--- a
+++ b/arm_model/model.ipynb
@@ -0,0 +1,1394 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "source": [
+    "# Simplified Arm Mode"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "source": [
+    "## Introduction"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "source": [
+    "This notebook presents the analytical derivations of the equations of motion for\n",
+    "three degrees of freedom and nine muscles arm model, some of them being\n",
+    "bi-articular, appropriately constructed to demonstrate both kinematic and\n",
+    "dynamic redundancy (e.g.  $d < n < m$). The model is inspired from [1] with some\n",
+    "minor modifications and improvements."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "source": [
+    "## Model Constants"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "source": [
+    "Abbreviations:\n",
+    "\n",
+    "- DoFs: Degrees of Freedom\n",
+    "- EoMs: Equations of Motion\n",
+    "- KE: Kinetic Energy\n",
+    "- PE: Potential Energy\n",
+    "- CoM: center of mass\n",
+    "\n",
+    "The following constants are used in the model:\n",
+    "\n",
+    "- $m$ mass of a segment\n",
+    "- $I_{z_i}$ inertia around $z$-axis\n",
+    "- $L_i$ length of a segment\n",
+    "- $L_{c_i}$ length of the CoM as defined in local frame of a body\n",
+    "- $a_i$ muscle origin point as defined in the local frame of a body\n",
+    "- $b_i$ muscle insertion point as defined in the local frame of a body\n",
+    "- $g$ gravity\n",
+    "- $q_i$ are the generalized coordinates\n",
+    "- $u_i$ are the generalized speeds\n",
+    "- $\\tau$ are the generalized forces\n",
+    "\n",
+    "Please note that there are some differences from [1]: 1) $L_{g_i} \\rightarrow\n",
+    "L_{c_i}$, 2) $a_i$ is always the muscle origin, 3) $b_i$ is always the muscle\n",
+    "insertion and 4) we don't use double indexing for the bi-articular muscles."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "autoscroll": false,
+    "ein.hycell": false,
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The autoreload extension is already loaded. To reload it, use:\n",
+      "  %reload_ext autoreload\n"
+     ]
+    }
+   ],
+   "source": [
+    "# notebook general configuration\n",
+    "\n",
+    "%load_ext autoreload\n",
+    "%autoreload 2\n",
+    "\n",
+    "# imports and utilities\n",
+    "import sympy as sp\n",
+    "from IPython.display import display, Image\n",
+    "sp.interactive.printing.init_printing()\n",
+    "\n",
+    "import logging\n",
+    "logging.basicConfig(level=logging.INFO)\n",
+    "\n",
+    "# plot\n",
+    "%matplotlib inline\n",
+    "from matplotlib.pyplot import *\n",
+    "rcParams['figure.figsize'] = (10.0, 6.0)\n",
+    "\n",
+    "# utility for displaying intermediate results\n",
+    "enable_display  = True\n",
+    "def disp(*statement):\n",
+    "    if (enable_display):\n",
+    "        display(*statement)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "autoscroll": false,
+    "ein.hycell": false,
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/latex": [
+       "$$\\left \\{ Iz_{1} : 0.0141, \\quad Iz_{2} : 0.012, \\quad Iz_{3} : 0.001, \\quad L_{1} : 0.31, \\quad L_{2} : 0.27, \\quad L_{3} : 0.15, \\quad Lc_{1} : 0.165, \\quad Lc_{2} : 0.135, \\quad Lc_{3} : 0.075, \\quad a_{1} : 0.055, \\quad a_{2} : 0.055, \\quad a_{3} : 0.22, \\quad a_{4} : 0.24, \\quad a_{5} : 0.04, \\quad a_{6} : 0.04, \\quad a_{7} : 0.22, \\quad a_{8} : 0.06, \\quad a_{9} : 0.26, \\quad b_{1} : 0.08, \\quad b_{2} : 0.11, \\quad b_{3} : 0.03, \\quad b_{4} : 0.03, \\quad b_{5} : 0.045, \\quad b_{6} : 0.045, \\quad b_{7} : 0.048, \\quad b_{8} : 0.05, \\quad b_{9} : 0.03, \\quad g : 9.81, \\quad m_{1} : 1.93, \\quad m_{2} : 1.32, \\quad m_{3} : 0.35\\right \\}$$"
+      ],
+      "text/plain": [
+       "{Iz₁: 0.0141, Iz₂: 0.012, Iz₃: 0.001, L₁: 0.31, L₂: 0.27, L₃: 0.15, Lc₁: 0.165\n",
+       ", Lc₂: 0.135, Lc₃: 0.075, a₁: 0.055, a₂: 0.055, a₃: 0.22, a₄: 0.24, a₅: 0.04, \n",
+       "a₆: 0.04, a₇: 0.22, a₈: 0.06, a₉: 0.26, b₁: 0.08, b₂: 0.11, b₃: 0.03, b₄: 0.03\n",
+       ", b₅: 0.045, b₆: 0.045, b₇: 0.048, b₈: 0.05, b₉: 0.03, g: 9.81, m₁: 1.93, m₂: \n",
+       "1.32, m₃: 0.35}"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# construct model\n",
+    "from model import ArmModel\n",
+    "model = ArmModel(use_gravity=1, use_coordinate_limits=0, use_viscosity=0)\n",
+    "\n",
+    "disp(model.constants)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "source": [
+    "## Dynamics"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "source": [
+    "The simplified arm model has three DoFs and nine muscles, some of them being\n",
+    "bi-articular. The analytical expressions of the EoMs form is given by\n",
+    "\n",
+    "\n",
+    "\\begin{equation}\\label{equ:eom-standard-form}\n",
+    "  M(q) \\ddot{q} + C(q, \\dot{q})\\dot{q} + \\tau_g(q) = \\tau\n",
+    "\\end{equation}\n",
+    "\n",
+    "\n",
+    "where $M \\in \\Re^{n \\times n}$ represents the inertia mass matrix, $n$ the DoFs\n",
+    "of the model, $q, \\dot{q}, \\ddot{q} \\in \\Re^{n}$ the generalized coordinates and\n",
+    "their derivatives, $C \\in \\Re^{n \\times n}$ the Coriolis and centrifugal matrix,\n",
+    "$\\tau_g \\in \\Re^{n}$ the gravity contribution and $\\tau$ the specified\n",
+    "generalized forces.\n",
+    "\n",
+    "As the model is an open kinematic chain a simple procedure to derive the EoMs\n",
+    "can be followed. Assuming that the spatial velocity (translational, rotational)\n",
+    "of each body segment is given by $u_b = [v, \\omega]^T \\in \\Re^{6 \\times 1}$, the\n",
+    "KE of the system in body local coordinates is defined as\n",
+    "\n",
+    "\n",
+    "\\begin{equation}\\label{equ:spatial-ke}\n",
+    "  K = \\frac{1}{2} \\sum\\limits_{i=1}^{n_b} (m_i v_i^2 + I_i \\omega_i^2) =\n",
+    "  \\frac{1}{2} \\sum\\limits_{i=1}^{n_b} u_i^T M_i u_i\n",
+    "\\end{equation}\n",
+    " \n",
+    "\n",
+    "where $M_i = diag(m_i, m_i, m_i, [I_i]_{3 \\times 3}) \\in \\Re^{6 \\times 6}$\n",
+    "denotes the spatial inertia mass matrix, $m_i$ the mass and $I_i \\in \\Re^{3\n",
+    "\\times 3}$ the inertia matrix of body $i$. The spatial quantities are related\n",
+    "to the generalized coordinates by the body Jacobian $u_b = J_b \\dot{q}, \\; J_b\n",
+    "\\in \\Re^{6 \\times n}$. The total KE is coordinate invariant, thus it can be\n",
+    "expressed in different coordinate system\n",
+    " \n",
+    "\n",
+    "\\begin{equation}\\label{equ:ke-transformation}\n",
+    "  K = \\frac{1}{2} \\sum\\limits_{i=1}^{n_b} q^T J_i^T M_i J_i q\n",
+    "\\end{equation}\n",
+    "\n",
+    "\n",
+    "Following the above definition, the inertia mass matrix of the system can be\n",
+    "written as\n",
+    "\n",
+    " \n",
+    "\\begin{equation}\\label{equ:mass-matrix}\n",
+    "  M(q) =  \\sum\\limits_{i=1}^{n_b}  J_i^T M_i J_i\n",
+    "\\end{equation}\n",
+    " \n",
+    "\n",
+    "Furthermore, the Coriolis and centrifugal forces $C(q, \\dot{q}) \\dot{q}$ can be\n",
+    "determined directly from the inertia mass matrix\n",
+    "\n",
+    "\n",
+    "\\begin{equation}\\label{equ:coriolis-matrix}\n",
+    "  C_{ij}(q, \\dot{q}) = \\sum\\limits_{k=1}^{n} \\Gamma_{ijk} \\; \\dot{q}_k, \\; i, j\n",
+    "  \\in [1, \\dots n], \\;\n",
+    "  \\Gamma_{ijk} = \\frac{1}{2} (\n",
+    "  \\frac{\\partial M_{ij}(q)}{\\partial q_k} +\n",
+    "  \\frac{\\partial M_{ik}(q)}{\\partial q_j} -\n",
+    "  \\frac{\\partial M_{kj}(q)}{\\partial q_i})\n",
+    "\\end{equation}\n",
+    "\n",
+    "\n",
+    "where the functions $\\Gamma_{ijk}$ are called the Christoffel symbols. The\n",
+    "gravity contribution can be determined from the PE function\n",
+    " \n",
+    "\n",
+    "\\begin{equation}\\label{equ:gravity-pe}\n",
+    "  \\begin{gathered}\n",
+    "    g(q) = \\frac{\\partial V(q)}{\\partial q}, \\; V(q) = \\sum\\limits_{i=1}^{n_b} m_i g h_i(q)\n",
+    "  \\end{gathered}\n",
+    "\\end{equation}\n",
+    "\n",
+    "\n",
+    "where $h_i(q)$ denotes the vertical displacement of body $i$ with respect to the\n",
+    "ground. In this derivation we chose to collect all forces that act on the system\n",
+    "in the term $f(q, \\dot{q})$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "autoscroll": false,
+    "ein.hycell": false,
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
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VfSoMjFdRI5gHY7TVXhZQtkGX+krs4mtimpJ23ZbmaKJHfYEx4cRepzBG7RFG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\nYDFG6ej/AWsOU/DO5GbFAAAAAElFTkSuQmCC\n",
+      "text/latex": [
