ────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                        ⎞             ⎛    ⎛                                  \n",
       "                        ⎟             ⎜    ⎜                                  \n",
       "cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎟             ⎜    ⎜                                  \n",
       "────────────────────────⎟⋅cos(q₂)   3⋅⎜m_c⋅⎜(-sin(q₂)⋅cos(q₃) - sin(q₃)⋅cos(q₂\n",
       "       4⋅l              ⎠             ⎝    ⎝                                  \n",
       "───────────────────────────────── - ──────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                          ⎛  3⋅cos(q₂)⋅u₁̇   3⋅u₂̇   9⋅(-u₁⋅co\n",
       "-sin(q₂)⋅sin(q₃) + cos(q₂)⋅cos(q₃))⋅u₁̇ + ⎜- ───────────── + ───── + ─────────\n",
       "                                          ⎝        2           2              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "         ⎛     3⋅(-u₁⋅cos(q₂) + u₂)⎞ ⎛       3⋅u₁⋅cos(q₂)   3⋅u₂⎞   ⎛  3⋅cos(q\n",
       "))⋅u₁̇ + ⎜u₃ + ────────────────────⎟⋅⎜l⋅u₃ - ──────────── + ────⎟ - ⎜- ───────\n",
       "         ⎝             2⋅l         ⎠ ⎝            2          2  ⎠   ⎝        2\n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                            ⎛  3⋅u₁⋅cos(q₂)   \n",
       "                                                          3⋅⎜- ──────────── + \n",
       "s(q₂) + u₂)⋅u₁⋅sin(q₂)⎞           3⋅cos(q₂)⋅u₁̇   3⋅u₂̇     ⎝       2         \n",
       "──────────────────────⎟⋅cos(q₃) - ───────────── + ───── + ────────────────────\n",
       "     4⋅l              ⎠                 2           2                         \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                         2                                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                              ⎛  3⋅u₁⋅cos(q₂) \n",
       "                                                            3⋅⎜- ──────────── \n",
       "₂)⋅u₁̇   3⋅u₂̇   9⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎞             ⎝       2       \n",
       "────── + ───── + ───────────────────────────────⎟⋅sin(q₃) + ──────────────────\n",
       "           2                   4⋅l              ⎠                             \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "3⋅u₂⎞                                                             ⎞           \n",
       "────⎟⋅(-u₁⋅cos(q₂) + u₂)⋅sin(q₃)                                  ⎟           \n",
       " 2  ⎠                              9⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎟           \n",
       "──────────────────────────────── + ───────────────────────────────⎟           \n",
       "    2⋅l                                          4⋅l              ⎠           \n",
       "───────────────────────────────────────────────────────────────────           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "  3⋅u₂⎞                           ⎞               ⎛                           \n",
       "+ ────⎟⋅(-u₁⋅cos(q₂) + u₂)⋅cos(q₃)⎟               ⎜                           \n",
       "   2  ⎠                           ⎟               ⎜                           \n",
       "──────────────────────────────────⎟⋅sin(q₃) - m_c⋅⎜l⋅u₃̇ + (-sin(q₂)⋅sin(q₃) +\n",
       "      2⋅l                         ⎠               ⎝                           \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                  2                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                        ⎛  3⋅cos(q₂)⋅u₁̇   3⋅u₂̇   9⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin\n",
       " cos(q₂)⋅cos(q₃))⋅u₁̇ + ⎜- ───────────── + ───── + ───────────────────────────\n",
       "                        ⎝        2           2                   4⋅l          \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                          ⎛  3⋅u₁⋅cos(q₂)   3⋅u₂⎞             \n",
       "                                        3⋅⎜- ──────────── + ────⎟⋅(-u₁⋅cos(q₂)\n",
       "(q₂)⎞           3⋅cos(q₂)⋅u₁̇   3⋅u₂̇     ⎝       2          2  ⎠             \n",
       "────⎟⋅cos(q₃) - ───────────── + ───── + ──────────────────────────────────────\n",
       "    ⎠                 2           2                             2⋅l           \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                ⎞        ⎞        ⎤\n",
       " + u₂)⋅sin(q₃)                                  ⎟        ⎟        ⎥\n",
