4080 Rigid Boddy Pendulum.ipynb

{
 "cells": [
  {
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   },
   "cell_type": "markdown",
   "id": "440d166c",
   "metadata": {
    "tags": []
   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "04a5d40f",
   "metadata": {},
   "source": [
    "![dedic.png](attachment:c9fff4c9-2c42-4f2f-9214-9bfc1d497739.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d63081bd-fe79-4f73-b676-7fe40a29086a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *\n",
    "from lib_Mechanics import *"
   ]
  },
  {
   "attachments": {
    "6f6601a8-9505-41c7-9fa0-3ec791e1b098.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "09e9954b-06a9-46f5-a077-51e0e57699ad",
   "metadata": {},
   "source": [
    "![image.png](attachment:6f6601a8-9505-41c7-9fa0-3ec791e1b098.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "3bbf5a54-9ebf-44aa-961d-7d135ae2d74c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "P=phybody(r=L*sin(alpha))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "8bd7bf39-fc38-4772-8987-9b85abfc793a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "P.add_weight()\n",
    "P.add_forza(T,pi/2-alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "caccb0bc-4d3d-4da9-8bda-6a916fb6101e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Fy =T \\cos{\\left(\\alpha \\right)} - g m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Fy=P.Fy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e1628511-7077-4c72-af61-c269cc451099",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T =\\frac{g m}{\\cos{\\left(\\alpha \\right)}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T=Fy.solve('T')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "aca90c24-743b-48ea-96b1-69e522f1e0db",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "P.set(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "85f89c22-105b-4063-83be-7b124a355081",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Fx =\\frac{g m \\sin{\\left(\\alpha \\right)}}{\\cos{\\left(\\alpha \\right)}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Fc=P.Fx()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "3cffb654-8df1-4221-a6d9-88c80064e0a6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{g m \\sin{\\left(\\alpha \\right)}}{\\cos{\\left(\\alpha \\right)}} = \\frac{m v^{2}}{L \\sin{\\left(\\alpha \\right)}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MQ(Fc,m*P.v*P.v/P.r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "0985594a-9ee7-417d-a59d-10d14167b7bc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{g}{\\cos{\\left(\\alpha \\right)}} = \\frac{v^{2}}{L \\sin^{2}{\\left(\\alpha \\right)}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "92fc6bfb-7866-47d3-9f9d-60a5d6e4a303",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle v=\\sqrt{\\frac{L g}{\\cos{\\left(\\alpha \\right)}}} \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v=Q.solve(v,'positive')"
   ]
  },
  {
   "attachments": {
    "baddecb4-e838-40d2-b5f0-cf399d0f02ce.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "7223d0a6-ac7b-4c9d-98d9-2a59c1c0ccff",
   "metadata": {
    "tags": []
   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "6553122f-2a4d-4627-aa95-a958d52786f9",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *\n",
    "from lib_Mechanics import *"
   ]
  },
  {
   "attachments": {
    "f90d56f6-96fc-47fb-a911-2dfe12cbe0c8.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "adb0c02c-895f-4cc0-8fc6-07c83092fcb7",
   "metadata": {},
   "source": [
