{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sm.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "mb, mc, Ib, Ic, r, l, d = sm.symbols('m_b, m_c, I_b, I_c, r, l, d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle m_{b}$"
      ],
      "text/plain": [
       "m_b"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABJElEQVQ4EZ2T3XHCQAyEDeMCqCElgNMBdEDSASkBHu1XpwOghKSDpINASnANdGC+PWTO5yjOTDSjkU4/q5XvPGnbNutLVVVbzo/o2uLf2BNak2ssFo0APC3LskXPXq4fm0ao6DFpaafPGPU9F4DSlZV/+G0x+htAYACTfzOYM+PPZvHII5mb19s/oW/xWlX4i67PW6HbP2FAk85SXeldPIBuf93/UJRLmHkAY/srlwAn38D21NRkigLk1CxZ48vqtW6GDNz9VY2Ivp7yAYBX7BdaDwHC+6cgoUmhROB7cpdwyjLZIicwwzmiD6YZsTf8BrvDdlLghGu0gK6yEYCQniw4ZjSof4XPnH98gzGA+6/M0BeBYd+TWxjrJieWR5oCEDZ88CtM9nyqAWgPMAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle I_{b}$"
      ],
      "text/plain": [
       "I_b"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle I_{b}^{2} + r$"
      ],
      "text/plain": [
       "   2    \n",
       "I_b  + r"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r+Ib**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHkAAAAVCAYAAABizEFoAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAFSklEQVRoBe2Z63EUORCA1y4HYLgM7Ax4RHAmAwMRGGcAxT//o3AGQAR3kAEmAsAZwEXAsRn4vk+nntNoZ3Z3Zh9nyu4qufXobrX6Jc165+rqajIWzs7ODuD9NpZ/KB/77Qzl+VXps22PwG+HnAH6Y+gvwd+Db2dFJ79H0BsEXoTAm4A5r8H9lfaC/iAnLGMfZO5D9x78aBn6mgY+/aJuydG7NcGyYwR40APwjXJwto9OsB3m8brRJwSeriD0BF4dnWB0JuPcN0j4CP6QZV0rhF6WLYPw/FoptkAZ9H0GyX3wKk6ewP8aOT/A53sL9uxchtEo9r5YSZFO4beTLzDBqDJdme4V479o45wM40uaytxIILi9qgz0Cf3LdRkhy1Vm82gaKxsZU+XQjgZnMkwe7hjcOFlBzBl9Hj7mLZfCQ9pnaM5p9+g/pf3I89fy0Zb19Ewa+y7NMz9l3jLqGb2qXPeqekybZJ53dF3/kxY0dP+zgYM5oM063zjIdz/tpz29cx/kMSjt33UtKevxXqIY9scstt6X8AglfM19ZNLDeVenTcEa6CcYlJ72KQgYeyAfB3dcEJjzIEk2/ftpcst/2Fd9X4NbJZNxuprAOt7z+rpugLEZbRD4Samjj+iHDRx/Y/yBNi9L3bN5MNEvobSxD7NXyqdpcx3e5WR1Od3lz9KAwMji5rOBOaPrcxbiYe66eSHUTBB+Y76M0siQf1f5m9el+dJMbr+jwR6gi2ctweAt4e9yUPR1ovyNDeiHYw3ieaD9ZuTCX9vYMhwPXpPi9x6hytofmsm+/OosdkM/vjWKSrYygLEKCj4ESpCudHqsaYiaNtZmMPuqT5fx1MeA83qoQZ1Tma0XmL+gaRyrj/qZKWZg47Sap2McTq2X6sCp1w38aT3JuLZxqirSZR07WNKUehw0ToY4GWoB0ynrrW9DxqFUH7/OVMmgC4Wk73KmQXEZRIswcuMN0CJl3utg7CeUV4XXkjoaRJbvt7TGuMzNg5lsnEe8aI19w3Z9Np4rIpVrhDyHyrugztKGOdPUJatZp6Mzu5yjYlFaEj2ynNuPecb2J+DIeh92z2n+6pPWXN8GsJ/VaAL2jeEd60+pOvcZ/WRk1zcEBse88/bZuE8dK8P3XRT3UN6xZtW9OQcxi+eVrCfwt8ov9CqsfEteCZbK9Ptq3j+MJ7bEmDXu5V3fG3isbQLU12upAXTRPgZqCoBmYf0dz65j+mDGxn2EeV59pzo5Smk8pmbKHzQeujeLWVeYDq2dmZzHesv50Pm4iTmDJzLdSPWzagoWxNJuG16ig+cpwXHoHPM1TcyPxVbCzq8K9Akb/zFAuLIu9oJBw9J0tGXJu6x8POj4zs0zvwoYLLURnI/gyaQJWTX8JKiDR4eWmeuepR6JeQt/1PkJ+unEKc13iPeyZ/RKift6wthr7oTmWet5z+m85V4weB7SOh99rJskfckUNu66EpXdBdrzpPXbNZsryG+r5pHBnI44BM9kOPNrBfbw/553wBp2Av4JOgFHpju9FMBzDOHYh9dSe2yCCL21vwmwUnDDb4B+BR/ulopmwRrUbJZI0LlG5DagORj7G1xfwIMdnBW1qnRVkW2cY5U9rGTrSCirSqoKrUxWM4xqOfLXnHj4GFVRbiTZGOS9VS45m/E6DrsxfTclmHNbtn2rNEE/ZC/4TNBP4HTFNndyCGHBV69130zy4dT3a0qwrA3nffvuq7Xt8wsI0gbe9T5Ex4C8jR1b5bqQZnk2GiyX02L+trsFC2Sbm8km2iDIPK0qMFOuQyLEK5WMkHOL/38L/AM1uw7HyG4PlAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\sqrt{m_{b}} + \\sin{\\left(r \\right)}$"
      ],
      "text/plain": [
       "  _____         \n",