       "                 9⋅(-u₁⋅cos(q₂) + u₂)⋅u₁⋅sin(q₂)⎟        ⎟        ⎥\n",
       "────────────── + ───────────────────────────────⎟⋅cos(q₃)⎟⋅cos(q₂)⎥\n",
       "                               4⋅l              ⎠        ⎠        ⎥\n",
       "──────────────────────────────────────────────────────────────────⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎥\n",
       "                                                                  ⎦"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Frstar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = Fr + Frstar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{F, T, q_{1}, q_{2}, q_{3}, u_{1}, u_{2}, u_{3}, \\dot{u}_{1}, \\dot{u}_{2}, \\dot{u}_{3}\\right\\}$"
      ],
      "text/plain": [
       "{F, T, q₁, q₂, q₃, u₁, u₂, u₃, u₁̇, u₂̇, u₃̇}"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "me.find_dynamicsymbols(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASIAAAAVCAYAAADituMXAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAJgklEQVR4Ae2cj3XXNhDHkzwGoO0GsAGFCYANgG4AG4THBH2wATABpRtAJwiwAWxAyQbp96PoFEmWbcmWA6TWe0L/7r46nU7nk38Oh2dnZwd5Ojw8fKy+35U/avxVPr63dw3sGtg10KIB+ZRbon+i/Fn5lfzKacx/GDsiEV/X4D/K79X/NCbc67sGdg3sGlirAfmYe8J4q3xXPuaT4R1ZxZePVN6ac0ICO1Z+q3zm80eVL5VvZHh7s0ID0tt15XfK35R5YqxOW2C2CiUZsJPPytgJT8Q9/c81IN/yXir4S/l1rIprcUP1m8pfsr5BU2Av6MTAVHxSm2vcnhZqQPojTL0vfX5U+WEhTMK2BWYyQUUDO9GaWNtL1cPTr4J1J/nJNaB954F6X/te8ifYBLevkPKIKAzMVTQRIRYJD7enPhoganjXByqgbIEZwCsqPKR2G6lQ1FUhkW94oLXcGHFCxWUudkRCu+8Rex+coqBXvXMLx74F5oJ94Lq/28gCxf3ELPiGpgh4jSNyEZG83v6062MxbN4X6ZOwtVfaArNaNjlC3hkSgu82Uq21K0GIb2ja8/wdUYsWCPmbJmsB35JWB+S58L9Gc/ArYZMHh1c4hKAcdnvBzH34ibDoa03J5nnsXwXC1ea5MEt37bk5tsCcmzMeZ/6DhbqFFz3izOwXXPRNuqN8IlzeQWGHfyizn/TzPmoTu9RcP5RMP5I8XpaH0j/7Rb6lvpcqP7NPKvOEbV8kEWEoLquXn9X4dij0leqiYUN4UX08MU44Dg3CcPApwaef++PkHFuMM68yTuOB4auOPLNrNnorxcOa3kVtsN16ra+2FB9RA7xOLpXHyuCZnh/XYhmdeKswRcc3Y9+U2Rv2yPbN2pTItkQGt98mU0up+XC+Kpw8yBRsTXVbG3q6Z7iq46i+Wbt3KewuMiGzMj9MNNtdvKZe8sSYa+uSiT0QzPj51jg2l9AEZ+ABMEh+vg/9pbpoOIRYySitxpyB5/yedzNjyeeL25obJ+SMyfrV5rAEx2T9UyX0yqz/ekzn+5qw4FcKeKpzuBwupXKzA2jBFD7rD+tgPmVBXNiA7wsHPh6bqosPewoOZIo2HhMPUY45ZfYsObBqm9PP93Ige4y7pt5bJuG5h/NSmXrLs1SOnE9y8TBL9iunoQ0NtDZGB5vOE4cNr4pURAeIMC6MNa9r3EVAhf5w6PKxLdtenoHzWDKnsDhgIRoCQwk9LsIXH7oCM2zMErlinhpM0eDoEkfh+fK1sWdVtmEyiN700cTndRk7YnSaOEG1izak/sURmMk9Vgq7q0zC4ww1P7RMvt7yGO7aUnINHvZjmKJlv6A/PhIR3wFxF+fzaz5MxIDmEjRz93DCz5MCEHMx52lhbMsufr3hXdCqeb1+OMAoMU6sd+nLZnjRJx//8WEjUdHaVINJZJH/CQ98+fuyU+mt9R0VOEv4eMLZHoFBO7c1bKika+h5qHZPG8jEGcr1XC33BvJUzz1GKLvlXGBTs3sgWhwxe3tT+QWVkNU/+0QRDZvNUyp5kmY4CARNcnWDRxkB3NMl5pmri4dQFn7KJCSv4DV5mvhKuJrbhf8qkye92ii/OaIRj8nmnvrgKg+igJIsY31LMXO+MfyafmGhj7fQglvDk9OIrxjmq3/w1FWf2aXbl3hO6spgYT/YODaY2GY+91hbfKtlYm5ld4ZUmkzfVUesV8nOGDKNnu8J3bg9iMeFM1iX+gZX6OCEIkF4y530x20vLFKPbqTGzChYEJNSBsPM8KCdfDelcQwnhOeqY0xN705Ej8xFHvVXh8jQghWvgTp9jOX9c23xJJuitjkme0fS7DyXYorP9m1gPHPryMeFFfStevMawFPCLhJetU0/wR48bXAQosGZm/6gx3E5e6VUBnzRGsXXQybOAzI5GVTSbn6I9dKRx0Eeexiio+b3uOLBkYX3Q6pzVgZ+wtMl+EfqbE2AcxKnwkq7fr0QHX9pS0nfiUIyFhyS+l3YrbKIJ3oMjDA8Ds+5JoDnEiGhMn/P5MI9689KriCBhzHP5/Cj9hyOk0O8GLtLqts1LZbR8OfwkCnwaZ2nHrZ4FfIyd8X081EgS+nKE5EEvc3JAM8X5FX5NQaoWYNo0C+8eZiPs8T+gs5oK91Wtj4+ofjb9Z4fjvzzjMEaL1km9Izjsb2mRP6QLlMezZWcMcnFWbwbhFGlRh6RsV/ObqFXnei0eK419q9ySFWOyAvBH7ly0N0BVJ02HrCU8KhmFPE4xnFDfM6ZMaA6eMVDx7jSI+U3rnbxD/iBx28obRwSChgk0fAOjIPxXPkxWW0iJIzWKasSB6PBkMDhjzrRAXMPjLsGT3zIiyHEie9mnoCv8s94YAvMCB+9jhlOIKuUAX3zXckz0SffkVTyO7sQbW5H9OfvtZANPbH/7GusT+wndmY4ssEaL1kmnE4sA9+KBXtWHUeLnU3atMZ76ijW2SDQqJSHs2B78Eg8yb5rbDyJmEldFhVAk1czo50qhVG8pqjfQv/wfkV9OCUcnAtPVSahnNpgxfQcXPoSOuRRAmtRyB2vpxVH9Bj6aGjdihfLMlbfCBMlFq+vJTnWyrCWvyRT3Cd8s5XYftgrnBVjA1tRXxcbiuXI65oDPYe5Vee6V7zW0x/T5lg92sJHnqCjKcwe8ghj4GeO1JmnX/OOlraeSHhpUvIk8/1cYbimxd7fwlS8JwKS48STA6Ox9FoVMOInio3dUf+pNVaUozhaB1FDSGojGw7WrmdhLKqM4kU0rdWumNG6Wv76f60Ma/kndeZtIdiDXyN7hf3xxA5jEdCmMvl5gv1LJpziB8liV8lIFFe9DHk4S3Zu3aSSK4mQIqE2kedaNAFV9wIt66tuSnicCB6cxNXlvHZwgHPjwD6UwhMHpb7byuZ8kkOufhLhPVgnKn9TflPaNI2Dn7yLULs5TeFoDDm5jv0SGTEOiPdg+brc3FN4zcJ5hp6YwuJgomNK0jP1cc20P6s4783+XSvDWv5MnKlmbD84ANZFH1F4ki5ZptfoGQGkax7Gg3TJ8jzVfJw/nDNnabD/HeUBn3kukpQQrmbUldig5JeKnKZnm/kMT3UOdfJriI3NleKrvlJMYU3hIJsyMvIUs6tkMaS2OaC1eq9yC8xW2dbKsJa/Vd4a+h9Npqsoj9bEGeIqmpzz5L+K1aBL8nxENXhpnETpxeA5YYd/NReCMRfRDE/isRC1w2w7xK6BXQPfQwM+2uIHDG5dg/+z+j/3Eq37qIgLmwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\left\\{I_{B_bo}, c, g, k, k_{T}, l, m_{a}, m_{b}, m_{c}, t\\right\\}$"
      ],
      "text/plain": [