    "![image.png](attachment:f90d56f6-96fc-47fb-a911-2dfe12cbe0c8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "a57b285e-43b1-4b6f-9b37-b5866d70a031",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "P=phybody()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "774d12c5-9454-45a1-bbcb-085b335e2aa7",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "P.add_weight()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "4f2bd153-1581-4cd9-90ae-1e1b2f5187e2",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "P.add_forza(T,pi/2+tetha2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "f86e8866-4a54-4af2-8278-90ff2956e539",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T - g m \\cos{\\left(𝜃_{2} \\right)} = \\frac{m v^{2}}{L}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1=MQ(P.fyrelative(tetha2),v*v*m/L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "2f2731d2-f9d1-43cb-8158-bc676d48d2bd",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGQAAAAVCAYAAACwnEswAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAABJ0AAASdAHeZh94AAAGE0lEQVR4nO3Zf8zXVRUH8NfjD8DQheLM5hIqAmU2AxKogImJrjVLa9XKYeimFi7rHy025/GIqG2lWcvSaQsoJ1vMWPiDBmk/TPNXjrHILBOZUzJ/JRkR+PTHvV/48OXzPPA885nZeG/f3X3Ouefec++558e9357e3l778L+D/d5oBfZhVxzwRiswUGTmWPwViyNi3hDNsRgfwTsj4p9DMP4UPIRzI+KmJm+fh3QhM0/AXFw9FMaAiHgYP8XCzDy4yXvTeQiexrF4eYjGX4R/4HttzMw8FgvxAiZgQUT8dhDzXIXf4UJc2SH27EvqO5GZ4/FH3BQR57Xw34+f49MRsTozL8TFSmj7zyDmW4+3VPnXaPGQzByBr+AsvAubcAO+jpfwZES8t/adjV/gm7gFl2IW9q/0L0bEs5k5EZfgZAzHrzE/Ip7qmvtj+DIm4jA8j8exLCKur33GaskhTTouw9V1voOxDpdFxMo97NE56MGyln05DLdjaUSsruQ/4ShMw2/2MHYbbq26zsEqunJIZo7E3Yo7vYrr6vel+KGyuEcaIpNrO74qtB034ymcjh9k5ml4oMourov4KJZ0zX0eVijG+Jli5DtwEM4ewCLH1PnGYqmyucdhRT1A/eHkuob7W3iLcIhGeFGMRzHKYHBvbed0CN0ecgOmKwa4IiJ6ITOXonMq2gwyFdMjYm3tf7lilFMwCXMi4r7KG4Y/Y1ZmjoiILXWM87EVx0fE35pKZebhA1jkiYo3ZEP+FtyFi5QDthvqYXwf1ncn88w8QjkUSyNiU4P17tpuHoB+TTxY21kdwg4PyczpOBMrImJhxxgQEWuUDabdIPM6xqj9X8GTSui6qGOMytuKx5TTNbJLwW3YLRZHxN/3bn1gA67okl9V9Z/aj9xRVd9nWnhzlVD7ky56Z/0bB6BfU6+XsQVHd2hND7mgtov6kH8e78Cj7DhR4/FERNzV0n+MUonsFo8r75WIeL5B+7ESpv6Qmbfil7g3Ip7rf1m74dGI2N5C34gP9CM3urYvtvDOUA7LJZm5oEGfpuzLOqi8TyjV17+V0LcgItb1M+8LeFvno5lDTqmDP9SH4NvxeD39cHyVX93dsSbYQ3FPd/VR6+5xqmE7iIhr8HnlhF+I27ApM++u1c3e4qU+6Nv0f+/6V21HdOk7DCdgTUTMjIgTI+JEzK997+xUSEq4vB4fxEl1ztW1IOgLBzXmLh5SK6sjlNO1Wx2cmcfgSNzTIHfc9eGWSab0w5ukhKtHuhkRsQRLMnNUXdQZSuWzKjOPGYS3DASdvDW6iz4Ow5Q7QxOfqe13OoSIOLXZITPnKvelDymFii7+fhilVIfYGbK219+hfSh7cW3b8kebR03phzepZaxdEBEvKRXWHVXpc5TEt7wvmdcBz+A5Jdw0Maq2O5J5Zh6AeVgVEQ/0M+Yhile2hUF1rh6NaLEf1LDyGMZk5oebEpl5gZ1lZ7dBtqrxswv9eUjHkLsYJDNnZ2ZPS/8javtqC+91Q40Mv8LhmTmuwerkuWZeOlfZ7PP3MOx1ymbf1wd/em13VH7NpH6VUrffnpnL8Cxm4D3K7XWCuomZOVy5L6ytVVM3pmBDV9LuYLISM9d30W/D5sy8X6nQejBTid8Pa8lVQ4Dl+CROVUpz+ItSoXUuw0crl9wzI2JDXwNl5jXK/s3oo8ig5O3tyv0LjSQXET9SkunT+Gz9PapsSCe/dFzvOByoxQMyc4wSh9t4w5V3qLUtSn5NqcsnKwnz7DrHVzF7ME8Tg8ByJZec1SFExDZ8DlMz80Z8C5+KiDv7GiQzr1X276SIeKKPPm9VLs8rI2JH2bzHt6yamJYo94lv7NWy3sSopeuVmBwRvx+E/HVKwp8dEd1RoNnvS/g2ZkbEjmeXTpW1P0a33JBPVl49N+L7A1XuTYpr8QVcjtMGIpiZ31Uukafjxcw8srI2R8TmRr+DsADLm8ZgZw6ZiAczc5USMw9UnhFmKJXHx5sD/j8jIrbUqDA7M0cO8D+R+bVd00VP5RGxg7G4UXkf3AU9vb29MnOCktSnKfH/NaU2Xolrut5v9mEI8V9oTi85ieQhewAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle g m \\sin{\\left(𝜃_{2} \\right)}$"
      ],
      "text/plain": [
       "g⋅m⋅sin(𝜃₂)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P.fxrelative(tetha2+pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "9ccedef3-2964-4ce4-acf3-f6846673b3f4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle g m \\sin{\\left(𝜃_{2} \\right)} = a_{t} m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q2=MQ(P.fxrelative(tetha2+pi),m*at)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "dfa9e20e-b7ae-43d7-8c8b-7624007923ac",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle g \\sin{\\left(𝜃_{2} \\right)} = a_{t}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q2.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "33723e34-b73e-4ec3-9af1-0a56af4e8f66",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a_{t} = g \\sin{\\left(𝜃_{2} \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q2.swap()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "9aeb4e66-3495-4fcc-865c-513f257b6ab1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle v = L g \\sin{\\left(\\theta \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q3=MQ(v,g*sin(tetha)*L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "8ad9b895-df0d-4b60-bd81-d815c29b047b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int v\\, dv = \\int\\limits_{𝜃_{2}}^{𝜃_{1}} L g \\sin{\\left(\\theta \\right)}\\, d\\theta$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q3.integral(v,tetha,'',[tetha2,tetha1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "8948dfce-0eb6-4479-b426-98457569a8bf",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{v^{2}}{2} = - L g \\cos{\\left(𝜃_{1} \\right)} + L g \\cos{\\left(𝜃_{2} \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q3.doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "bbf6f202-cfcd-4640-95fb-9e761531b0a3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle v =- \\sqrt{2} \\sqrt{- L g \\left(\\cos{\\left(𝜃_{1} \\right)} - \\cos{\\left(𝜃_{2} \\right)}\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v=Q3.solve('v','pos')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "39c63e39-4699-44f3-a818-1bbe2b714c60",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T - g m \\cos{\\left(𝜃_{2} \\right)} = - 2 g m \\left(\\cos{\\left(𝜃_{1} \\right)} - \\cos{\\left(𝜃_{2} \\right)}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1.set(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "83692963-85a3-41be-8c20-34dd18859a27",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T =g m \\left(- 2 \\cos{\\left(𝜃_{1} \\right)} + 3 \\cos{\\left(𝜃_{2} \\right)}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T=Q1.solve('T')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "ff942f50-97b4-4bda-bcfd-e88b64a5df42",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T - g m \\cos{\\left(𝜃_{2} \\right)} = a_{n} m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q4=MQ(P.fyrelative(tetha2),an*m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "e6118ae3-86fe-48f2-aca3-bf88551cdaf5",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle g m \\left(- 2 \\cos{\\left(𝜃_{1} \\right)} + 3 \\cos{\\left(𝜃_{2} \\right)}\\right) - g m \\cos{\\left(𝜃_{2} \\right)} = a_{n} m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q4.set(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "3d580459-c331-474f-bf13-2c5ce4dcf070",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a_{n} = 2 g \\left(- \\cos{\\left(𝜃_{1} \\right)} + \\cos{\\left(𝜃_{2} \\right)}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q4.alone(an)"
   ]
  },
  {
   "attachments": {
    "baddecb4-e838-40d2-b5f0-cf399d0f02ce.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "93731799-b1a3-47ea-b3b9-e22b2f940592",
   "metadata": {
    "tags": []
   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "66791010-e0e5-48d2-a375-697832b175b3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *\n",
    "from lib_Mechanics import *"
   ]
  },
  {
   "attachments": {
    "98b68228-379f-481d-9846-8f3e2f48d514.png": {
     "image/png": 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q129gEITr16+jdu3assND6tSpESZMGIPP2HoCEzlbI877GYsAEzljEdPJfCZyOjGkRq/BRE6jhrHWsXx9AT8/nDl/Hldv3oCbWz3lnd6+fYP06dNj167d8v//yYOnvKCFJzKRszCgvJzFEWAiZ3FIHWNBJnKOYSdHPSUTOUe1nGnn9unUFQHT58GvRUO4TpmIcOHCKS9E/xa9evVS5suNGzceBQsWVH7WFhOZyNkCZd7DHASYyJmDngM/y0TOgY3nAEdnIucARrLgEX2atUTA4nlwadAUYRbPN2nlK1euYMiQwWjQoAEqVKho0hrWeIiJnDVQ5TUtiQATOUui6UBrMZFzIGM54FGZyDmg0Yw5sr8/vtUS4dPXb74/deg/oHoRhB7QG66ZMxuz0k9zvb29sWLFcumVq1mzlsnrWPJBJnKWRJPXsgYCTOSsgaoDrMlEzgGM5MBHZCLnwMYL4egBN2/Cd8gICIVfBCxf/NNMl179EGbkMLMvTl0g9u/fL/PltNABgomc2SblBayMABM5KwOs1eWZyGnVMvo4FxM5fdgx8Bb+x4/Db/M24MHD3wicnFOyAkL17opQxYpZ5OJ79uzGsWPHNNEBgomcRUzKi1gRASZyVgRXy0szkdOydbRxtmXLluL9+/cmHebMGWrFdAQdOnQw6fnAh7JnzyG7AvCwLwJ+Bw7A33MVAp4+A7Zv/O0wrlNnIHS7NhY9JHWA2LdvH3Lnzo1q1apbdG1jFmMiZwxaPNceCDCRswfqGtiTiZwGjGDnI3h5eeHp0yd/PAWRsIcPH9r1lLVq1RJSFn9usE5CsgkT/mXXMzrT5uSZ8y1Y4OcrpxdivmMGI1R5y3VouHDhgojeBoj2Xm+kxlzNmjVQqlRpu0DNRM4usPOmRiDARM4IsPQ0lYmcnqwZ8l2o1+X16zd+m9SzZw/8888/IT5MeUoRI0Y0Gqx3797hxYuXSJ48mdHPBj7w6NEj0H8hjeHDR6BkyZI/TQkfPjwyZcpk8r78YPAIBLx+Bb91G+Hfyh1ImQ24cVZODLV+I0JVqWwx2G6KPLz58+fBXxRUuLu3kF7h/v37iYrWociaNStChw5tsb1UFmIip4ISz7EnAkzk7Im+HfdmImdH8K289cuXL/D169egXXbs2IGWLVsGu2vcuHERIUKEP55owYIFoPCmsWP9+nWYN28etm/fYeyjQfNJimLDhg1/fP7169cgwvjrSJ06jQjJ7f3pr6lhuymE1OTD6+3Bjx/hu2w5/Nu2kiQu7KUT+BY2rrilH0JtX41QZSzjLXvx4jl69+6NHDlyyJZdx4UHcNy4cfgo9i9TpgzWr9+AVKlS2bQDBBM5vb3M+rsPEzn92VTpRkzklGByyEnlypXF7t27lc4+fvwENG/eXGmuMZMsQeQM7VdehPLog15lLFy4EI0aNVaZynOCQcB3yjT4d+0EpM2JsBdPyC4ORORCe++Ca86cFsOsZMkSaNq0aVB7rx+LZr58+YKUKVPILweZzZA4MfawTOSMRYzn2xoBJnK2Rlwj+zGR04ghzDwG5bnVq/dzDhnlFb19+/anlSkk5em5/LfdokePJjxVkcw8xe+P24LIffc8fvtp8xMnvCUR+HXEjx//p24DWbJkEd6+35P2LQ6EDhb0GTEKAQP7AUVKI8zKJXARXlwaAY8fwyV2bAj3mMVuSR65SJEiSy9cQIA/evbsJbxxHxA7dhyZM0c5nfXq1cOAAQNQrFhxi+0b0kJM5GwCM29iBgJM5MwAz5EfZSLnyNaDIGXLMGPGDBlyosTwX0ePHj1QtmzZoL8mspY2bVqbXdoWRC64y7x//07kA17/6Ue9evXCqVOnfvq7WLFiCe9OShm+27x5M2LEiGkzbH7diGQ2qEL43LlzUjutXbv2yJAhg/zzxo0bEC9ePFStWhVJkiTF58+fcebMGemJTJo0idVFc30GDEbAyJlAxcIIPX4UXEVY0xajR4/uwunnh4kTJ/22Hb3v48ePQ/Xq1VG5chWrH4eJnNUh5g3MRICJnJkAOurjTOQcz3L9+vXF5cuX5cFv376Df/89L/93okSJMHr06J8ulDlzFiROnNhul7QXkQvuwl5ex/Hy5cugH504cQJTp06Vf6bCiGJC+yxs2LDyz61bt0bp0mVsituzZ0+lAO7SpUtlgv+kSZMlwYwWLSomT56MA0L6g/LGChcuDCIV1P2AchcpD3L+/PmIGTOW/HtLD59+AxEwWrTbqlkUofv0gKvw6tpiTJgwQRY70BeR4IgcnYHI74YN60FVy7Vr17HqsayBrVUPzIs7HQJM5JzO5N8vzERO+4Z//PgRhg37n1L+zp07cffu3aCDU0K4m1s9RIkS2eofZsaipSUi9+vZb926JcnRa1GFOWKE6FLwwyhevLhMpqeRMWNGtG3bztirmzT/wIH9srCDCjKaNGmKyJEjIUGChKLnaHnpTaRzVqpUCVGjRsOWLZsxaNAgGYLcunWLlF+xNNnwGTgEASPmALVLIHS3ThbNgwsJoIkTJwqSOl9+YcmWLZvUkEuePAW6d+/+22P79++TVddp0qSRvwfWGpbG1lrn5HWdFwEmck5qeyZy2jX8+fPnZbiP8oWmT5/+00Hpw5w+uGhQqLRGjZqavIiWiVwgYG/fvvkJX8L82rVrQXhSeLNWrdqCVEVG586dLU6WAjfy9fUVYfLpMmRKUipZsmSVZPLz509SboO8hkTcqGozXLjw8PDwAIUeiejs339AEPkoljubjw98JkxCQD/h4a1eFqF7d4Or+MJgq0GeuOnTZyBu3DhBQtDkWW7RIviqa+oAcfToURmStpZnjomcrazP+5iKABM5U5Fz8OeYyGnPgJT3dOnSRVABA4XOaNCHdIUKFYK0sxo1aiTCSbm1d/hfTuQIRO5XECnn8MqV76Fr0jILrIgliRbyjNIHeuXKlREnzvdkf0sNKtoYOHCg1Ppr374dcooqUEruJ68UeeQofNi1azfpnSJyP3PmTCxatAjlypUTEi8i9Gmp8e4tfJd4wr9Te6BcFYQeNRSudtDja9CgviSzlOepMsgzR97qAgUKoEqVqvKRFSuWCwHhUhJHcwcTOXMR5OetjQATOWsjrNH1mchpxzBEGEi0lzwtmzZtkgdLkCCBDO1RqG327NnCK/NnrTft3OR/J3FEIvcjjrt27ZT5Z+/ffxDE+n8SJxT6S506tSxG+PvvJBaBnpL3R44cIfP4qDCjePES+PTpkwyhdurUCQ0bNhS5e22QIkUK6bWbNm2qJHlDhw61WD6fFPtduwH+rVsA+YohzLL5cEma1CL3M2YRyv8j8V/KU1QlcrQ+5cx5eMwVXrnacrsWLVrIqmQiweYOJnLmIsjPWxsBJnLWRlij6zORs69hKJx26dIlmavYvHkznD37XSU/YcKE0ouQLVtWkeg+xb6HNGN3RydygVe/cuUKWrUSIrhi3L59K6j3LBUfUCgvZswYoqjkbzOQghC5XSeLL5IkSYJRo0bJnDfy0vXp0xfr1q2VBQ+B+XGrV6/ClClTZLiXBJepktXsIb5E+BKJo44NaXIgrJcQUxa5ePYYpCNHeaD9+vWTuYLGDCpiyZcvb9Aj1NqrQoWKIq8wqjHL/DaXiZxZ8PHDNkCAiZwNQNbiFkzk7GOVb9++iW4Eb/Hs2XORA5Rbel5okBwGVU6SBlqPHj3tczgL7qoXIvcjJEWKFMbz58+l5EtgR4m6detKYkVto6h7hLGDqlSbNm0icyLd3d2Fftp4Se7v3Lkt5VGoInXPnj0yV472HTp0iPTQUr7c6tVr5FyziIaQM/FdtAT+7UXD+9TZEfbyzzItxt7H3Pm/CgKrrke/V4cOHfxJcoeeXb9+fVC4VXWtX+eZha+pm/JzjIARCDCRMwIsPU1lImcfa27fvg0NGjSQH8A/tpci7wp5XUh2IlQo2/aStAYSeiRyPj7fpN2IbG/fvl3CRoUI4cKFk6TrxImTRkP58OEDdOzYUT7XuXMXFCpUSGrFkbBx+fLlRe7cIDRr1lTm5ZFHcNSo0bh48aKY20noqNWQXwTIO2cq2fAVhQ3+PbsBWfIJT9wBiG8TRt/Bkg+YSuQ2bdqIxo0bB3lMA8/ERM6S1uG1tIoAEzmtWsbK52IiZ2WAf1l+8uRJmDNnjvyQvn//ftBPiRCQzARV6Vmjw4Jtb/m/3fRI5AJv9+zZM0mg5s3zkKLMNCh8R90jaFDivWrI8+TJkzInLFmy5FJigwghhVXXrVuHbt26CaHgZShRoqQka1SdOXHiBCmU2759e5AXKlas2LIIwhQi5zNkOAKGDgfE+mEWzYWLCOv/OkhceebMGfJONP7++28hhTJSFmT8Ok6fPi2KMBZi796f+9zSn//6K5HSq2gqkSN7UNeHJ0+eomDBAkF7UcXr8OHDxZenhkr7BzfJFGxN3owfZARMQICJnAmg6eERJnK2sWLPnj2Ed+UEHj58CNIvo0HyIZT3RIMkJEhSQm9Dz0Qu0FYPHjzAgwf3cfr0GUnGAgcRK/LS9e/fX8iJlArRtCS3QWSQQqU9e/aUHSbu3r2DMWPGSIHgo0ePIV26dLJJ/D//HBJEbqL05LZt2xaZMmWWRTGm5IB9F/udC1QpgtAjh8D1D10/6IvHvXv3cPLkCdFlYpMotjiNNm3aBluI8P79e9llhCpG6QtKnz59xLueVhYcEB6GBrWaIxFgqsZdtWqVFEfu2FH0dzViELml3zcabdu2kd5LkvChM5s6mMiZihw/ZysEmMjZCmmN7cNEznoGIY9JmzZtZC4cfagEivhSBwGqQIwWLZqsTNTzcAYiF2i/p0+fiqrJozKHrW/fvkHhvfz58wtP1F8yRNqoUeNgzU26dTdv3hDdORJLwka5doFt1+7duytITXkh/BtJetxIeuTKlauio8MXqTMXN248Gdo1dgR1bKhdHKF7doWr+DJhaFDRBzWw37p1qyRlnp6e8syUCvDjoDMeOnRIkNvTkuwZ0/osY8YM0qsZW/RvzZAho0w1oNxAUwdpzL1+/RrZs+eQnk5TBxM5U5Hj52yFABM5WyGtsX2YyFneIJSgTonv5ElYvnw5Xr16JTepVq26DEWlS5fWZo2+LX8741Z0JiIXiAwRrEWLFsvQJ4UYA3u+kkcqX758okNBcnTo8D0fzl7DZ/AwBAwTvVNrlzSqYwOFdSlESnmCpGE3adIkQbQq/0YkyZtIgtb0ZaVIkaJGXZMwe/PmjXymYMFCwYZvjVrQQpOZyFkISF7GaggwkbMatNpemImc5exD3od9+/aJ3Ld7Uqw1cLi5uYkk9TioWLGiQ4j4Wg6R75IaVMCxffsOSy7rMGvR3el9IH0zarFFg/TnmjZtJr1u7dq1Uwo3WuzCX77Ad9oM+PceCFSthND9esI1e3al5X1Et4d9+/YKuZzLMkxK6QLkOaOQcPz4CeDq6hq0DnnBqG0WeaRJRkUPg