       "╲╱ m_b  + sin(r)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.sin(r) + sm.sqrt(mb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = sm.symbols('t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\theta{\\left(t \\right)}$"
      ],
      "text/plain": [
       "θ(t)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = sm.Function('theta')(t)\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\omega{\\left(t \\right)}$"
      ],
      "text/plain": [
       "ω(t)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "omega = sm.Function('omega')(t)\n",
    "omega"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\theta{\\left(t \\right)}$"
      ],
      "text/plain": [
       "d       \n",
       "──(θ(t))\n",
       "dt      "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.diff(theta, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\theta{\\left(t \\right)} \\cos{\\left(\\frac{\\theta^{2}{\\left(t \\right)}}{2} \\right)} \\frac{d}{d t} \\theta{\\left(t \\right)} + 2 \\theta{\\left(t \\right)} \\frac{d}{d t} \\theta{\\left(t \\right)}$"
      ],
      "text/plain": [
       "        ⎛ 2   ⎞                           \n",
       "        ⎜θ (t)⎟ d                 d       \n",
       "θ(t)⋅cos⎜─────⎟⋅──(θ(t)) + 2⋅θ(t)⋅──(θ(t))\n",
       "        ⎝  2  ⎠ dt                dt      "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.diff(theta**2+sm.sin(theta**2/2), t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIMAAAAaCAYAAACU9O/tAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAEKElEQVRoBe2a7U0cMRCGAVHAJSVAB0A6gA5IUkGgg6D84x+CDkg6IHQAqSCIDkIHieiAvI/jsfZ83o/syt5ldSMZ39pezzsfOzO22Hx5edmYE52fn19LnpM5yVRKlu1SjErwkSPsiM+O+s0S/ObGY2tmAl1KHtqaemhgNs5QiQr3PfSwfkUamFOaOJM8tFFIzkhEWqiRqp7UzjT2rH4y1IZxFs4gITHCgfrTMTTvlXytHifYUP9d3Q+1fZ6nQF0wziVNfJHCL0ZU+nHEGyx7MgBRYirUijFEBgH/LNR8WQiwr+fHqUjRhEM4iQqH6oukCPHZEz9SwoHajZ4tGqE3FxnUW3qojmk4PwlPkx2reFYwVp3hShuxgHD3KhzBq5aowN1CEfK6OVLPBc0dTPV7N2KOw0AP/7pyf4UlaccuGIMzeLjkuNdWjR8nBM2qffE79AzqdEXk6F1Aan9COvclVz0F6WLHFYxbEbMPenbeHo1P8lHKIiQiVGk6EsMn8bdQG/hrDDz3AwwZ9hrwo9GOdRhDZNAC8skCQQaAKP3qqXDHIboEBiLDip6EhWvwhXqrI0pgWeLRZscmjMEZtKMLfVo8er0gDCh05aurSq15okL2WkF8+EgoTsHzWw0noCbgxBBI69DfrnrnCP75j/rS+qy1YxvGqjMQ+la8PUhb4IfAonjS1K1a2+kge1TwyuPOgNOV3SFYGg260pydMC70245wOMV7tdKUtGMXjFVnwKOWvL2kFAILf5wBpRNua51Ba5nHYbKReJAycQQKQTsywo/fjxqrRi4umGw9axxFa2w4d19nx1aMzhkEGs9GmFYFay3r2Ph/6JPeawyXmndfmnqUfaf+RO1rDRMcpfF2T+8OxUkhyB43EQaUvaQn8XoTren0qPfgwX4xwfet5j/GE3qmcE1GHI3X2lFzrRidM4gBgJ71QvULSOBwZ+pnTTQaIvlix0FhoBIHBwZfcQbNEYZv1YOjlvz8EJxU5GAJfPQbI1kqq+XddUL7JaOfxvseLTvbMYVxyw+GPOMFTq0tOUZhyDk79dVwyZQ1nXkdYPg4mjk8mg/1QkmldOA1yI7mDAhphRHKHpssIrjK3MDICHwxD+rD12pzmfqf0b6EbecgYFEjSkyJBtnRnAGByEV8DRyfRiVvbBwiVjiOmv2SyfPn6w/G1hhFKznZUuk7jdlvDU+Gettx24tgxyDu3JN5bARRMToGABsVPV6PoKUMQJH2Tfy4z4BwDsLwpR+zSMrcVGiQHZ0zSDgLy1MRakOYMDwGsGMmTrqUNnKCFW9SUapqT43lhNJ5b2EeZEeLDJ0ZFl5IdOCYyXm/02mnML5c7EYpUDen/q/ycoRf0ji5+9X8j0UuD8m9b7WAzM2r7/4cMznvx8e8vvut36vRwOQjQw3u9XAGDfwFi/SiapVKKVgAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle l - \\sqrt{- d^{2} + l^{2}}$"
      ],
      "text/plain": [
       "       ___________\n",
       "      ╱    2    2 \n",
       "l - ╲╱  - d  + l  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h = l - sm.sqrt(l**2 - d**2)\n",
    "h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}