       "{I_{B_bo}, c, g, k, k_T, l, mₐ, m_b, m_c, t}"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.free_symbols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linearize\n",
    "\n",
    "Create a state vector with all of the u's and q's."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}u_{1}\\\\u_{2}\\\\u_{3}\\\\q_{1}\\\\q_{2}\\\\q_{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡u₁⎤\n",
       "⎢  ⎥\n",
       "⎢u₂⎥\n",
       "⎢  ⎥\n",
       "⎢u₃⎥\n",
       "⎢  ⎥\n",
       "⎢q₁⎥\n",
       "⎢  ⎥\n",
       "⎢q₂⎥\n",
       "⎢  ⎥\n",
       "⎣q₃⎦"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sm.Matrix([u1, u2, u3, q1, q2, q3])\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this model, an equilibrium point happens to be when $\\bar{x}=0$, so create that vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0⎤\n",
       "⎢ ⎥\n",
       "⎢0⎥\n",
       "⎢ ⎥\n",
       "⎢0⎥\n",
       "⎢ ⎥\n",
       "⎢0⎥\n",
       "⎢ ⎥\n",
       "⎢0⎥\n",
       "⎢ ⎥\n",
       "⎣0⎦"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xeq = sm.zeros(6, 1)\n",
    "xeq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make sure the dynamical equations are functions of the correct variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\left\\{F, T, q_{1}, q_{2}, q_{3}, u_{1}, u_{2}, u_{3}, \\dot{u}_{1}, \\dot{u}_{2}, \\dot{u}_{3}\\right\\}, \\  \\left( 3, \\  1\\right)\\right)$"
      ],
      "text/plain": [
       "({F, T, q₁, q₂, q₃, u₁, u₂, u₃, u₁̇, u₂̇, u₃̇}, (3, 1))"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "me.find_dynamicsymbols(f), f.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Express the kinematical equations in the form $\\bar{g}(\\bar{x},\\dot{\\bar{x}}, t)=0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- u_{1} + \\dot{q}_{1}\\\\\\dot{q}_{2} - \\frac{3 \\left(- u_{1} \\operatorname{cos}\\left(q_{2}\\right) + u_{2}\\right)}{2 l}\\\\- u_{3} + \\dot{q}_{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡        -u₁ + q₁̇         ⎤\n",
       "⎢                          ⎥\n",
       "⎢      3⋅(-u₁⋅cos(q₂) + u₂)⎥\n",
       "⎢q₂̇ - ────────────────────⎥\n",
       "⎢              2⋅l         ⎥\n",
       "⎢                          ⎥\n",
       "⎣        -u₃ + q₃̇         ⎦"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = sm.Matrix([q1.diff() - u1,\n",
    "               q2.diff() - qdots[q2.diff()],\n",
    "               q3.diff() - u3])\n",
    "g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Form the vector function of both the dynamical and kinematical equations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "h = f.col_join(g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a holomic system h should be 2n in length: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( 6, \\  1\\right)$"
      ],
      "text/plain": [
       "(6, 1)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This vector is just there to help us avoid an incorrect substitution in the following steps. We don't want to sub in for things inside derivatives."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}u_{{1d}}\\\\u_{{2d}}\\\\u_{{3d}}\\\\q_{{1d}}\\\\q_{{2d}}\\\\q_{{3d}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡u_{1d}⎤\n",
       "⎢      ⎥\n",
       "⎢u_{2d}⎥\n",
       "⎢      ⎥\n",
       "⎢u_{3d}⎥\n",
       "⎢      ⎥\n",
       "⎢q_{1d}⎥\n",
       "⎢      ⎥\n",
       "⎢q_{2d}⎥\n",
       "⎢      ⎥\n",
       "⎣q_{3d}⎦"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q1d, q2d, q3d, u1d, u2d, u3d = me.dynamicsymbols('q_{1d}, q_{2d}, q_{3d}, u_{1d}, u_{2d}, u_{3d}')\n",
    "xd = sm.Matrix([u1d, u2d, u3d, q1d, q2d, q3d])\n",
    "xd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ \\dot{q}_{1} : q_{{1d}}, \\  \\dot{q}_{2} : q_{{2d}}, \\  \\dot{q}_{3} : q_{{3d}}, \\  \\dot{u}_{1} : u_{{1d}}, \\  \\dot{u}_{2} : u_{{2d}}, \\  \\dot{u}_{3} : u_{{3d}}\\right\\}$"
      ],
      "text/plain": [
       "{q₁̇: q_{1d}, q₂̇: q_{2d}, q₃̇: q_{3d}, u₁̇: u_{1d}, u₂̇: u_{2d}, u₃̇: u_{3d}}"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{k: v for k, v in zip(x.diff(), xd)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "h = h.subs({k: v for k, v in zip(x.diff(), xd)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{F, T, q_{1}, q_{2}, q_{3}, q_{{1d}}, q_{{2d}}, q_{{3d}}, u_{1}, u_{2}, u_{3}, u_{{1d}}, u_{{2d}}, u_{{3d}}\\right\\}$"
      ],
      "text/plain": [