+       "$$\\left [ \\left[\\begin{matrix}Lc_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )}\\\\Lc_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )}\\\\0\\\\0\\\\0\\\\\\theta_{1}{\\left (t \\right )}\\end{matrix}\\right], \\quad \\left[\\begin{matrix}L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + Lc_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\\\L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + Lc_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\\\0\\\\0\\\\0\\\\\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )}\\end{matrix}\\right], \\quad \\left[\\begin{matrix}L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + L_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\\\L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + L_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\\\0\\\\0\\\\0\\\\\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )}\\end{matrix}\\right]\\right ]$$"
+      ],
+      "text/plain": [
+       "⎡⎡Lc₁⋅cos(θ₁(t))⎤  ⎡L₁⋅cos(θ₁(t)) + Lc₂⋅cos(θ₁(t) + θ₂(t))⎤  ⎡L₁⋅cos(θ₁(t)) + \n",
+       "⎢⎢              ⎥  ⎢                                      ⎥  ⎢                \n",
+       "⎢⎢Lc₁⋅sin(θ₁(t))⎥  ⎢L₁⋅sin(θ₁(t)) + Lc₂⋅sin(θ₁(t) + θ₂(t))⎥  ⎢L₁⋅sin(θ₁(t)) + \n",
+       "⎢⎢              ⎥  ⎢                                      ⎥  ⎢                \n",
+       "⎢⎢      0       ⎥  ⎢                  0                   ⎥  ⎢                \n",
+       "⎢⎢              ⎥, ⎢                                      ⎥, ⎢                \n",
+       "⎢⎢      0       ⎥  ⎢                  0                   ⎥  ⎢                \n",
+       "⎢⎢              ⎥  ⎢                                      ⎥  ⎢                \n",
+       "⎢⎢      0       ⎥  ⎢                  0                   ⎥  ⎢                \n",
+       "⎢⎢              ⎥  ⎢                                      ⎥  ⎢                \n",
+       "⎣⎣    θ₁(t)     ⎦  ⎣            θ₁(t) + θ₂(t)             ⎦  ⎣                \n",
+       "\n",
+       "L₂⋅cos(θ₁(t) + θ₂(t)) + Lc₃⋅cos(θ₁(t) + θ₂(t) + θ₃(t))⎤⎤\n",
+       "                                                      ⎥⎥\n",
+       "L₂⋅sin(θ₁(t) + θ₂(t)) + Lc₃⋅sin(θ₁(t) + θ₂(t) + θ₃(t))⎥⎥\n",
+       "                                                      ⎥⎥\n",
+       "                  0                                   ⎥⎥\n",
+       "                                                      ⎥⎥\n",
+       "                  0                                   ⎥⎥\n",
+       "                                                      ⎥⎥\n",
+       "                  0                                   ⎥⎥\n",
+       "                                                      ⎥⎥\n",
+       "        θ₁(t) + θ₂(t) + θ₃(t)                         ⎦⎦"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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mjCn9kNWPKo7Q9fXuU0DOuWJq8U5mg7Zd3/1SSzq0fZA0uOljJM5O+vOSnjWn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\nn716OfPw/6M08EiQ3osywI3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RJs4tBbsX9eOFgykL11a8rvHWPbgxKIXB1gqtMV5hMmTT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\nIFkGaHaCrf8DTXB0zfz26qwAAAAASUVORK5CYII=\n",
+      "text/latex": [
+       "$$\\left [ \\left[\\begin{matrix}- Lc_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )}\\\\Lc_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )}\\\\0\\\\0\\\\0\\\\\\frac{d}{d t} \\theta_{1}{\\left (t \\right )}\\end{matrix}\\right], \\quad \\left[\\begin{matrix}- L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} - Lc_{2} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right) \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\\\L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + Lc_{2} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right) \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\\\0\\\\0\\\\0\\\\\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\end{matrix}\\right], \\quad \\left[\\begin{matrix}- L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} - L_{2} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right) \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} - Lc_{3} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\right) \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\\\L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + L_{2} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right) \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\right) \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\\\0\\\\0\\\\0\\\\\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\end{matrix}\\right]\\right ]$$"
+      ],
+      "text/plain": [
+       "⎡⎡                d        ⎤  ⎡                d               ⎛d           d \n",
+       "⎢⎢-Lc₁⋅sin(θ₁(t))⋅──(θ₁(t))⎥  ⎢- L₁⋅sin(θ₁(t))⋅──(θ₁(t)) - Lc₂⋅⎜──(θ₁(t)) + ──\n",
+       "⎢⎢                dt       ⎥  ⎢                dt              ⎝dt          dt\n",
+       "⎢⎢                         ⎥  ⎢                                               \n",
+       "⎢⎢               d         ⎥  ⎢               d               ⎛d           d  \n",
+       "⎢⎢Lc₁⋅cos(θ₁(t))⋅──(θ₁(t)) ⎥  ⎢ L₁⋅cos(θ₁(t))⋅──(θ₁(t)) + Lc₂⋅⎜──(θ₁(t)) + ──(\n",
+       "⎢⎢               dt        ⎥  ⎢               dt              ⎝dt          dt \n",
+       "⎢⎢                         ⎥  ⎢                                               \n",
+       "⎢⎢            0            ⎥, ⎢                                    0          \n",
+       "⎢⎢                         ⎥  ⎢                                               \n",
+       "⎢⎢            0            ⎥  ⎢                                    0          \n",
+       "⎢⎢                         ⎥  ⎢                                               \n",
+       "⎢⎢            0            ⎥  ⎢                                    0          \n",
+       "⎢⎢                         ⎥  ⎢                                               \n",
+       "⎢⎢        d                ⎥  ⎢                          d           d        \n",
+       "⎢⎢        ──(θ₁(t))        ⎥  ⎢                          ──(θ₁(t)) + ──(θ₂(t))\n",
+       "⎣⎣        dt               ⎦  ⎣                          dt          dt       \n",
+       "\n",
+       "       ⎞                   ⎤  ⎡                d              ⎛d           d  \n",
+       "(θ₂(t))⎟⋅sin(θ₁(t) + θ₂(t))⎥  ⎢- L₁⋅sin(θ₁(t))⋅──(θ₁(t)) - L₂⋅⎜──(θ₁(t)) + ──(\n",
+       "       ⎠                   ⎥  ⎢                dt             ⎝dt          dt \n",
+       "                           ⎥  ⎢                                               \n",
+       "      ⎞                    ⎥  ⎢               d              ⎛d           d   \n",
+       "θ₂(t))⎟⋅cos(θ₁(t) + θ₂(t)) ⎥  ⎢ L₁⋅cos(θ₁(t))⋅──(θ₁(t)) + L₂⋅⎜──(θ₁(t)) + ──(θ\n",
+       "      ⎠                    ⎥  ⎢               dt             ⎝dt          dt  \n",
+       "                           ⎥  ⎢                                               \n",
+       "                           ⎥, ⎢                                               \n",
+       "                           ⎥  ⎢                                               \n",
+       "                           ⎥  ⎢                                               \n",
+       "                           ⎥  ⎢                                               \n",
+       "                           ⎥  ⎢                                               \n",
+       "                           ⎥  ⎢                                               \n",
+       "                           ⎥  ⎢                                               \n",
+       "                           ⎥  ⎢                                               \n",
+       "                           ⎦  ⎣                                               \n",
+       "\n",
+       "      ⎞                          ⎛d           d           d        ⎞          \n",
+       "θ₂(t))⎟⋅sin(θ₁(t) + θ₂(t)) - Lc₃⋅⎜──(θ₁(t)) + ──(θ₂(t)) + ──(θ₃(t))⎟⋅sin(θ₁(t)\n",
+       "      ⎠                          ⎝dt          dt          dt       ⎠          \n",
+       "                                                                              \n",
+       "     ⎞                          ⎛d           d           d        ⎞           \n",
+       "₂(t))⎟⋅cos(θ₁(t) + θ₂(t)) + Lc₃⋅⎜──(θ₁(t)) + ──(θ₂(t)) + ──(θ₃(t))⎟⋅cos(θ₁(t) \n",
+       "     ⎠                          ⎝dt          dt          dt       ⎠           \n",
+       "                                                                              \n",
+       "                       0                                                      \n",
+       "                                                                              \n",