4mcHqyo7zswkdO3ff94OyZyljE86b9NnToFS5YskQvGjBlTtlmi0bdvP6kN5ozD2YlcoM0pHLl//36RS/dAkjoalNNGOXB16tQRnqvo1n89RCsyX8+V8O8g8sRKVUToiWPgmj6d8r5UfHHu3DkR0v0qczpJ/mT8+PFCsHgL8ubNJ0WradDP16xZjSNHjsocUFPCvsqHsuFEJnI2BJu3MgkBJnImweb4DzGRM9+GJOhLivwrVqyQSedUxEC6X9QRwNkHE7mf34CDBw/IsPvnz1/g7e0lf0heu6pVqxqVR2bsexXw6iX81m383rEhZyGEWbsMLqKS05hBBQwkk0KVtfTFhDzQderUlkSUOk9QrhyRnSdPHkthayJ0VatWM2YLTc9lIqdp8/DhBAJM5Jz0NWAiZ7rhSc/r69dvUn1+48YNiBcvnswXGjdunOmL6uxJJnLBG5QKX4gE0f//IsKd1JYtf/4CUn6GvgRYdJAnbvW67ySOOjacOUzCd0ZvsWPHdpm7Vi9gx3AAACAASURBVLFiJdn795Ugh127dpWFD/QlpnDhIjJM/N9//8lwcqpUqWUxhl4GEzm9WFK/92Aip1/bhngzJnLGG54wo4rCAgXyS5kFGhQmo0rU4cNHGL+gjp9gIvdn43769FGQt/xC9+ypJHM0Bg4ciN69+1gub07IcPh6zId/x3bfSdwl48WK6Vz0zi9btlSes0WLlvKs9L+PHz8mha2pVRl55kiweOvWLcIr90T8ua5Jkiha/XVgIqdVy/C5AhFgIuek7wITOeMNT5pamTJlxOPHj4M+gKnJeZcuXXSpBWc8Qv97goncn9ELCPCXXwhKly6Ny5cvy4lU5dm8eXPZossSw2fMWAT07Q3kLoKwe7dCaJiYtCzp5FEKAeXy5cmTR65BVdnklcuRI4fUiRs5ciTSCh068twRySPxXT2RHz3dxaSXgB/SPAJM5DRvIusckImccbiSrAJVn5KoL31YUZPzPHnyCs2rWJYPiRl3NE3OZiJn2Cx37tyR3Rmof+q2bdtkJWiNGjXEuzXN8MMhzPAZNBQBwwUhLFscYWZNhYvoxmDqoIrbtyJESzpsP3arIIkVD4+5mDZtmmgX1ll0l8gjOyv8SPhM3VNrzzGR05pF+Dy/IsBEzknfCSZyaoYn2YXRo8cI8vY5qOqQPrwqVKhg1SR1tdNpdxYTOXXbkNjuhAnjsXbtWikgTF6uOHFiCy3CFX9chCpJ//33X9HxIawI9ReAT426wONn3+efuCLEC4si9JABcM2QXv0gwcxcsGC+eM9jCFHjCj+FfenfDzq3m1td+YUmvaiCpUII8tIlTmw6cTTrsFZ6mImclYDlZS2GABM5i0HpWAsxkTNsr23btsoChsOHRZK4GJQPN3jwYOk1iRo1muEFnHgGEznjjE8iurNnz8LKlSvlgyRjQ18WqNL1R4kSCnU+ePBQVL9+AvV8pc4K1Mc0U8FKCItXcGndHi65c8E1UwZlnbg/nZT6l1K7LSKXZcuW+20a/bxfv76ifddJeV7STSTxa73IjgRemImcce8yz7Y9AkzkbI+5JnZkIheyGbZs2SzDp6QBRmGl+vUbSCHXFi3cOR9O4Q1mIqcA0i9Tzp49I9pb/SP78s6b54GwYcPC3d1d9iwNFNelytBLly7+tniSXXuRThCuKA3qwVXI4Jg7KOTr5XVc5vBlyZJV6MXlDXZJEgAeMGCArNwmKRI9tp5jImfu28TPWxsBJnLWRlij6zOR+7Nhtm/fJlsQEYmjJO7GjZugdevWGrWkNo/FRM50u5A0yfjx40S16DK5SLdu3WSnBBLepXAmVYYGN1KnTiNlPyJHjmzy5lTIQCHbI0cOy1QCktlJkSK5bGYfHEl7/vyZFL5OlCiR+LJT36yepiYf2soPMpGzMsC8vNkIMJEzG0LHXICJ3O92IwL34cMH2XroyJEjksQ1bNgIbdsKRXweRiHARM4ouH6bTDlw3bt3x4EDB0SxwVvRFqunUgN5ypcjgV5TBxUxkJdt/foNePfubdAy1K3E3V3o0QUzdu7cIchjFFDT++jRY5i6tWafYyKnWdPwwf4fASZyTvoqMJH7n+F9fX1x4sQJQdoagCoJaaRIkULqZrVq1cpJ3xDzrs1Ezjz86Gk/P1+pUejt7S3kPl6hSpUqsv1brFjBCweThEl20T81btx45m/OKwQhwESOXwatI8BETusWstL5mMh9B5ZygUgnq0SJ4lK9PrFoX0Qq9e3bt5chVR6mIcBEzjTcgnuqbt06uHnzJl6/fo1ixYqhevXq4r0NhTdvw4uG9QGIHeuTfOw7yYttuY15JYkAEzl+EbSOABM5rVvISudjIvdd2JSqBXPmzCFRpvZDVDVILZN4mIcAEznz8Avu6W7dukoh4aqVKuHM2XgYt6koEPozPAfsENWrASKHrTgTOcvDzkTOCpjykpZFgImcZfF0mNWYyEEUM+yTbYaoVRKNvXv3InPmzFKbi4d5CDCRMw+/4J7++PEDbty4CZflK/Fw7lPUS7lK9E4NwLtjfqKiGrLKlb1HlsedMbU8pryiZRFgImdZPB1mNWcnctTsnmQdrl27JnOOVq1aJdpvZRIfhuEcxoZaPigTOctbh/qbkm5c5hOn4TqgL3agJpqkWoHkcYBDq12RMIGL5TflFZkc8zugeQSYyGneRNY5oDMTORI5HT9+PM6dO4fkyZMLVf0JKFSokPiQFG4NHhZBgImcRWAMWuTYsaPS40aahjHWbkC4Hl1xBhFQIHJlIN5i5E0VCvMmuCJdWiZzlkWec+QsjSevZ3kEmMhZHlOHWNFZidyyZUulvAhVqWbMmBE9evRA5cpVHMJmjnRIJnKWsxZ54sKECSMrqWPEiAmXeQv+n8gBBSDkPqIIMhd7DEpnj4VhvV2RMzuTOcuhz0TOkljyWtZBgImcdXDV/KrOSOSWL/fE9OnTpZxDtmzZpMhv7dp1NG8rRzwgEznzrRYQ4C/bX5G2W7p06YI02gKJ3CPExdRObpg1axa+RRAab9G7onL+v9Gzgyvy5WEyZ74Fvq/AOXKWQpLXsRYCTOSshazG13U2Irdu3VqMHj0aZ86ckVpbzZs3R7169TVuJcc9HhM582z37dtXKYtD+nG5cuUSFdVRgxYMJHJ+iTPi1dHtGDJkKDZs2IBX/o2BaC1RtWAKdG/HZM48C/zvaSZylkKS17EWAkzkrIWsxtd1JiK3a9dO2eaI+kZmzpxFtDtqjbp13TRuIcc+HhM50+335ctn3L59B9evX0OZMmV+6+37I5Hz+feI3Khjxw7YvXs3nn5tKMhcC1TKnxwDurkiRzb2zJluCfbImYsdP28bBJjI2QZnze3iDETOx8dHFjTUrFkDDx48QOrUqdG7d29Uq1Zdc/bQ24GYyJlmUSJxd+/eE186LqFq1WrBLhIckaOJ7du3kxI6T78KT3P0DiiVPRGmjHBFmtRM5kyzBhM5c3DjZ22HABM522GtqZ30TuSIxF24cAEFCxbAly9fkCBBAkyePBmlS5fRlB30ehgmcsZb1sfnm/DC3RCSOFf/SOJo1T8RuUDP3LZt2/DKry4QczBypYqBTYtdES8ukznjLcJEzlTM+DnbIsBEzrZ4a2Y3vRO506dPI3fuXEF4U9gpV67cmsFf7wdhIme8hc+ePSM9x5UqiSrUEEZIRI4eo0rsefM8RDWrCLPGW4DEomvXnaOhjD8QPyER4Bw5fhG0jgATOa1byErncyYit2/fPin2yx0brPQyBbMsEznjsPb29sLnz5+RN29ehA8fwSwi9+7dW0yaNEl4oBcDkUsBCTyRMCZwbV8oRAh5aeMO7SSzmcg5iaEd+JpM5BzYeOYcXc9E7vDhwzL5+9mzZ1iyZAmyZMnCHRvMeVlMeJaJnDpopBPn6uqK9OnT/1Sd+qcVDHnk6LknT55g4cIFGDt2oSBzRQSZW4G0CYAdS1zxd2IOs6pbhz1yxmDFc+2DABM5++Bu9131SuR27tyB4cOH4/jx40iUKJEsduCODbZ/3ZjIqWH+Y8eG6NGFuK/CUCFytIyn5zJRANFe/C8RW41cUoRZPVAwbXhMH+mKTBlNI3OkaUeew+fPn+HRo8cyny9//gJSrDi0aPh6/fp18Tt3Fn/9lUj8fX6F22h/CnvktG8jZz8hEzknfQP0SOS2bNksCxoOHjyIZMmSoXv37nBzcxM5Lq5OamX7XZuJnGHsvbyOy96psu2W6NigOlSJHPURnj9/PubOnSOWjgZErSEKIIaibM54GNTDFblzGk/mbt68iVGjRuLDhw949+4dXrx4ga5du6J8+QqIGjWqFDBevHgRvn79Cg+PeapX0vQ8JnKaNg8fTiDARM5JXwO9ETkicVOnTsX+/fuRJk0auLu3EP+5O6l17X9tJnJ/toG/vx+oGIcqqzNkyIBo0aIbZTBVIkeL3rp1S3QzmSbCrCLESiNaByFN0hFVCiSVosH58xpH5h48uI/Zs2fj06dPWLp0qRQsHjNmLBo2bIB48eLj4cMH2Lx5M06dOiVI5AKj7qXVyUzktGoZPlcgAkzknPRd0BORI8HfMWPG4NChQ7KVUcOGjYTobxsntaw2rs1ELng7fP36BVevXsPTp0+QL18+RI4cxWiDGUPkaPFHjx6J7g+DsXXrVknAEL2bFA2mDhA92rsib27jyJy/v7/wxr1FrVq1QZW2LVrQl6YWMrxKP7t7945MadCLXiMTOaNfUX7AxggwkbMx4FrZTi9E7ujRo0Juobvsn5o6dRo0bdpU9lDlYV8EmMj9jj+J/d65c1cQuSsiFFne5CpqY4kcneTjxw9o1aqVzB0lL9p3MtcKFfImw5BersiWxXgyRxInY8eORbFixUQuXgdZVERE8fVrsb4YlCenh8FETg9W1PcdmMjp275/vJ1eiFyuXDll/9QkSZKgQ4eOsocqD/sjwETuZxuQJ45IXEgdG1StZgqRC1zbza0uTpw4IclcghSj8ThiNxRNBswZ74qUKdTJHP374eXlhZYtWwi9xtzyd4+I3MuXL2T+XNKkYlGdDCZyOjGkjq/BRE7Hxg3panogcq9evUSJEiVF6Oghhg4dKgob6jmpNbV3bSZy/7OJr68Prly5ips3b6BKlapmG8scIkeb16vnBvJkd+7cBeEjd0HfBZGQNSGwd3UoUXShdjz694N6FxMxpGKNbt26I3v27Hjz5jXoZwkSiAV1MpjI6cSQOr4GEzkdG1fPRI4SxdOmTSPzfxYsWIBy5coJLS5Wr9fK68xE7n+WOH36lNQ0LFOmjEXeUXOJHLUCa9WqNfbs2S3y21ojU7bRaDY0AIliAXePqf0OEVmjL1CVKlUSoeKrmDhxomgrVlUWcFBIVU/kR0930cq/D3wOyyLARM6yeDrMao7skaPKuBIlSogKuYcyJ2flypXiQ7Ksw2DvDAdlIvfdyiQx8u3bN9EeLpfoqhDRIqY3l8jRIdzdm2PdunWIEycOKlSsjRKlp6DhwADZAeLCjlCikjbko/5I5M6fP4+RI0cJcthSFm+QnpyeBhM5PVlTn3dhIqdPuxq8lSMTOaqKS548ubzj9OnTUaFCBaiKqRoEhidYBAEmcgCJ/RKpSZs2rdBYM8CMjEDdEkSOhHvHjBktyVydOnWEpMgKbNvljwb9A5AlMbDWwxXJk4WcM0cEtWDBAlJKZdy48bLIKGJEy5BVI+Cw+lQmclaHmDcwEwEmcmYC6KiPOyqRozAOVakeOHBAeAFGynCOsTpcjmozRzq3sxO5wI4NJMlhjNivio0tQeRon//++w8zZ86QxQ/16tUTv1dDsX6zP5oOD0CRNMCEwYarWfPkyS37GLdp0xZZs2aVAsd6G0zk9GZR/d2HiZz+bKp0I0clcseOHUOhQgVFCCey8AScQdy4cZXuy5Nsi4AzEzkKp1Lv1FSpUlmcxJEVLUXkaK1p06Zh4MABKFKkiBDTPgBfX1HBOt8fHWcFoHw6oF+XkHXmli/3FNqN6aV+Y/jw4W37ktloNyZyNgKatzEZASZyJkPn2A86IpEjb9y0aVOxZs0aNGjQQLbgihQpsmMbQoOn//z5E+bNmw/qq/nriBMnNjJmzISECRPK/Ko/DWckclSdSvlilLeZOXNmq3mKLUnkjh49ghkzZoiK2pvo0qWLkBNpJU06brI/+nsGoEJamNQBQoOvtclHYiJnMnT8oI0QYCJnI6C1to2jEbkrV66IPJ5Z0oNA+XHkjeNhHQTev3+HXr164cGDB7h06ZL0elLvWvKCxowZE4kSJZYepxo1aggyFzvYXrbORuRIJ+769RsCs/soXLiwyBWLZB3jWNgjR4dcu3aN7M6QKFEijB49Wti1JsKGDYuR4/wwbg1QTIRZe3V0RZ5c33PmqDnEuk3+qFnVVRRwWO2amlmYiZxmTMEH+QMCTOSc9NVwNCI3deoU6TEgLxB9UJLHiId1Edi5c4do7TREymY0btxEkrnnz5/LBHnyjHbs2AnNmjUNtkOBMxG5Hzs2VKxYUeSJWbdq05IeOXqDDh06KO189uxZEQqOIQjp9aCQ8Kjxfui/EiiXEhjZzxWZM7ng6bMA1Gruj24tXVC8qCuiGN9lzLovroVXZyJnYUB5OYsjwETO4pA6xoKOROSeP3+GqVOnYs6cOSKXp6hoxs0kzhZvGX3A9+3bV5C15qKysXZQX9CDBw+IPprVEDt2bPnhH1y/UGchcuSJu337jhD8vSwKb6rZwiwWzZELPDBp3VF/YiLqO3bslF0awoULJ388foo/ei0IQKGkwOyxrvLvKOqeuY4/vBe7Imd29Y4QNgHIwpswkbMwoLycxRFgImdxSB1jQUcicr179xLyBuOEKn4VLFq02DEA1sEpKYy9bNlS9OvXD5UrV5E3CgjwlxXDbm5u0jtKbZpsQeRoX1+RiU//Ue4ehf7ChAkTbFjXVtD7+fmK0PNl3Lp10yIdG1TPbWmPXOC+lCeXM2cO+cfz5/8VuZAZg440y8Mf7ScFCAb38ykPzHdB/ryuQmZF9fSON4+JnOPZzNlOzETO2Sz+//dlIuekhjfi2nnz5pHN3Rs2bCTDqjTevXuLzZs3Y/z48TIcRxp+oUOH+W1VS3vkyFN04MB+6S2iBH3yHlFLtvjx4xtxI8tOPXXqpOxZWrx48WAxsOxu/1vNHkRONGzAyrX+aDJYkLkfh1Ab2TLRBeXLfvfU6XEwkdOjVfV1JyZy+rKn8m0chcj16tUTnp6eQnKkEAYNGiyrJXlYFwHyNFG4sGbNGujTp49sf0aCtkSm1q5diw0b1qN06dKSTJEArIvL7x/iliJydBZvb2/x3wmUKlVK5nB9/PhR5EjOE83ac4l8ySJ2kaA5fvwY/P39pXaarSunrUXkqHXX5ctXRLFDdYkz5aEWLFhQhlYnrwzA46/ivfv4+7u3YYILKldkImfd30penRH4MwJM5Jz07XAUIte4cSMR3lsmqupaYuzYsU5qLdtem/K+9u7di549e6JAgQL4+vWr8MS9k9XCJP5KXrDMmbOESKotQeRIzuPIkSOSXGTLllXmbQW2uaJ8yTt3bsuuBFmzZrMpQCT2S2Hd1KlTW01iJKQLWYvI0Z4kPUPklHrDbt++Xba+u3krAHfuBuCfYwEYvuT3k6WIJ+RKerigSiV9kjn2yNn014s3MwEBJnImgKaHRxyByFHnhqVLlyBDhoxo164tcuTIqQfoNX+HN29eo1GjRrIalYocqBUT9bMl+ZG2bdsq9Q21BJEjTTbqOhAzZgyULVv2J8/XihXLsXjxEnTq1FF4DMvbDFNrdmxQvYQ1iRx5QDdt2oShQ4ciZcpUIj+yrywwonHvfgAOHg7Ay5dCW276zyHWad1c0LYlEzlVG/I8RsCSCDCRsySaDrSW1okc5WDNnTtHCpUOHDhQSI90dSB0Hfeo9EF+//4D2T2jffv2UnYkatQo6N+/v/SMtW7dSimx31wi9/LlC3h4eMBHJGfVqlVb9iv9ccycOVOE/jzkuapXr2ETwL29veQ+5ImzdNstYy5gTSIXeA6y/4ULF2SOZOfOnVGiRMmgI75/D8yY+73qod8y8X+ErlyR9EJrrq0LypTSH5ljj5wxbyfPtQcCTOTsgboG9tQ6kcuSJbP8IKEPEPLGFStWXAOo6f8IFFo7efIk6tevj+nTp8tE/ihRokrpF8qNy5Mnj8ybCx8+ZCVYc4ncrl07ZT5epkyZ0bx5s9/y0Jo3b44XL56jW7duMk/OmoNyx6gv6XvBYLJlyybzBe05bEHkJk2aKLzhS0Wu5G3hnRsmK5eDG2Mm+mH4CsHl3gG96wEjBnGvVXu+G7y3cyLARM457S5kJH6pPtMIDiQvsWXLZtl+K3HixDJPq2DBQho5nf6PQQUNS5YsllWp27ZtkzlxFGKlMOeMGdPx4cMHjBo1GkmSJAkRDHOI3MePHzB8+HDhAbwsiRO1u/p1DBgwQEqgNGjQ0OBZzLEaif3eunVbSoyUKFEiKEfPnDXNfdYWRI7OOG7cWKxatUqG0rt1647s2bMHe3TqAHHqX6Bovuei24OfyJ38y9wraup59shpyhx8mGAQYCLnpK+FVokcEYWUKVPICsn169ezJ86G7ydptVGbqS5dOuPJkyciV2qzbNtE49Wrl5gyZYqsIKUOG5QEH9Iwh8idO3dWeoDoHYgVi1qA/W8nf/8A8ffPZDI+kb3KlStbLcxJJO7u3XtS7Jf2Ca4614bmCdrKVkSONmzbtg1WrFghK5SnT58R4nVJHPrp0ycilzWH0BiMaw9orLInEzmrwMqLWhABJnIWBNORltIikaN8qKtXr4pwXjGZWD9r1izky5ffkWB16LNSWJWqRFu3bi2LGqj/5o9hRMpLW7x4sZAeKSWJVkjhVXOIHDVxX7lyBZo0aSr+a/xTyyvy1lH18pYtW2Tf3bx581qlJda3b19FfuYtXLt2VSkn0JaGtyWR69+/H9asWSPlZkiUO25cUaIawqAQ9NWrVyTRj6KT3l1M5Gz5dvNepiDARM4U1HTwjBaJHJG49OnTSXSPH/f6LcFdB7Br8grkiSNNNPLGeXjMlVWLFLokL1T06NGDPFEnTngLcj1bhhnp59Tz9k/dFcwhcqVKlZQCu927d/spyd7f3w+PHj0Wkij5ZVVt69Zt8Ndflg/jER4USr53715QRwstGc6WRI7uPXToEEyaNEm2IKM+u4YG9WqlNm4kGaSHwUROD1bU9x2YyOnbvn+8HRM5JzV8MNd+/Pgxli/3lFWipBn36dMn6U2hNlhLliwRbZtyyaco3Er5cxRijRQpkvDWRRWesa3CSxPnN6+YqUTu/ft3shUbtYciIkA5eoGDfrZnzx4hOdJJht1JVy5s2O/9QC05iLBSiJ/EcK2xvrln1TqRoxZq5F0PHz68uVfVxPNM5DRhBj5ECAgwkXPS10NrRI70wtzdm+Phw4cyJ4eS3MOF08cHgdZfMarKfPXqtcxJ+3UkT55MdG+IJP+aBHpfv34j8qCeyj+7uroiVaqUwnsW+rf8MVOJHLUAq1q1qpS9qFev/k+iw+Sxbdq0CapVqyYqWZvL7gOWzlsjnTj64CYCGVwPWS3Y0tZEjgg8SQGRMDd111i6lDRHnGcwkXMeWzvqTZnIOarlzDy31ogc9dEsWbKkEH+NCUqatrfEg5nwOv3j5hK5KlWqyqrUuHG/J82T15AkSSgHq1OnziKkmtDiuXGBYr8pU6YUIeUYmrWhrYkcATF37lxQu7y8efOJXrdHNYuNNQ7GRM4aqPKalkSAiZwl0XSgtbRE5Ly8vDBixHD8+++/6Nu3r+jxWVNKXvBwXARMJXLkHWzXrp0kcHXruskQK3kKT58+Jfu/Ul5eunRphTfQsnplWujYYMjaLkuWwfXIMbhevIFQl04gAGHhW6umfMxv9HCIb0GGljD551euXJH9bXfu3CHboo0bN97ktRztQSZyjmYx5zsvEznns7m8sZaInKfnMpm8niZNGnh5eTupRfR1bVOJHKGwb99eKUr8+fNnqRFHEigUviVvraX7qlIBxalTp0B5XenSpdO2J277DoSaMAOhzxwJellIDdKne2/4tW8Dl2jWFSrevHmT6PTRGMmSJcONGzf19cKGcBsmck5jaoe9KBM5hzWdeQdnImcefvx0yAiYQ+QoF49yJimER9WrOXJkFyQ/LeLFC1n6wlibkMTIpUuXRH7gK+TOnVuzOXE/3st16AiEnTQu6K/8ERXfXtwCQoU29vpGz2ciZzRk/AAjYBMEmMjZBGbtbaIVIkdSBXPmzJZN2cuVK4cJEyZqDyw+kdEImEPkjN7MhAdI7JdCtTduXJcaaY5SWGNPIkfVvMOGDZP9j0nrr2zZcgI3y1cNm2BOqz7CHjmrwsuLWwABJnIWANERl9AKkSOR0d69e8ncJ+okwEMfCGiZyBGJu3PnruzYQNpojjTsSeQIp5MnT0jiS9IiROjix0/gSPCZdFYmcibBxg/ZEAEmcjYEW0tbMZHTkjX0dxYicnPnemDDhvUmXY407EJZIVxIxRQkfHz9+jXNdWxQAcpl0hSEHToIgV3L/OKlg8/FwzYJrTKRU7EQz2EEbI8AEznbY66JHZnIacIMuj0EETnytnbr1s2kO1JrNmt0bThz5rTUKqxUqbJJ59LCQ/aQHwm8N3vktPAG8BkYgZ8RYCLnpG+EFojckCGDZT/VPHnyyG4BMWPGclJr6O/a5nrkqEXWy5cvkSJFSou1avP29sKXL1/k+xZSn1itW8OeRI48mqTlV6JECfz9998yHSJz5sxah8ys83Fo1Sz4+GEbIMBEzgYga3ELLRC5rl27SAJHunEeHvO0CBOfyUQEzM2R+/DhvWzz9PjxE3mC9OnTm3iS74+RTlyoUKHkOlGiRDVrLbs/TB04RB9YRIhAwNj8OA8ePBCdLzLKfU+cOCmqinPY/Ay23JCJnC3R5r1MQYCJnCmo6eAZexO5sWPHYuHChUidOhW6du0qWnJl1wGqfIVABMwlcoHrUH/VR48eC+/cC8FbIpj0njhKxwZHeXuoWIR63nbv3h0ZMmTAyJGjpHyLXgcTOb1aVj/3YiKnH1sadRN7E7m6detgzZo1aN++vZA0EKr0PHSFgKWIHIFCZO7Zs+dStJdCoxkzZlDu7HD8+DEpJkxtt2LEsF7nA10ZT+Eyfn6+Qpw5K8g7t3HjRofOOTR0XSZyhhDin9sbASZy9raAnfZnImcn4J1kW0sSuUDIyBNEHQVcXV2RKlXKENu4EdE4c+aMDM+S1yhatOhOgrxtrslEzjY48y6MgAoCTORUUNLhHCZyOjSqhq5kDSJH16OuD1QIQcQsUaK/gi1a+Pr1C65evYanT58gf/78iBQpsoaQ+fko9+/fF8UD/8rCjsSJE0svV6RIkUR/2Re4du2qaBkWXbauixAhIqid2MOHj4R38qksDKJWWT+Op0+fitS5u9JLyZAKSAAAIABJREFURmQ3efIUwhOZQj5r6cFEztKI8nqMgOkIMJEzHTuHftKeRM7Lywt9+/aRzdBbtmwp+jc2cWgs+fC/I2AtIhe4E8lgxI4dBwkSxP+JzAWK/RIJok4hYcKE1bR5qFvCsmXLcPDgQeTKlRt9+vRBrFgxcffuXVEA5CHImz969Ogpes7+Lfsj7927F7t37xYkLjnatGktW5gRwbty5aoguOdEPuEjKdRLg8LJ1Kc2RowYQRgUKFAAESNGMhsT2pN+dw8dOoS2bduhWbOmgoj+bfa6WlyAQ6tatAqf6UcEmMg56ftgTyJXtGgRHD58GMOHj0C7du2c1AL6vra1iRyhRySIyNxffyWULbbIE0dttxytY8PZs2ckaYsVKxY6duwkcwGJzPXp0xfr1q3F4sWLkTNnTlnssWXLFtkeiypvFy5cIEhZRJk/2LdvX0SNGgX169eXXr2vX79iyZKlGD16lJgbBXHixJUv3NKlS6VsiKVGiRLFZQibztS6dRtLLaupdZjIacocfJhgEHAJ8PcN+HdKS0wP3QQj2hRCbFfGyRkQYCLnDFa23x1tQeToduSZozAjeazIK3Xz5g2H69iwbNlSkft3QxRxZBQad3nFXZLgxYvnQkMvhSRhRPIKFSokwqwxMGrUSPEFaLjQcSuJRYsWgkjGvHnzMXPmDEydOhVFixaVpDYgwB+enp5i/ihRiFBJELoxVnkZmMhZBVZelBEwCgHpkfN7chAjmrTA8ohtsHxxF2SPEtgAxqi1eLIDIcBEzoGM5YBHtRWRI8JC4/Tp0zJUX6ZMGeWKVq3