       "{F, T, q₁, q₂, q₃, q_{1d}, q_{2d}, q_{3d}, u₁, u₂, u₃, u_{1d}, u_{2d}, u_{3d}}"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "me.find_dynamicsymbols(h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ q_{1} : 0, \\  q_{2} : 0, \\  q_{3} : 0, \\  u_{1} : 0, \\  u_{2} : 0, \\  u_{3} : 0\\right\\}$"
      ],
      "text/plain": [
       "{q₁: 0, q₂: 0, q₃: 0, u₁: 0, u₂: 0, u₃: 0}"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xeq_sub = {k: v for k, v in zip(x, xeq)}\n",
    "xeq_sub"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the linearization using the first two terms of the Taylor Series\n",
    "\n",
    "$\\bar{h}_{lin} = \\bar{h}(\\bar{x}_{eq}) + J_h(\\bar{x}_{eq})(\\bar{x} - \\bar{x}_{eq})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "h_lin = h.subs(xeq_sub) + h.jacobian(x).subs(xeq_sub)*(x - xeq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "h_lin.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{- 9 I_{B_bo} \\left(u_{{1d}} - u_{{2d}}\\right) + 4 l^{2} \\left(- c u_{1} + g \\left(m_{b} + 3 m_{c}\\right) q_{2} - k q_{1} - m_{a} u_{{1d}} + 2 m_{c} \\left(l u_{{3d}} - 2 u_{{1d}} + 3 u_{{2d}}\\right) + F\\right) + 6 l \\left(\\left(g l m_{c} - k_{T}\\right) q_{3} - T\\right)}{4 l^{2}}\\\\\\frac{9 I_{B_bo} \\left(u_{{1d}} - u_{{2d}}\\right) - 4 l^{2} \\left(g \\left(m_{b} + 3 m_{c}\\right) q_{2} + m_{b} u_{{2d}} + 3 m_{c} \\left(l u_{{3d}} - 2 u_{{1d}} + 3 u_{{2d}}\\right)\\right) + 6 l \\left(- \\left(g l m_{c} - k_{T}\\right) q_{3} + T\\right)}{4 l^{2}}\\\\l m_{c} \\left(- g q_{2} - g q_{3} - l u_{{3d}} + 2 u_{{1d}} - 3 u_{{2d}}\\right)\\\\q_{{1d}} - u_{1}\\\\\\frac{2 l q_{{2d}} + 3 u_{1} - 3 u_{2}}{2 l}\\\\q_{{3d}} - u_{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                   2                                         \n",
       "⎢-9⋅I_{B_bo}⋅(u_{1d} - u_{2d}) + 4⋅l ⋅(-c⋅u₁ + g⋅(m_b + 3⋅m_c)⋅q₂ - k⋅q₁ - mₐ⋅\n",
       "⎢─────────────────────────────────────────────────────────────────────────────\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                           2                                 \n",
       "⎢         9⋅I_{B_bo}⋅(u_{1d} - u_{2d}) - 4⋅l ⋅(g⋅(m_b + 3⋅m_c)⋅q₂ + m_b⋅u_{2d}\n",
       "⎢         ────────────────────────────────────────────────────────────────────\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                     l⋅m_c⋅(-g⋅q₂ - g⋅q₃ - l⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                          q_{\n",
       "⎢                                                                             \n",
       "⎢                                                                    2⋅l⋅q_{2d\n",
       "⎢                                                                    ─────────\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎣                                                                          q_{\n",
       "\n",
       "                                                                              \n",
       "u_{1d} + 2⋅m_c⋅(l⋅u_{3d} - 2⋅u_{1d} + 3⋅u_{2d}) + F) + 6⋅l⋅((g⋅l⋅m_c - k_T)⋅q₃\n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "    2                                                                         \n",
       " 4⋅l                                                                          \n",
       "                                                                              \n",
       "                                                                              \n",
       " + 3⋅m_c⋅(l⋅u_{3d} - 2⋅u_{1d} + 3⋅u_{2d})) + 6⋅l⋅(-(g⋅l⋅m_c - k_T)⋅q₃ + T)    \n",
       "──────────────────────────────────────────────────────────────────────────    \n",
       "    2                                                                         \n",
       " 4⋅l                                                                          \n",
       "                                                                              \n",
       "u_{3d} + 2⋅u_{1d} - 3⋅u_{2d})                                                 \n",
       "                                                                              \n",
       "1d} - u₁                                                                      \n",
       "                                                                              \n",
       "} + 3⋅u₁ - 3⋅u₂                                                               \n",
       "───────────────                                                               \n",
       " 2⋅l                                                                          \n",