+       "                       0                                                      \n",
+       "                                                                              \n",
+       "                       0                                                      \n",
+       "                                                                              \n",
+       "       d           d           d                                              \n",
+       "       ──(θ₁(t)) + ──(θ₂(t)) + ──(θ₃(t))                                      \n",
+       "       dt          dt          dt                                             \n",
+       "\n",
+       "                 ⎤⎤\n",
+       " + θ₂(t) + θ₃(t))⎥⎥\n",
+       "                 ⎥⎥\n",
+       "                 ⎥⎥\n",
+       "                 ⎥⎥\n",
+       "+ θ₂(t) + θ₃(t)) ⎥⎥\n",
+       "                 ⎥⎥\n",
+       "                 ⎥⎥\n",
+       "                 ⎥⎥\n",
+       "                 ⎥⎥\n",
+       "                 ⎥⎥\n",
+       "                 ⎥⎥\n",
+       "                 ⎥⎥\n",
+       "                 ⎥⎥\n",
+       "                 ⎥⎥\n",
+       "                 ⎥⎥\n",
+       "                 ⎦⎦"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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pw/Q4gnrtgTZ72PAxdphR+Cnm/JBT3NbIuz+mZexd3DBc6EsNYCEqn/a6kqbU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\nKQxkiVO0+ZTcyCDCgDAgDCQwgNM57f0fuGHBOl3Qv8UAAAAASUVORK5CYII=\n",
+      "text/latex": [
+       "$$\\left [ \\left[\\begin{matrix}- Lc_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} & 0 & 0\\\\Lc_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\1 & 0 & 0\\end{matrix}\\right], \\quad \\left[\\begin{matrix}- L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} - Lc_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} & - Lc_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} & 0\\\\L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + Lc_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} & Lc_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\1 & 1 & 0\\end{matrix}\\right], \\quad \\left[\\begin{matrix}- L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} - L_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} - Lc_{3} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} & - L_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} - Lc_{3} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} & - Lc_{3} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\\\L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + L_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} & L_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} & Lc_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\1 & 1 & 1\\end{matrix}\\right]\\right ]$$"
+      ],
+      "text/plain": [
+       "⎡⎡-Lc₁⋅sin(θ₁(t))  0  0⎤  ⎡-L₁⋅sin(θ₁(t)) - Lc₂⋅sin(θ₁(t) + θ₂(t))  -Lc₂⋅sin(θ\n",
+       "⎢⎢                     ⎥  ⎢                                                   \n",
+       "⎢⎢Lc₁⋅cos(θ₁(t))   0  0⎥  ⎢L₁⋅cos(θ₁(t)) + Lc₂⋅cos(θ₁(t) + θ₂(t))   Lc₂⋅cos(θ₁\n",
+       "⎢⎢                     ⎥  ⎢                                                   \n",
+       "⎢⎢       0         0  0⎥  ⎢                   0                               \n",
+       "⎢⎢                     ⎥, ⎢                                                   \n",
+       "⎢⎢       0         0  0⎥  ⎢                   0                               \n",
+       "⎢⎢                     ⎥  ⎢                                                   \n",
+       "⎢⎢       0         0  0⎥  ⎢                   0                               \n",
+       "⎢⎢                     ⎥  ⎢                                                   \n",
+       "⎣⎣       1         0  0⎦  ⎣                   1                               \n",
+       "\n",
+       "₁(t) + θ₂(t))  0⎤  ⎡-L₁⋅sin(θ₁(t)) - L₂⋅sin(θ₁(t) + θ₂(t)) - Lc₃⋅sin(θ₁(t) + θ\n",
+       "                ⎥  ⎢                                                          \n",
+       "(t) + θ₂(t))   0⎥  ⎢L₁⋅cos(θ₁(t)) + L₂⋅cos(θ₁(t) + θ₂(t)) + Lc₃⋅cos(θ₁(t) + θ₂\n",
+       "                ⎥  ⎢                                                          \n",
+       " 0             0⎥  ⎢                                   0                      \n",
+       "                ⎥, ⎢                                                          \n",
+       " 0             0⎥  ⎢                                   0                      \n",
+       "                ⎥  ⎢                                                          \n",
+       " 0             0⎥  ⎢                                   0                      \n",
+       "                ⎥  ⎢                                                          \n",
+       " 1             0⎦  ⎣                                   1                      \n",
+       "\n",
+       "₂(t) + θ₃(t))  -L₂⋅sin(θ₁(t) + θ₂(t)) - Lc₃⋅sin(θ₁(t) + θ₂(t) + θ₃(t))  -Lc₃⋅s\n",
+       "                                                                              \n",
+       "(t) + θ₃(t))   L₂⋅cos(θ₁(t) + θ₂(t)) + Lc₃⋅cos(θ₁(t) + θ₂(t) + θ₃(t))   Lc₃⋅co\n",
+       "                                                                              \n",
+       "                                          0                                   \n",
+       "                                                                              \n",
+       "                                          0                                   \n",
+       "                                                                              \n",
+       "                                          0                                   \n",
+       "                                                                              \n",
+       "                                          1                                   \n",
+       "\n",
+       "in(θ₁(t) + θ₂(t) + θ₃(t))⎤⎤\n",
+       "                         ⎥⎥\n",
+       "s(θ₁(t) + θ₂(t) + θ₃(t)) ⎥⎥\n",
+       "                         ⎥⎥\n",
+       "         0               ⎥⎥\n",
+       "                         ⎥⎥\n",
+       "         0               ⎥⎥\n",
+       "                         ⎥⎥\n",
+       "         0               ⎥⎥\n",
+       "                         ⎥⎥\n",
+       "         1               ⎦⎦"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# define the spatial coordinates for the CoM in terms of Lcs' and q's\n",
+    "disp(model.xc[1:])\n",
+    "# define CoM spatial velocities\n",
+    "disp(model.vc[1:])\n",
+    "#define CoM Jacobian\n",
+    "disp(model.Jc[1:])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "autoscroll": false,
+    "ein.hycell": false,
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'M_{1,1} = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/latex": [
+       "$$Iz_{1} + Iz_{2} + Iz_{3} + L_{1}^{2} m_{2} + L_{1}^{2} m_{3} + 2 L_{1} L_{2} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + 2 L_{1} Lc_{2} m_{2} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + 2 L_{1} Lc_{3} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + L_{2}^{2} m_{3} + 2 L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{1}^{2} m_{1} + Lc_{2}^{2} m_{2} + Lc_{3}^{2} m_{3}$$"
+      ],
+      "text/plain": [
+       "                    2        2                                                \n",
+       "Iz₁ + Iz₂ + Iz₃ + L₁ ⋅m₂ + L₁ ⋅m₃ + 2⋅L₁⋅L₂⋅m₃⋅cos(θ₂(t)) + 2⋅L₁⋅Lc₂⋅m₂⋅cos(θ₂\n",
+       "\n",
+       "                                          2                                  2\n",
+       "(t)) + 2⋅L₁⋅Lc₃⋅m₃⋅cos(θ₂(t) + θ₃(t)) + L₂ ⋅m₃ + 2⋅L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₁ \n",
+       "\n",
+       "         2         2   \n",
+       "⋅m₁ + Lc₂ ⋅m₂ + Lc₃ ⋅m₃"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'M_{1,2} = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAABG8AAAAYBAMAAAC2Fc2oAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
+      "text/latex": [
+       "$$Iz_{2} + Iz_{3} + L_{1} L_{2} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + L_{1} Lc_{2} m_{2} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + L_{1} Lc_{3} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + L_{2}^{2} m_{3} + 2 L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{2}^{2} m_{2} + Lc_{3}^{2} m_{3}$$"
+      ],
+      "text/plain": [
+       "                                                                              \n",
+       "Iz₂ + Iz₃ + L₁⋅L₂⋅m₃⋅cos(θ₂(t)) + L₁⋅Lc₂⋅m₂⋅cos(θ₂(t)) + L₁⋅Lc₃⋅m₃⋅cos(θ₂(t) +\n",
+       "\n",
+       "            2                                  2         2   \n",
+       " θ₃(t)) + L₂ ⋅m₃ + 2⋅L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₂ ⋅m₂ + Lc₃ ⋅m₃"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'M_{1,3} = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkoAAAAYBAMAAAD31M9/AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n",
+      "text/latex": [
+       "$$Iz_{3} + L_{1} Lc_{3} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{3}^{2} m_{3}$$"
+      ],
+      "text/plain": [
+       "                                                               2   \n",
+       "Iz₃ + L₁⋅Lc₃⋅m₃⋅cos(θ₂(t) + θ₃(t)) + L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₃ ⋅m₃"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'M_{2,1} = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAABG8AAAAYBAMAAAC2Fc2oAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAibvNqyLdMnZEZpkQ\nVO8ACCSdAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAMDElEQVRoBe1ZbWwcRxl+z/H5fPae79ykISCh\nGATCRJHitvwABLLbOGmBSrlEIUKlNFeJuBK05PqDpBUCX0hAVsLHVSCE8iM5gSKlFBGHqlVoKrEN\nVYQaCbs/qCohJSYSpEBonY+STzjej5ndmdmd88VO8qsjze4777xfz7Nzs2MvwHvttjMQ9I+Gtz2p\nJ+ErSx70zJjq9qxMj/fkW8BAL/RWbkHYeYWchBfb8GvPqo1AN2yStTzKNKILC9bUfAdWJM5GFzvt\nfGOTnx0pAuANGVlYhYl5sZ695HVc6ISnUFsdJ7kCm6vxyCe1Z+XzXoj+h6Zz9zSNfq66OTNvWUJq\nd86WrwFQvznNA8AXvCXEnvAWLhxPoT4mft3Wwkm1uqP5iZRfRWbVhTUprHSvu7BCq01Z6zz3Qgkn\ndtyvZl/nO3FrPW8znil7YlpqCtm9pCo6zgZAFFo07mre3RALAFPWuhZ3HwDHZS6IOm2m4jjqYfbo\n3QjCRG/K2qrF3Vuol4ml3mgmR2lW/0n1LFbmVHtMUvz+gLqOxnGZCYYAgi0An8Eh9aiZ8Uw5MvAK\nFBJWBBUxoGzHy7AoBO6ipKuJ1JRjC5/kBWA5zA1RlbAttPziwUbIXMGRid6UY0Of5C2U2IhbjD73\neKx1pdZWuXO2/V4ZjpfmVLsmtoM5egkHd0CxyrreBkBhFuA5HFEHSEnZfmwKQCEzA6BODpTtFEDP\npHR8Y+E0NhOpKfNk64sXALmp8C0hWiVkV6ZkYxIeBHgb50z0ppzi5qi8hRIbUakG+g2hE6Ftq25a\n4kZ7U+Qf1w0diilq18R2MEcz+NSuQHGadX147R0C6AulLzA2xaSQ43X4L8kAM9ifx35WdSjUUMI3\ngIHUlHmy9WXGB4DcVPiWEK0SNsI3k+mY4HdCWFcGMJk15aSXq5nxFkps6FJj9NmRHOZzmlUszaVa\ndczabmqFrLK1euEMG2pTNtRJMY/LpLMC4w2e+gleu0r4GsEh9WjhmPFMmUxaNwq5FnJX2YqywaPY\nP626pmuRgdSU2avlxQ+A3PTCaQVR2XDa7Me2v5xMx7yvBVhXBTDRm3LSy9G0KJTY0KXG6Dds/1bo\nxGjXqog858aqD2l3tXAu4Nij1pZkwi2/5IvLHsgt+7geB4f7p+HExO8gt3uCnmJvCWCqBqfqbHAY\n4KerPlKDzAi+X7BHCyeKhyqRMxPvo3l4Zs36XbUnvyv+OD7R/0EIjuypw1MHd9I8hgwuQ0F2FMyW\nv+/8AwBLcIa6pouQ6qbkZTuqpJk/APLWC6cVRGXDafuazdkEJP3LhK0Ycd5M+JlOYwLRv9NsJuk1\niwXwWe2v4Q9/x+AkUUBNFk7+MoopauNAlI/kTMcgTD0LJ9kfL49M58/ktkBH7RhAheI0cPetwvIy\nyrIRnMJ7Dz5H6lHKKB4+SZazT8BvaR5KH64FV+uFGR7gzvlv2FfdVobBYAC6SIe/pu5LkHmX5ykb\nnaHgl6rrJ7u/xPN8EXnTdO8ADecPgLz1wmkFUdnEJTiQNAmQQ+JjZrXcLhN+ppkNXaqN3qW3Tavl\nVYCHIUMMcJOFk6GDZoraOCbw+Z9dnu4bgM0lOCQBAO6Bwt/wZZS7tC8Eelhd0wCrRkf/J/NP4O15\n7IWKdM1ZHA+fJOfBGG+RT65+GrLnoGeWBtgWDcHJMr6Mxp8+K4VjyI6Lo+tmeJay0RkK3lBdE7G8\nzvN8EflR6KvRcP4AyFsvnFYQlU1UggtJkwBdkxo9hdZyu0z4mWY2dKk2+kQtVrGao4QVv0ODl4G/\noLw4Nvb22NhX8dnMUtWozu7eVQVXTb9lZUKfMcKpOpwK4T4xhoC2i/FpgHNd579Hln34xE7Ty4S/\nefwDNXQEyWEK7C1i/z7EEvDDThBcgcJ16ByQADBVQk88CRdLWwfLGAkwJK7dqRpjoGxINJbAvXds\n7Bt/Hxsb0SeH14ZQLaeI3usofeng/QsAAHF4gUjhqB4TYmzDZFP+GBI7RCTAUZwU8uUDkcjEBD0J\nxy3BRMR0ogxkwymD0du1UMq5rTg2wHnyXY8/UvUFRXac4oBSd5a6Z0hUamS9p/zU90lD7+ueMn/G\nwDcP7iFvgRjTbssHmvPB4uYkygTnMvRcBzZGVnEh4CY8I90f+zRacVmFWdpDcHfgADBew585higO\nvDJ8DW3oQRVrcChkY8qGKxlgn+r6d0YnhwO5iQre+BRxABcbwL3wI/7rfX4AKFahRlcFkcMlISob\nLoGNI0jsgCohmP9qNphVLBMTTK7j5jJB2JnpRBnMhi6Vy2D0di1C71xWUjEfZvI1CPUXFAGwv4Yh\nSZ2rZoYoeqzulJcAkEkn8GeM1fQDy78biHFAD5N2nGsPw2v0yls0TUsFN2E2/iwGnoUw8aqSeLKl\nssw7F5fVOUR7yP5yKB9NpibVjvNCGByqYgIMiUvl68DGmA32Q5B4VTHSEU4LItPOBdthMcC8AWAA\nzbNA5HBJiLJwJC3vixEkdsAoQvDrkC2bzIrMTDC5jpvLBGL3lGG+qgz0vK1FQdU3KbNY5oj3mMhK\nKubDzF6AEf0FRQDQyYf+MTeC234DRYWL1LvVwhGZP2P8lcrtHPqKMr4HyeybhPwljPV59O2oAa6Z\nkyGw8SC+uIcKZegZwB0Luz/2VVxiXFZfiRbG6uy0fDTBMw5M/wuXx7dr0NnAABiyWC+cBTambIvh\nzwC/wBnq6skS0u6GLByRiw2AOsDXAOYNIA6vIHK4JER5FpJW9kUNiR0wDPOeK0F3CAazSiYmmNyI\nCXFzmYiYTpSRZILR8x4TBVXfpMxi2Yr3mMhKUnfN4q/3Q4NLcUVkKkSDLJytKIm6+5OkjdUZPBjQ\nsZP+biQZlgJ+s8OD66ISombjRxpwZ+4MKk6G8FG0yIzgAgoeQwmN6e/CzpE/4kuoJt0f+ygA/jmO\nZW2u0sn7LjrBYwDI/hMy5e9U4S5cKx1lVFDIxnGEQMaUbTSoARzBMXW1cAjp8lAWjsi9k5Cpws7a\nAgDE4TVEDJcCUZ6FpOV9MYZEDtjepMumo0fXmsxqmZkgch03l4mYabeMJBOMnveYOCjTa/HFVrzH\nxFYUe+PwxRL+ZXLyU1j1thAvDCC7unkvPgRRH6tpdbC6Obq6OcILJ5LxY0e+At2TUDiCz5CNgy/0\nl+HL/Z+DZw7uqKMzzsOJPTgL9GXkZ/jkVzTw94MK6pIyioeLUsuZZRMhl4UuewD+gidt+bTy6uE7\nIXt4ST3/gYn3UwCcD468QNK2kLNt+BXKW1QXIl4dvjg6fBFXUQVAy/0TP0DPwQUAwBSKZw0Rw6VA\n5IWj0vK+GEMiB2y8cIabzQsaPWHVsjCB5LpuDhMx024ZzIbNBKHnPSYOKvSaxQJzRLtybKUq5rLx\nkl3JEgPQOrrn6JiidhySsL0hN75uCI2BMjY1JD+mFWTcVZXRJrxRbxGbJlVZJGKzs4kuDinGKlu2\ngs7Y4ydLsuw4LOnLuCqIx4JWT+m7FwAZyG6iTQHDJSHaNrK3aw/Jn+A9idWuzSpbx4oKdctIYUJ8\nlmpXugu9drGk31mja9Ts1OoLCh5szPanahZfsNGHSJkyFo71GUMbmwFIfk4p2Jj/cEDFS6r7Y7OX\n9WHHyqaC4k2HBDZW2Xob+CrEjjseX0nCRjuO0YIzsLkRjW8YAHma4SWcrieGaNrovZ2zRvn3RkUo\nwcVq1Ra5OV4Ke7KMFCbYVfYYO6VdLM2Ze4ybOv0LCnSFPWdV2PhmLBzrY0eqMbrxQQTvYkzHHtwM\nBqTzwLgYsUlrl2VlM5wkpDJW2TbgPHWnOQsHHoffhJHJjQKIHCNBwrWGaG2iVv4oDAouVrs2j5tm\n2i0jjQlOZm3hbsq4HHOPcVLzF5TYUku5Zbv4HKLHdF8/fCQa8scOPUozprlgQCzE+BgPOkJcUNid\nZsamKbssK5vhKSGVscq2Euep2y27+FrN0jw5sSYe3yiA2FNLEq4lRNkXbQc9Mu4uVrs2q+zYSzPt\nlpHCBDvZ25qbUsV19hhP6riImyg9ZMbKNmh0QHWSF9yyDTMEZ+vB9U795jQPAF/wbINmPBDtTZQM\nb2LzFOpjwr/HmDU5e4w59Z58+xiwN9Hblzctk2ePcUyTe8z/ASz0V/rMJ8mrAAAAAElFTkSuQmCC\n",
+      "text/latex": [
+       "$$Iz_{2} + Iz_{3} + L_{1} L_{2} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + L_{1} Lc_{2} m_{2} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + L_{1} Lc_{3} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + L_{2}^{2} m_{3} + 2 L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{2}^{2} m_{2} + Lc_{3}^{2} m_{3}$$"
+      ],
+      "text/plain": [
+       "                                                                              \n",
+       "Iz₂ + Iz₃ + L₁⋅L₂⋅m₃⋅cos(θ₂(t)) + L₁⋅Lc₂⋅m₂⋅cos(θ₂(t)) + L₁⋅Lc₃⋅m₃⋅cos(θ₂(t) +\n",
+       "\n",
+       "            2                                  2         2   \n",
+       " θ₃(t)) + L₂ ⋅m₃ + 2⋅L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₂ ⋅m₂ + Lc₃ ⋅m₃"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'M_{2,2} = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAh8AAAAYBAMAAACo6YJzAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n5DoAAAAASUVORK5CYII=\n",
+      "text/latex": [
+       "$$Iz_{2} + Iz_{3} + L_{2}^{2} m_{3} + 2 L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{2}^{2} m_{2} + Lc_{3}^{2} m_{3}$$"
+      ],
+      "text/plain": [
+       "              2                                  2         2   \n",
+       "Iz₂ + Iz₃ + L₂ ⋅m₃ + 2⋅L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₂ ⋅m₂ + Lc₃ ⋅m₃"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'M_{2,3} = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATwAAAAYBAMAAACVYVyhAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n3uBIao0XnC4r+/UP/zZhYhOcFQoAAAAASUVORK5CYII=\n",
+      "text/latex": [
+       "$$Iz_{3} + L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{3}^{2} m_{3}$$"
+      ],
+      "text/plain": [
+       "                                2   \n",
+       "Iz₃ + L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₃ ⋅m₃"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'M_{3,1} = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkoAAAAYBAMAAAD31M9/AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n",
+      "text/latex": [
+       "$$Iz_{3} + L_{1} Lc_{3} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{3}^{2} m_{3}$$"
+      ],
+      "text/plain": [
+       "                                                               2   \n",
+       "Iz₃ + L₁⋅Lc₃⋅m₃⋅cos(θ₂(t) + θ₃(t)) + L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₃ ⋅m₃"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'M_{3,2} = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATwAAAAYBAMAAACVYVyhAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n3uBIao0XnC4r+/UP/zZhYhOcFQoAAAAASUVORK5CYII=\n",
+      "text/latex": [
+       "$$Iz_{3} + L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{3}^{2} m_{3}$$"
+      ],
+      "text/plain": [
+       "                                2   \n",
+       "Iz₃ + L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₃ ⋅m₃"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'M_{3,3} = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHIAAAAYBAMAAADUnLRyAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAAAASUVORK5CYII=\n",
+      "text/latex": [
+       "$$Iz_{3} + Lc_{3}^{2} m_{3}$$"
+      ],
+      "text/plain": [
+       "         2   \n",
+       "Iz₃ + Lc₃ ⋅m₃"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# generate the inertial mass matrix\n",
+    "M = model.M\n",
+    "for i in range(0, M.shape[0]):\n",
+    "    for j in range(0, M.shape[1]):\n",
+    "        disp('M_{' + str(i + 1) + ',' + str(j + 1) + '} = ', M[i, j])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "autoscroll": false,
+    "ein.hycell": false,
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'f_1 = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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ndsSJPc1JFZviJzAhX8Obk6mNP1REIYKpzWl3UwrpSrDw7IOLTDBI1wAisahY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\n/z+PJ7GvAW9NGAAAAABJRU5ErkJggg==\n",
+      "text/latex": [
+       "$$Lc_{1} g m_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + g m_{2} \\left(L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + Lc_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\right) + g m_{3} \\left(L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + L_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\right) - 2 L_{1} L_{2} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + L_{1} L_{2} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right)^{2} + 2 L_{1} Lc_{2} m_{2} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + L_{1} Lc_{2} m_{2} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right)^{2} + 2 L_{1} Lc_{3} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + 2 L_{1} Lc_{3} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )} + L_{1} Lc_{3} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right)^{2} + 2 L_{1} Lc_{3} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )} + L_{1} Lc_{3} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\right)^{2} + 2 L_{2} Lc_{3} m_{3} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )} + 2 L_{2} Lc_{3} m_{3} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )} + L_{2} Lc_{3} m_{3} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\right)^{2}$$"
+      ],
+      "text/plain": [
+       "                                                                              \n",
+       "                                                                              \n",
+       "Lc₁⋅g⋅m₁⋅cos(θ₁(t)) + g⋅m₂⋅(L₁⋅cos(θ₁(t)) + Lc₂⋅cos(θ₁(t) + θ₂(t))) + g⋅m₃⋅(L₁\n",
+       "                                                                              \n",
+       "\n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "⋅cos(θ₁(t)) + L₂⋅cos(θ₁(t) + θ₂(t)) + Lc₃⋅cos(θ₁(t) + θ₂(t) + θ₃(t))) - 2⋅L₁⋅L\n",
+       "                                                                              \n",
+       "\n",
+       "                                                                     2        \n",
+       "                d         d                               ⎛d        ⎞         \n",
+       "₂⋅m₃⋅sin(θ₂(t))⋅──(θ₁(t))⋅──(θ₂(t)) + L₁⋅L₂⋅m₃⋅sin(θ₂(t))⋅⎜──(θ₂(t))⎟  + 2⋅L₁⋅\n",
+       "                dt        dt                              ⎝dt       ⎠         \n",
+       "\n",
+       "                                                                        2     \n",
+       "                  d         d                                ⎛d        ⎞      \n",
+       "Lc₂⋅m₂⋅sin(θ₂(t))⋅──(θ₁(t))⋅──(θ₂(t)) + L₁⋅Lc₂⋅m₂⋅sin(θ₂(t))⋅⎜──(θ₂(t))⎟  + 2⋅\n",
+       "                  dt        dt                               ⎝dt       ⎠      \n",
+       "\n",
+       "                                                                              \n",
+       "                             d         d                                      \n",
+       "L₁⋅Lc₃⋅m₃⋅sin(θ₂(t) + θ₃(t))⋅──(θ₁(t))⋅──(θ₂(t)) + 2⋅L₁⋅Lc₃⋅m₃⋅sin(θ₂(t) + θ₃(\n",
+       "                             dt        dt                                     \n",
+       "\n",
+       "                                                                  2           \n",
+       "    d         d                                        ⎛d        ⎞            \n",
+       "t))⋅──(θ₁(t))⋅──(θ₃(t)) + L₁⋅Lc₃⋅m₃⋅sin(θ₂(t) + θ₃(t))⋅⎜──(θ₂(t))⎟  + 2⋅L₁⋅Lc₃\n",
+       "    dt        dt                                       ⎝dt       ⎠            \n",
+       "\n",
+       "                                                                              \n",
+       "                       d         d                                        ⎛d  \n",
+       "⋅m₃⋅sin(θ₂(t) + θ₃(t))⋅──(θ₂(t))⋅──(θ₃(t)) + L₁⋅Lc₃⋅m₃⋅sin(θ₂(t) + θ₃(t))⋅⎜──(\n",
+       "                       dt        dt                                       ⎝dt \n",
+       "\n",
+       "       2                                                                      \n",
+       "      ⎞                           d         d                                 \n",
+       "θ₃(t))⎟  + 2⋅L₂⋅Lc₃⋅m₃⋅sin(θ₃(t))⋅──(θ₁(t))⋅──(θ₃(t)) + 2⋅L₂⋅Lc₃⋅m₃⋅sin(θ₃(t))\n",
+       "      ⎠                           dt        dt                                \n",
+       "\n",
+       "                                                       2\n",
+       " d         d                                ⎛d        ⎞ \n",
+       "⋅──(θ₂(t))⋅──(θ₃(t)) + L₂⋅Lc₃⋅m₃⋅sin(θ₃(t))⋅⎜──(θ₃(t))⎟ \n",
+       " dt        dt                               ⎝dt       ⎠ "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'f_2 = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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ZVJNV5GiaWvXWrglwIM8l1bxgJbIElqKRz1uPnHY5iWn3J4z6NvyRdNdyLxZlZs2RV9lM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\njxMuegAAAABJRU5ErkJggg==\n",
+      "text/latex": [
+       "$$- L_{2} Lc_{3} m_{3} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\right) \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )} - L_{2} Lc_{3} m_{3} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )} + Lc_{2} g m_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + g m_{3} \\left(L_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\right) + \\left(L_{1} \\left(L_{2} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + Lc_{2} m_{2} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\right) \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} - L_{2} Lc_{3} m_{3} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\right) \\frac{d}{d t} \\theta_{1}{\\left (t \\right )}$$"
+      ],
+      "text/plain": [
+       "            ⎛d           d           d        ⎞            d                  \n",
+       "- L₂⋅Lc₃⋅m₃⋅⎜──(θ₁(t)) + ──(θ₂(t)) + ──(θ₃(t))⎟⋅sin(θ₃(t))⋅──(θ₃(t)) - L₂⋅Lc₃⋅\n",
+       "            ⎝dt          dt          dt       ⎠            dt                 \n",
+       "\n",
+       "              d         d                                                     \n",
+       "m₃⋅sin(θ₃(t))⋅──(θ₂(t))⋅──(θ₃(t)) + Lc₂⋅g⋅m₂⋅cos(θ₁(t) + θ₂(t)) + g⋅m₃⋅(L₂⋅cos\n",
+       "              dt        dt                                                    \n",
+       "\n",
+       "                                                    ⎛                         \n",
+       "(θ₁(t) + θ₂(t)) + Lc₃⋅cos(θ₁(t) + θ₂(t) + θ₃(t))) + ⎜L₁⋅(L₂⋅m₃⋅sin(θ₂(t)) + Lc\n",
+       "                                                    ⎝                         \n",
+       "\n",
+       "                                             d                                \n",
+       "₂⋅m₂⋅sin(θ₂(t)) + Lc₃⋅m₃⋅sin(θ₂(t) + θ₃(t)))⋅──(θ₁(t)) - L₂⋅Lc₃⋅m₃⋅sin(θ₃(t))⋅\n",
+       "                                             dt                               \n",
+       "\n",
+       "d        ⎞ d        \n",
+       "──(θ₃(t))⎟⋅──(θ₁(t))\n",
+       "dt       ⎠ dt       "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'f_3 = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/latex": [
+       "$$Lc_{3} g m_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + Lc_{3} m_{3} \\left(L_{1} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )}\\right)^{2} + L_{2} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )}\\right)^{2} + 2 L_{2} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + L_{2} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right)^{2}\\right)$$"
+      ],
+      "text/plain": [
+       "                                             ⎛                                \n",
+       "                                             ⎜                      ⎛d        \n",
+       "Lc₃⋅g⋅m₃⋅cos(θ₁(t) + θ₂(t) + θ₃(t)) + Lc₃⋅m₃⋅⎜L₁⋅sin(θ₂(t) + θ₃(t))⋅⎜──(θ₁(t))\n",
+       "                                             ⎝                      ⎝dt       \n",
+       "\n",
+       " 2                            2                                               \n",
+       "⎞                  ⎛d        ⎞                    d         d                 \n",
+       "⎟  + L₂⋅sin(θ₃(t))⋅⎜──(θ₁(t))⎟  + 2⋅L₂⋅sin(θ₃(t))⋅──(θ₁(t))⋅──(θ₂(t)) + L₂⋅sin\n",
+       "⎠                  ⎝dt       ⎠                    dt        dt                \n",
+       "\n",
+       "                   2⎞\n",
+       "        ⎛d        ⎞ ⎟\n",
+       "(θ₃(t))⋅⎜──(θ₂(t))⎟ ⎟\n",
+       "        ⎝dt       ⎠ ⎠"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# total forces from Coriolis, centrafugal and gravity\n",