       "                                                                              \n",
       "3d} - u₃                                                                      \n",
       "\n",
       "     ⎤\n",
       " - T)⎥\n",
       "─────⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎥\n",
       "     ⎦"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_lin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, solve for $\\dot{\\bar{x}}$ by forming $\\mathbf{M}\\dot{\\bar{x}} = \\mathbf{G}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{- 9 I_{B_bo} + 4 l^{2} \\left(- m_{a} - 4 m_{c}\\right)}{4 l^{2}} & \\frac{9 I_{B_bo} + 24 l^{2} m_{c}}{4 l^{2}} & 2 l m_{c} & 0 & 0 & 0\\\\\\frac{9 I_{B_bo} + 24 l^{2} m_{c}}{4 l^{2}} & \\frac{- 9 I_{B_bo} - 4 l^{2} \\left(m_{b} + 9 m_{c}\\right)}{4 l^{2}} & - 3 l m_{c} & 0 & 0 & 0\\\\2 l m_{c} & - 3 l m_{c} & - l^{2} m_{c} & 0 & 0 & 0\\\\0 & 0 & 0 & 1 & 0 & 0\\\\0 & 0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                 2                                      2                    \n",
       "⎢-9⋅I_{B_bo} + 4⋅l ⋅(-mₐ - 4⋅m_c)       9⋅I_{B_bo} + 24⋅l ⋅m_c                \n",
       "⎢────────────────────────────────       ──────────────────────       2⋅l⋅m_c  \n",
       "⎢                 2                                 2                         \n",
       "⎢              4⋅l                               4⋅l                          \n",
       "⎢                                                                             \n",
       "⎢                      2                            2                         \n",
       "⎢     9⋅I_{B_bo} + 24⋅l ⋅m_c       -9⋅I_{B_bo} - 4⋅l ⋅(m_b + 9⋅m_c)           \n",
       "⎢     ──────────────────────       ────────────────────────────────  -3⋅l⋅m_c \n",
       "⎢                 2                                 2                         \n",
       "⎢              4⋅l                               4⋅l                          \n",
       "⎢                                                                             \n",
       "⎢                                                                      2      \n",
       "⎢            2⋅l⋅m_c                           -3⋅l⋅m_c              -l ⋅m_c  \n",
       "⎢                                                                             \n",
       "⎢               0                                 0                     0     \n",
       "⎢                                                                             \n",
       "⎢               0                                 0                     0     \n",
       "⎢                                                                             \n",
       "⎣               0                                 0                     0     \n",
       "\n",
       "        ⎤\n",
       "        ⎥\n",
       " 0  0  0⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       " 0  0  0⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       " 0  0  0⎥\n",
       "        ⎥\n",
       " 1  0  0⎥\n",
       "        ⎥\n",
       " 0  1  0⎥\n",
       "        ⎥\n",
       " 0  0  1⎦"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = h_lin.jacobian(xd)\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "xdot = M.LUsolve(-(h_lin - M*xd))\n",
    "xdot.simplify()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can put it into state space form now: $\\dot{\\bar{x}}=\\mathbf{A}\\bar{x}+\\mathbf{B}\\bar{u}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{- 9 I_{B_bo} c - 4 c l^{2} m_{b}}{9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}} & 0 & 0 & \\frac{- 9 I_{B_bo} k - 4 k l^{2} m_{b}}{9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}} & \\frac{9 I_{B_bo} g m_{c} + 4 g l^{2} m_{b}^{2} + 4 g l^{2} m_{b} m_{c}}{9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}} & \\frac{9 I_{B_bo} g m_{c} - 2 g l^{2} m_{b} m_{c} - 6 k_{T} l m_{b}}{9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}}\\\\- \\frac{9 I_{B_bo} c}{9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}} & 0 & 0 & - \\frac{9 I_{B_bo} k}{9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}} & \\frac{9 I_{B_bo} g m_{c} - 4 g l^{2} m_{a} m_{b}}{9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}} & \\frac{9 I_{B_bo} g m_{c} + 6 g l^{2} m_{a} m_{c} + 6 k_{T} l m_{a}}{9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}}\\\\\\frac{9 I_{B_bo} c - 8 c l^{2} m_{b}}{l \\left(9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}\\right)} & 0 & 0 & \\frac{9 I_{B_bo} k - 8 k l^{2} m_{b}}{l \\left(9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}\\right)} & \\frac{- 9 I_{B_bo} g m_{a} - 9 I_{B_bo} g m_{b} - 9 I_{B_bo} g m_{c} + 8 g l^{2} m_{a} m_{b} + 8 g l^{2} m_{b}^{2} + 8 g l^{2} m_{b} m_{c}}{l \\left(9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}\\right)} & \\frac{- 9 I_{B_bo} g m_{a} - 9 I_{B_bo} g m_{b} - 9 I_{B_bo} g m_{c} - 4 g l^{2} m_{a} m_{b} - 18 g l^{2} m_{a} m_{c} - 4 g l^{2} m_{b} m_{c} - 18 k_{T} l m_{a} - 12 k_{T} l m_{b}}{l \\left(9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}\\right)}\\\\1 & 0 & 0 & 0 & 0 & 0\\\\- \\frac{3}{2 l} & \\frac{3}{2 l} & 0 & 0 & 0 & 0\\\\0 & 0 & 1 & 0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                2                                            \n",
       "⎢           -9⋅I_{B_bo}⋅c - 4⋅c⋅l ⋅m_b                                -9⋅I_{B_\n",
       "⎢  ────────────────────────────────────────────     0   0    ─────────────────\n",
       "⎢                                      2                                      \n",
       "⎢  9⋅I_{B_bo}⋅mₐ + 9⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b              9⋅I_{B_bo}⋅mₐ + 9\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                 -9⋅I_{B_bo}⋅c                                             -9\n",
       "⎢  ────────────────────────────────────────────     0   0    ─────────────────\n",
       "⎢                                      2                                      \n",
       "⎢  9⋅I_{B_bo}⋅mₐ + 9⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b              9⋅I_{B_bo}⋅mₐ + 9\n",
       "⎢                                                                             \n",
       "⎢                               2                                             \n",
       "⎢           9⋅I_{B_bo}⋅c - 8⋅c⋅l ⋅m_b                                 9⋅I_{B_b\n",
       "⎢────────────────────────────────────────────────   0   0  ───────────────────\n",
       "⎢  ⎛                                    2       ⎞            ⎛                \n",
       "⎢l⋅⎝9⋅I_{B_bo}⋅mₐ + 9⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b⎠          l⋅⎝9⋅I_{B_bo}⋅mₐ + \n",
       "⎢                                                                             \n",
       "⎢                       1                           0   0                     \n",
       "⎢                                                                             \n",
       "⎢                      -3                           3                         \n",
       "⎢                      ───                         ───  0                     \n",
       "⎢                      2⋅l                         2⋅l                        \n",
       "⎢                                                                             \n",
       "⎣                       0                           0   1                     \n",
       "\n",
       "             2                                                                \n",
       "bo}⋅k - 4⋅k⋅l ⋅m_b                                        9⋅I_{B_bo}⋅g⋅m_c + 4\n",
       "───────────────────────────                               ────────────────────\n",
       "                   2                                                          \n",
       "⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b                                 9⋅I_{B_bo}⋅mₐ + 9⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "⋅I_{B_bo}⋅k                                                      9⋅I_{B_bo}⋅g⋅\n",
       "───────────────────────────                                ───────────────────\n",
       "                   2                                                          \n",
       "⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b                                9⋅I_{B_bo}⋅mₐ + 9⋅I\n",
       "                                                                              \n",
       "            2                                                                 \n",
       "o}⋅k - 8⋅k⋅l ⋅m_b              -9⋅I_{B_bo}⋅g⋅mₐ - 9⋅I_{B_bo}⋅g⋅m_b - 9⋅I_{B_bo\n",
       "─────────────────────────────  ───────────────────────────────────────────────\n",
       "                    2       ⎞                               ⎛                 \n",
       "9⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b⎠                             l⋅⎝9⋅I_{B_bo}⋅mₐ + 9\n",