+    "f = model.f\n",
+    "for i in range(0, f.shape[0]):\n",
+    "    disp('f_' + str(i + 1) + ' = ',  f[i])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "source": [
+    "## Muscle Moment Arm"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "source": [
+    "The muscle forces $f_m$ are transformed into joint space generalized forces\n",
+    "($\\tau$) by the moment arm matrix ($\\tau = -R^T f_m$). For a n-lateral polygon\n",
+    "it can be shown that the derivative of the side length with respect to the\n",
+    "opposite angle is the moment arm component. As a consequence, when expressing\n",
+    "the muscle length as a function of the generalized coordinates of the model, the\n",
+    "moment arm matrix is evaluated by $R = \\frac{\\partial l_{mt}}{\\partial q}$. The\n",
+    "analytical expressions of the EoMs following our convention are provided below\n",
+    "\n",
+    "\\begin{equation}\\label{equ:eom-notation}\n",
+    "  \\begin{gathered}\n",
+    "    M(q) \\ddot{q} + f(q, \\dot{q}) = \\tau \\\\\n",
+    "    \\tau = -R^T(q) f_m\n",
+    "  \\end{gathered}\n",
+    "\\end{equation}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "autoscroll": false,
+    "ein.hycell": false,
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'l_m = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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JTDAmhYXq/0jiuzyYxoHRhv9h7yaCRLRNHM3vFSHzsCaMxPfC6H4Vyj41LntG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\n",
+      "text/latex": [
+       "$$\\left[\\begin{matrix}\\sqrt{a_{1}^{2} + 2 a_{1} b_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + b_{1}^{2}}\\\\\\sqrt{a_{2}^{2} - 2 a_{2} b_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + b_{2}^{2}}\\\\\\sqrt{b_{3}^{2} + b_{3} \\left(2 L_{1} - 2 a_{3}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{3}\\right)^{2}}\\\\\\sqrt{b_{4}^{2} - b_{4} \\left(2 L_{1} - 2 a_{4}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{4}\\right)^{2}}\\\\\\sqrt{L_{1}^{2} + 2 L_{1} a_{5} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + 2 L_{1} b_{5} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{5}^{2} + 2 a_{5} b_{5} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + b_{5}^{2}}\\\\\\sqrt{L_{1}^{2} - 2 L_{1} a_{6} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} - 2 L_{1} b_{6} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{6}^{2} + 2 a_{6} b_{6} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + b_{6}^{2}}\\\\\\sqrt{b_{7}^{2} + b_{7} \\left(2 L_{2} - 2 a_{7}\\right) \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{2} - a_{7}\\right)^{2}}\\\\\\sqrt{b_{8}^{2} - b_{8} \\left(2 L_{2} - 2 a_{8}\\right) \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{2} - a_{8}\\right)^{2}}\\\\\\sqrt{L_{2}^{2} + 2 L_{2} b_{9} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + L_{2} \\left(2 L_{1} - 2 a_{9}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + b_{9}^{2} + b_{9} \\left(2 L_{1} - 2 a_{9}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{9}\\right)^{2}}\\end{matrix}\\right]$$"
+      ],
+      "text/plain": [
+       "⎡                                           ________________________________  \n",
+       "⎢                                          ╱   2                          2   \n",
+       "⎢                                        ╲╱  a₁  + 2⋅a₁⋅b₁⋅cos(θ₁(t)) + b₁    \n",
+       "⎢                                                                             \n",
+       "⎢                                           ________________________________  \n",
+       "⎢                                          ╱   2                          2   \n",
+       "⎢                                        ╲╱  a₂  - 2⋅a₂⋅b₂⋅cos(θ₁(t)) + b₂    \n",
+       "⎢                                                                             \n",
+       "⎢                                   __________________________________________\n",
+       "⎢                                  ╱   2                                      \n",
+       "⎢                                ╲╱  b₃  + b₃⋅(2⋅L₁ - 2⋅a₃)⋅cos(θ₂(t)) + (L₁ -\n",
+       "⎢                                                                             \n",
+       "⎢                                   __________________________________________\n",
+       "⎢                                  ╱   2                                      \n",
+       "⎢                                ╲╱  b₄  - b₄⋅(2⋅L₁ - 2⋅a₄)⋅cos(θ₂(t)) + (L₁ -\n",
+       "⎢                                                                             \n",
+       "⎢               ______________________________________________________________\n",
+       "⎢              ╱   2                                               2          \n",
+       "⎢            ╲╱  L₁  + 2⋅L₁⋅a₅⋅cos(θ₁(t)) + 2⋅L₁⋅b₅⋅cos(θ₂(t)) + a₅  + 2⋅a₅⋅b₅\n",
+       "⎢                                                                             \n",
+       "⎢               ______________________________________________________________\n",
+       "⎢              ╱   2                                               2          \n",
+       "⎢            ╲╱  L₁  - 2⋅L₁⋅a₆⋅cos(θ₁(t)) - 2⋅L₁⋅b₆⋅cos(θ₂(t)) + a₆  + 2⋅a₆⋅b₆\n",
+       "⎢                                                                             \n",
+       "⎢                                   __________________________________________\n",
+       "⎢                                  ╱   2                                      \n",
+       "⎢                                ╲╱  b₇  + b₇⋅(2⋅L₂ - 2⋅a₇)⋅cos(θ₃(t)) + (L₂ -\n",
+       "⎢                                                                             \n",
+       "⎢                                   __________________________________________\n",
+       "⎢                                  ╱   2                                      \n",
+       "⎢                                ╲╱  b₈  - b₈⋅(2⋅L₂ - 2⋅a₈)⋅cos(θ₃(t)) + (L₂ -\n",
+       "⎢                                                                             \n",
+       "⎢   __________________________________________________________________________\n",
+       "⎢  ╱   2                                                        2             \n",
+       "⎣╲╱  L₂  + 2⋅L₂⋅b₉⋅cos(θ₃(t)) + L₂⋅(2⋅L₁ - 2⋅a₉)⋅cos(θ₂(t)) + b₉  + b₉⋅(2⋅L₁ -\n",
+       "\n",
+       "                                       ⎤\n",
+       "                                       ⎥\n",
+       "                                       ⎥\n",
+       "                                       ⎥\n",
+       "                                       ⎥\n",
+       "                                       ⎥\n",
+       "                                       ⎥\n",
+       "                                       ⎥\n",
+       "______                                 ⎥\n",
+       "    2                                  ⎥\n",
+       " a₃)                                   ⎥\n",
+       "                                       ⎥\n",
+       "______                                 ⎥\n",
+       "    2                                  ⎥\n",
+       " a₄)                                   ⎥\n",
+       "                                       ⎥\n",
+       "__________________________             ⎥\n",
+       "                        2              ⎥\n",
+       "⋅cos(θ₁(t) + θ₂(t)) + b₅               ⎥\n",
+       "                                       ⎥\n",
+       "__________________________             ⎥\n",
+       "                        2              ⎥\n",
+       "⋅cos(θ₁(t) + θ₂(t)) + b₆               ⎥\n",
+       "                                       ⎥\n",
+       "______                                 ⎥\n",
+       "    2                                  ⎥\n",
+       " a₇)                                   ⎥\n",
+       "                                       ⎥\n",
+       "______                                 ⎥\n",
+       "    2                                  ⎥\n",
+       " a₈)                                   ⎥\n",
+       "                                       ⎥\n",
+       "_______________________________________⎥\n",
+       "                                     2 ⎥\n",
+       " 2⋅a₉)⋅cos(θ₂(t) + θ₃(t)) + (L₁ - a₉)  ⎦"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'R = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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lZLWLyHAJBIAAEAACQOBuBL7N0bdxh57R0eizEVDsf7ton/soa7d917HWxRJrh7Y4RC8N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\n",
+      "text/latex": [
+       "$$\\left[\\begin{matrix}- \\frac{a_{1} b_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )}}{\\sqrt{a_{1}^{2} + 2 a_{1} b_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + b_{1}^{2}}} & 0 & 0\\\\\\frac{a_{2} b_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )}}{\\sqrt{a_{2}^{2} - 2 a_{2} b_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + b_{2}^{2}}} & 0 & 0\\\\0 & - \\frac{b_{3} \\left(2 L_{1} - 2 a_{3}\\right) \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )}}{2 \\sqrt{b_{3}^{2} + b_{3} \\left(2 L_{1} - 2 a_{3}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{3}\\right)^{2}}} & 0\\\\0 & \\frac{b_{4} \\left(2 L_{1} - 2 a_{4}\\right) \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )}}{2 \\sqrt{b_{4}^{2} - b_{4} \\left(2 L_{1} - 2 a_{4}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{4}\\right)^{2}}} & 0\\\\- \\frac{a_{5} \\left(L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + b_{5} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\right)}{\\sqrt{L_{1}^{2} + 2 L_{1} a_{5} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + 2 L_{1} b_{5} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{5}^{2} + 2 a_{5} b_{5} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + b_{5}^{2}}} & - \\frac{b_{5} \\left(L_{1} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{5} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\right)}{\\sqrt{L_{1}^{2} + 2 L_{1} a_{5} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + 2 L_{1} b_{5} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{5}^{2} + 2 a_{5} b_{5} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + b_{5}^{2}}} & 0\\\\\\frac{a_{6} \\left(L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} - b_{6} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\right)}{\\sqrt{L_{1}^{2} - 2 L_{1} a_{6} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} - 2 L_{1} b_{6} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{6}^{2} + 2 a_{6} b_{6} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + b_{6}^{2}}} & \\frac{b_{6} \\left(L_{1} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} - a_{6} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\right)}{\\sqrt{L_{1}^{2} - 2 L_{1} a_{6} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} - 2 L_{1} b_{6} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{6}^{2} + 2 a_{6} b_{6} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + b_{6}^{2}}} & 0\\\\0 & 0 & - \\frac{b_{7} \\left(2 L_{2} - 2 a_{7}\\right) \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )}}{2 \\sqrt{b_{7}^{2} + b_{7} \\left(2 L_{2} - 2 a_{7}\\right) \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{2} - a_{7}\\right)^{2}}}\\\\0 & 0 & \\frac{b_{8} \\left(2 L_{2} - 2 a_{8}\\right) \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )}}{2 \\sqrt{b_{8}^{2} - b_{8} \\left(2 L_{2} - 2 a_{8}\\right) \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{2} - a_{8}\\right)^{2}}}\\\\0 & \\frac{- \\frac{L_{2}}{2} \\left(2 L_{1} - 2 a_{9}\\right) \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} - \\frac{b_{9}}{2} \\left(2 L_{1} - 2 a_{9}\\right) \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}}{\\sqrt{L_{2}^{2} + 2 L_{2} b_{9} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + L_{2} \\left(2 L_{1} - 2 a_{9}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + b_{9}^{2} + b_{9} \\left(2 L_{1} - 2 a_{9}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{9}\\right)^{2}}} & \\frac{- L_{2} b_{9} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} - \\frac{b_{9}}{2} \\left(2 L_{1} - 2 a_{9}\\right) \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}}{\\sqrt{L_{2}^{2} + 2 L_{2} b_{9} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + L_{2} \\left(2 L_{1} - 2 a_{9}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + b_{9}^{2} + b_{9} \\left(2 L_{1} - 2 a_{9}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{9}\\right)^{2}}}\\end{matrix}\\right]$$"
+      ],
+      "text/plain": [
+       "⎡                                     -a₁⋅b₁⋅sin(θ₁(t))                       \n",
+       "⎢                            ───────────────────────────────────              \n",
+       "⎢                               ________________________________              \n",
+       "⎢                              ╱   2                          2               \n",
+       "⎢                            ╲╱  a₁  + 2⋅a₁⋅b₁⋅cos(θ₁(t)) + b₁                \n",
+       "⎢                                                                             \n",
+       "⎢                                      a₂⋅b₂⋅sin(θ₁(t))                       \n",
+       "⎢                            ───────────────────────────────────              \n",
+       "⎢                               ________________________________              \n",
+       "⎢                              ╱   2                          2               \n",
+       "⎢                            ╲╱  a₂  - 2⋅a₂⋅b₂⋅cos(θ₁(t)) + b₂                \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                             0                               \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                             0                               \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                        -a₅⋅(L₁⋅sin(θ₁(t)) + b₅⋅sin(θ₁(t) + θ₂(t)))          \n",
+       "⎢─────────────────────────────────────────────────────────────────────────────\n",
+       "⎢   __________________________________________________________________________\n",
+       "⎢  ╱   2                                               2                      \n",
+       "⎢╲╱  L₁  + 2⋅L₁⋅a₅⋅cos(θ₁(t)) + 2⋅L₁⋅b₅⋅cos(θ₂(t)) + a₅  + 2⋅a₅⋅b₅⋅cos(θ₁(t) +\n",
+       "⎢                                                                             \n",
+       "⎢                         a₆⋅(L₁⋅sin(θ₁(t)) - b₆⋅sin(θ₁(t) + θ₂(t)))          \n",
+       "⎢─────────────────────────────────────────────────────────────────────────────\n",
+       "⎢   __________________________________________________________________________\n",
+       "⎢  ╱   2                                               2                      \n",
+       "⎢╲╱  L₁  - 2⋅L₁⋅a₆⋅cos(θ₁(t)) - 2⋅L₁⋅b₆⋅cos(θ₂(t)) + a₆  + 2⋅a₆⋅b₆⋅cos(θ₁(t) +\n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                             0                               \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                             0                               \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎢                                             0                               \n",
+       "⎢                                                                             \n",
+       "⎢                                                                             \n",
+       "⎣                                                                             \n",
+       "\n",
+       "                                                                              \n",
+       "                                                                         0    \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                         0    \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                           -b₃⋅(2⋅L₁ - 2⋅a₃)⋅s\n",
+       "                                               ───────────────────────────────\n",
+       "                                                    __________________________\n",
+       "                                                   ╱   2                      \n",
+       "                                               2⋅╲╱  b₃  + b₃⋅(2⋅L₁ - 2⋅a₃)⋅co\n",
+       "                                                                              \n",
+       "                                                            b₄⋅(2⋅L₁ - 2⋅a₄)⋅s\n",
+       "                                               ───────────────────────────────\n",
+       "                                                    __________________________\n",
+       "                                                   ╱   2                      \n",
+       "                                               2⋅╲╱  b₄  - b₄⋅(2⋅L₁ - 2⋅a₄)⋅co\n",
+       "                                                                              \n",
+       "                                                    -b₅⋅(L₁⋅sin(θ₂(t)) + a₅⋅si\n",
+       "──────────────              ──────────────────────────────────────────────────\n",
+       "______________                 _______________________________________________\n",
+       "            2                 ╱   2                                           \n",
+       " θ₂(t)) + b₅                ╲╱  L₁  + 2⋅L₁⋅a₅⋅cos(θ₁(t)) + 2⋅L₁⋅b₅⋅cos(θ₂(t)) \n",
+       "                                                                              \n",