       "                                                                              \n",
       "    0                                                                         \n",
       "                                                                              \n",
       "                                                                              \n",
       "    0                                                                         \n",
       "                                                                              \n",
       "                                                                              \n",
       "    0                                                                         \n",
       "\n",
       "    2    2        2                                                           \n",
       "⋅g⋅l ⋅m_b  + 4⋅g⋅l ⋅m_b⋅m_c                                                   \n",
       "───────────────────────────                                                   \n",
       "                  2                                                           \n",
       "I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b                                                    \n",
       "                                                                              \n",
       "           2                                                                  \n",
       "m_c - 4⋅g⋅l ⋅mₐ⋅m_b                                                           \n",
       "─────────────────────────                                                     \n",
       "                 2                                                            \n",
       "_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b                                                     \n",
       "                                                                              \n",
       "               2               2    2        2                                \n",
       "}⋅g⋅m_c + 8⋅g⋅l ⋅mₐ⋅m_b + 8⋅g⋅l ⋅m_b  + 8⋅g⋅l ⋅m_b⋅m_c  -9⋅I_{B_bo}⋅g⋅mₐ - 9⋅I\n",
       "──────────────────────────────────────────────────────  ──────────────────────\n",
       "                   2       ⎞                                                  \n",
       "⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b⎠                                                  \n",
       "                                                                              \n",
       "   0                                                                          \n",
       "                                                                              \n",
       "                                                                              \n",
       "   0                                                                          \n",
       "                                                                              \n",
       "                                                                              \n",
       "   0                                                                          \n",
       "\n",
       "                                             2                                \n",
       "                     9⋅I_{B_bo}⋅g⋅m_c - 2⋅g⋅l ⋅m_b⋅m_c - 6⋅k_T⋅l⋅m_b          \n",
       "                     ───────────────────────────────────────────────          \n",
       "                                                           2                  \n",
       "                       9⋅I_{B_bo}⋅mₐ + 9⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b           \n",
       "                                                                              \n",
       "                                              2                               \n",
       "                      9⋅I_{B_bo}⋅g⋅m_c + 6⋅g⋅l ⋅mₐ⋅m_c + 6⋅k_T⋅l⋅mₐ           \n",
       "                      ─────────────────────────────────────────────           \n",
       "                                                           2                  \n",
       "                       9⋅I_{B_bo}⋅mₐ + 9⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b           \n",
       "                                                                              \n",
       "                                        2                2               2    \n",