+       "                                                     b₆⋅(L₁⋅sin(θ₂(t)) - a₆⋅si\n",
+       "──────────────              ──────────────────────────────────────────────────\n",
+       "______________                 _______________________________________________\n",
+       "            2                 ╱   2                                           \n",
+       " θ₂(t)) + b₆                ╲╱  L₁  - 2⋅L₁⋅a₆⋅cos(θ₁(t)) - 2⋅L₁⋅b₆⋅cos(θ₂(t)) \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                         0    \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                         0    \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                          L₂⋅(2⋅L₁ - 2⋅a₉)⋅sin(θ₂(t))   b₉⋅(2⋅\n",
+       "                                        - ─────────────────────────── - ──────\n",
+       "                                                       2                      \n",
+       "                ──────────────────────────────────────────────────────────────\n",
+       "                   ___________________________________________________________\n",
+       "                  ╱   2                                                       \n",
+       "                ╲╱  L₂  + 2⋅L₂⋅b₉⋅cos(θ₃(t)) + L₂⋅(2⋅L₁ - 2⋅a₉)⋅cos(θ₂(t)) + b\n",
+       "\n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "in(θ₂(t))                                                                     \n",
+       "──────────────────────                                                        \n",
+       "______________________                                                        \n",
+       "                    2                                                         \n",
+       "s(θ₂(t)) + (L₁ - a₃)                                                          \n",
+       "                                                                              \n",
+       "in(θ₂(t))                                                                     \n",
+       "──────────────────────                                                        \n",
+       "______________________                                                        \n",
+       "                    2                                                         \n",
+       "s(θ₂(t)) + (L₁ - a₄)                                                          \n",
+       "                                                                              \n",
+       "n(θ₁(t) + θ₂(t)))                                                             \n",
+       "─────────────────────────────────────────                                     \n",
+       "_________________________________________                                     \n",
+       "    2                                  2                                      \n",
+       "+ a₅  + 2⋅a₅⋅b₅⋅cos(θ₁(t) + θ₂(t)) + b₅                                       \n",
+       "                                                                              \n",
+       "n(θ₁(t) + θ₂(t)))                                                             \n",
+       "─────────────────────────────────────────                                     \n",
+       "_________________________________________                                     \n",
+       "    2                                  2                                      \n",
+       "+ a₆  + 2⋅a₆⋅b₆⋅cos(θ₁(t) + θ₂(t)) + b₆                                       \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "L₁ - 2⋅a₉)⋅sin(θ₂(t) + θ₃(t))                                                 \n",
+       "─────────────────────────────                                                 \n",
+       "           2                                                                  \n",
+       "──────────────────────────────────────────────────────  ──────────────────────\n",
+       "______________________________________________________     ___________________\n",
+       " 2                                                  2     ╱   2               \n",
+       "₉  + b₉⋅(2⋅L₁ - 2⋅a₉)⋅cos(θ₂(t) + θ₃(t)) + (L₁ - a₉)    ╲╱  L₂  + 2⋅L₂⋅b₉⋅cos(\n",
+       "\n",
+       "                                                                              \n",
+       "                                   0                                          \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                   0                                          \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                   0                                          \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                   0                                          \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                   0                                          \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                   0                                          \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                     -b₇⋅(2⋅L₂ - 2⋅a₇)⋅sin(θ₃(t))                             \n",
+       "         ─────────────────────────────────────────────────────                \n",
+       "              ________________________________________________                \n",
+       "             ╱   2                                          2                 \n",
+       "         2⋅╲╱  b₇  + b₇⋅(2⋅L₂ - 2⋅a₇)⋅cos(θ₃(t)) + (L₂ - a₇)                  \n",
+       "                                                                              \n",
+       "                      b₈⋅(2⋅L₂ - 2⋅a₈)⋅sin(θ₃(t))                             \n",
+       "         ─────────────────────────────────────────────────────                \n",
+       "              ________________________________________________                \n",
+       "             ╱   2                                          2                 \n",
+       "         2⋅╲╱  b₈  - b₈⋅(2⋅L₂ - 2⋅a₈)⋅cos(θ₃(t)) + (L₂ - a₈)                  \n",
+       "                                                                              \n",
+       "                            b₉⋅(2⋅L₁ - 2⋅a₉)⋅sin(θ₂(t) + θ₃(t))               \n",
+       "        -L₂⋅b₉⋅sin(θ₃(t)) - ───────────────────────────────────               \n",
+       "                                             2                                \n",
+       "──────────────────────────────────────────────────────────────────────────────\n",
+       "______________________________________________________________________________\n",
+       "                                         2                                    \n",
+       "θ₃(t)) + L₂⋅(2⋅L₁ - 2⋅a₉)⋅cos(θ₂(t)) + b₉  + b₉⋅(2⋅L₁ - 2⋅a₉)⋅cos(θ₂(t) + θ₃(t\n",
+       "\n",
+       "                ⎤\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "                ⎥\n",
+       "────────────────⎥\n",
+       "________________⎥\n",
+       "              2 ⎥\n",
+       ")) + (L₁ - a₉)  ⎦"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# assert that moment arm is correctly evaluated\n",
+    "# model.test_muscle_geometry() # slow\n",
+    "# muscle length\n",
+    "disp('l_m = ', model.lm)\n",
+    "# moment arm\n",
+    "disp('R = ', model.R)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "autoscroll": false,
+    "ein.hycell": false,
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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XOHLE57EOHTrwWhCOqH76advZYtgwtyMRkXCmBFlEpAA0bmzbkX32mR3kEWwi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\nhS5d4PBhv7xkZCSMHAmrV9t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btgDGKFLIKEEWEZGgltH6bcEC280hLNWqBTNmQJEimWtH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\nCoQTGAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<Figure size 720x720 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# draw model\n",
+    "fig, ax = subplots(1, 1, figsize=(10, 10), frameon=False)\n",
+    "model.draw_model([60, 70, 50], True, ax, 1, False)\n",
+    "fig.tight_layout()\n",
+    "fig.savefig('results/arm_model.pdf', dpi=600, format='pdf',\n",
+    "            transparent=True, pad_inches=0, bbox_inches='tight')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "ein.tags": "worksheet-0",
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "source": [
+    "[1] K. Tahara, Z. W. Luo, and S. Arimoto, “On Control Mechanism of Human-Like\n",
+    "Reaching Movements with Musculo-Skeletal Redundancy,” in International\n",
+    "Conference on Intelligent Robots and Systems, 2006, pp. 1402–1409."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.15"
+  },
+  "name": "model.ipynb"
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}