       "_{B_bo}⋅g⋅m_b - 9⋅I_{B_bo}⋅g⋅m_c - 4⋅g⋅l ⋅mₐ⋅m_b - 18⋅g⋅l ⋅mₐ⋅m_c - 4⋅g⋅l ⋅m_b\n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                       ⎛                                    2       ⎞         \n",
       "                     l⋅⎝9⋅I_{B_bo}⋅mₐ + 9⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b⎠         \n",
       "                                                                              \n",
       "                                            0                                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                            0                                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                            0                                 \n",
       "\n",
       "                                 ⎤\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "⋅m_c - 18⋅k_T⋅l⋅mₐ - 12⋅k_T⋅l⋅m_b⎥\n",
       "─────────────────────────────────⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎥\n",
       "                                 ⎦"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = xdot.jacobian(x)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{9 I_{B_bo} + 4 l^{2} m_{b}}{9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}} & - \\frac{6 l m_{b}}{9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}}\\\\\\frac{9 I_{B_bo}}{9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}} & \\frac{6 l m_{a}}{9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}}\\\\\\frac{- 9 I_{B_bo} + 8 l^{2} m_{b}}{l \\left(9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}\\right)} & \\frac{- 18 l m_{a} - 12 l m_{b}}{l \\left(9 I_{B_bo} m_{a} + 9 I_{B_bo} m_{b} + 4 l^{2} m_{a} m_{b}\\right)}\\\\0 & 0\\\\0 & 0\\\\0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                             2                                               \n",
       "⎢             9⋅I_{B_bo} + 4⋅l ⋅m_b                                   -6⋅l⋅m_b\n",
       "⎢  ────────────────────────────────────────────      ─────────────────────────\n",
       "⎢                                      2                                      \n",
       "⎢  9⋅I_{B_bo}⋅mₐ + 9⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b      9⋅I_{B_bo}⋅mₐ + 9⋅I_{B_bo\n",
       "⎢                                                                             \n",
       "⎢                   9⋅I_{B_bo}                                          6⋅l⋅mₐ\n",
       "⎢  ────────────────────────────────────────────      ─────────────────────────\n",
       "⎢                                      2                                      \n",
       "⎢  9⋅I_{B_bo}⋅mₐ + 9⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b      9⋅I_{B_bo}⋅mₐ + 9⋅I_{B_bo\n",
       "⎢                                                                             \n",
       "⎢                              2                                              \n",
       "⎢             -9⋅I_{B_bo} + 8⋅l ⋅m_b                             -18⋅l⋅mₐ - 12\n",
       "⎢────────────────────────────────────────────────  ───────────────────────────\n",
       "⎢  ⎛                                    2       ⎞    ⎛                        \n",
       "⎢l⋅⎝9⋅I_{B_bo}⋅mₐ + 9⋅I_{B_bo}⋅m_b + 4⋅l ⋅mₐ⋅m_b⎠  l⋅⎝9⋅I_{B_bo}⋅mₐ + 9⋅I_{B_b\n",
       "⎢                                                                             \n",
       "⎢                       0                                                 0   \n",
       "⎢                                                                             \n",
       "⎢                       0                                                 0   \n",
       "⎢                                                                             \n",
       "⎣                       0                                                 0   \n",
       "\n",
       "                     ⎤\n",
       "                     ⎥\n",
       "───────────────────  ⎥\n",
       "           2         ⎥\n",
       "}⋅m_b + 4⋅l ⋅mₐ⋅m_b  ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "───────────────────  ⎥\n",
       "           2         ⎥\n",
       "}⋅m_b + 4⋅l ⋅mₐ⋅m_b  ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "⋅l⋅m_b               ⎥\n",
       "─────────────────────⎥\n",
       "            2       ⎞⎥\n",
       "o}⋅m_b + 4⋅l ⋅mₐ⋅m_b⎠⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎦"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = xdot.jacobian([F, T])\n",
    "B"
   ]
  }
 ],
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