A2q5dWxk2rVu3rgyZUrj42rXrKFasKIoUKYL+/QcgXbq0smJ3zJgx/9+wvixWrFgp8gCfCumPXHj37h127dol/nceea2PHz9Ij9z06dOYyJlpaPbImQkgP251BIJCqy5fL2NS5dKYFL439qxth9RhrL43b2BHBJjI2RF8J9jaVkSOoPTyOi6rU7+HHy2f2G9Nc1FhQp8+vaVnrVWrVrLrBIVFjxw5gkaNGsHd3V3moCVMmEB4G29h8uRJsnK3fft2qFixEkg4mbqjkNdu4sSJKF68uCx0IJ03+jtaa9KkyWYLKv8JA/bIWfPt4LUZATUEXDoM2h8wfnAxhAkA/O8vRfXcXfCq4y7s7ZsDYcXf8dAnAvYicnXq1JYJ0vQB1bBhI+F9SKBPgJ38VrYickePHhEFDWFkG6+oUaM5HOqkczd69GghjJ1G5Md1lJWrT548Ed60xYKATRIetekoXbq0zInbvn0b5syZIytZBw8eIqtWqeiAcuQ2bdokiyA+fvyIpEmTiIrV5LJXLVW8UgutsGHDWQWbf//9F71798KrV6+ksLe7ewur7GPPRdkjZ0/0eW8VBFxabnkfMLvC9/J8F/jgaI+cKL0sPiZ7b4f736FU1uA5DoiAvYgchYiuXbsm8nrmoUaNmg6IHB9ZBQFbEDnq2BAuXDhJWhxV7LdHjx7Ytm2r9L4RESLCRb1MW7ZsIaRE7uHAgYMiVy65aC8WWghnD8Xy5ctln9Px48f/VK1LuYL0XPjw4RE/fnzEixcfcePGFbhEl5Wt1hxubnWxc+dOEQLujyFDhlpzK7uszUTOLrDzpkYg4LLqlX9Arej/y4n7eqQnspSeiQhd9uLkyLwIzV45I+B0nKlM5BzHVo54UmsTOQqnfhcGTuWwJI7y2OrVqyfDwtThpHz5CuJ/f8PRo0fRvHlzme9H3jryNL558xo9e/bEpUuX0LRpM/lzGt++fQ/DbtiwQeTUFZMtzH6VZLH2+8NEztoI8/qMQMgICAYXJaDgGG8c7JkOroK0uXxYj9p/18CahJ1x/Nwk5AnNEOoRASZyerSqdu5kLSIXKAj86dMnGTJ05I4NVKlKuW7Up7RZs+YiJJoUb9++ER66bRgxYgSmTZuGggULBnnpRowYjsiRIwsi11SETROJcGtk6YFbsGChLGrIli2bXCNmzJgyRJslS1YRWk0tvXnWHEzkrIkur80IGEbA5Zv4RP/R6+bi9x8G5syPYbfTYbTI3+iZzrr/CBg+Is+wBgK2JnKUdE2aWL179xb5TOmEd6FHUIWdNe7Ha9oXAWsQOdKJu379huhccB+FCxe2iLCtPVGikCp53OrUqStCqw2l5+3OnTtSVoT6l27btl2ESeNJIvbPP4cwYcIEmfdGXjyaS7pzoUKFwtatW3Hq1EnhtXsj/6OQLHWHIEFkN7d6ouI1nVWvSYSTRI3Tp0+P7t27I1++fFbdz9aLc2jV1ojzfsYi8JsgsEvAM8wqmwZtD4VBo5W3saiq+Srgxh6K51sfAVsTuZcvX8gw2Nu3b6XHIX/+Ata/JO9gNwQsTeR+7NhQoUIFq3uZbAHc6tWrhGTIbkHkasu8NyJst27dwtq1a2SLsfnz5wcdg4oKVq5cIT1wdH8iZ+/evRedHvbI4gciT2/fvpNtvfbu3YfLly+J3LjQskVZr169rX6dLl06CwK6SHoWqVpWT4OJnJ6sqc+7/E7k8Bme1ROhwUY/VPC4jC3uoqqQ8+R0Z30mcrozqaYuZEkiR564W7duC3JzBVWrVtPUPe11GJIt8fRcJjs1UO/ZX8Onr1+/EsRvFby9vQTBWmz1YzKRszrEvAEj8EcEgiFyX7CiViI0XueLUnMvYWuLhEzkdPgCMZHToVE1dCVLETlqzn7p0mXReusWKleuoqEb2vcou3btlL1OqfMDiSGHDRtWaNF9b8tDIsnUo/XixUtCc+46qlevYfXDMpGzOsS8ASNgDJF7g/kVk8N9ryvqL7+LpdU5tKrH94eJnB6tqp07WYrIkazG69evpdCttWU0tIOe4ZPcvn1bhDDnYs2aNRg5ciRKlSol8uaiyq4W799TiPWaqGj9Jgoestgkl5CJnGGb8QxGwFoI/O6R87uGEflzoP/V1BhxxBt9MnKxg7XAt+e6TOTsib629yYvGDWfJ4mPtWvXCsHZZ7LjAJGFTJkyy4pIQ8MSRI7EcsmzRE3gI0X6rnXJ4zsCJFPy5MlTGTq9f/8BtmzZLFt4kZ3ov8yZswjB4KQypy7QU2dN7JjIWRNdXpsRCBkBlxd+AQExf2it6vJ5Bxonq4wl0Vri0IUZKGRdLUm2j50QYCJnJ+A1vi3plZG4K8l7kJzF58+fpc4ZEQJS7yfSQJWU5cuXD9FDZi6Ro44NFC5MnTq1Q0uMWNPcRLg/fPggKlXfykpeX19fIT0SS8qPkBBwxIi2i6YwkbOmpXltRsAAkXvpHxAQ44c5PqcGIWeRcfBrswNnJhSRbbo+ew1FwbLD8bLcQhxfUR/cVMnxXytbErn79+9JWYLt27eLvpJ9RZVeHcSJE8fxQdTZDagB+/79+3D27DnRPq2h7CgQIUIE6dEhD9CLFy9BoU6qoKSQXaVKlf+IgDlETg8dG3T2ahi8Dr0XM2bMEAUpV9GkSVNQxwq9DK5a1Ysl9XuPn0KrLvDFqQH5UGRuZIw9vhdtk39v0fXp+GAUKDsEL8otg/fK+hDlDzwcHAFbEjn64M+WLatE7MyZs7JHJA9tIUCVodRRYO7cuUIKo6SQkWgarMTH3bt3pcbZiRPeGDt2nOwiQHlZvw5TiRyFCmlQj9Do0X/8iqktvPg0vyMwZsxoqYtH3totW7bqBiImcroxpW4v8hORC3ixCY1yNsMd953YOyAXwrHsiG4Nz0ROt6Y16WKPHz+WOmWrV6+WchWpUqUMlqAR4du1axcGDhwoen8Ok6KzwRUhGEvkyONHvULfv38vQ7okeMvDsRBgIudY9uLT6geBICLn4ncfyxqURN/3bbFrQyek5dw4/Vg5mJswkdO1eY2+HIUzJ06chOfPn8kcuZCS5A8ePIAWLVrIXqC/Nm8P3NgYIkdivzdv3pISIyVLlvypGbzRF+EH7IYAEzm7Qc8bOzkCksj5PffGtLYtMOdrfSz17ImcUX6ofnBygPR6fSZyerWsafdavHgROnfuLHPfDh48FOIiROSqVauG2LFji3y6s6L/Z5Tf5qsSucCODST2W6VKVdMOz09pAgEmcpowAx/CCRFwCfD3DTg/uQWmBtTH8I4lEP/3dBcnhEX/V2Yip38bG3PDFSuWo3//AUJaJJESkXNzcxP5cQlw+PDhYKVBVIjct29fhWDtTdE/9RqTOGOMpdG5TOQ0ahg+lu4R+E1HTvc35gtKBJjI8YvwIwJUkDJ79izRReESDhw4EKL22IED+9GuXTu0adMWrVq1FDIh4Yz2yFH3AWotdf/+/RCrX9lKjoMAEznHsRWfVF8IMJHTlz2Vb8NEThkqp5hI0iMrV67EqlUrsWTJUik9EpyQ7MePH7Bt2zZZnThr1izkzJkz2OpWQx45qk79+PEjChYsGCwRdArQdXZJJnI6Myhfx2EQYCLnMKay7EGZyFkWT0dfzdfXR+a7LVmyRFSsphYet7bBErQLFy5g06aNCBMmDDp06PDHooiQiBwVVpCkQ6ZMmYLNr3N0LJ31/EzknNXyfG97I8BEzt4WsNP+TOTsBLyGt6UenRRiPXLkCJInT44CBQoibtw4Ul7k06ePUuyVyJ6fn7+sLg1JD/BPRI46NoQLFw4pU6ZknTgNvwumHI2JnCmo8TOMgPkIMJEzH0OHXIGJnEOazaqHprw1as1FDdcfPnwoW3OdOnUK7969E8QrFZIk+Vs2Zk+SJKns4xmcEHDgAYMjcuSJo7ZbKVKkEC2kYlr1Lry47RFgImd7zHlHRoAQYCLnpO8BEzknNbzCtf39/fD06TNRiHBPduIgTx1539KlS4+//kqo5En7kcjRekQI/fz8xBrplJ5XOCZP0RgCTOQ0ZhA+jtMgwETOaUz980WZyDmp4W107UAiR+28qBL21atXyJ07N+fE2Qh/e2zDRM4eqPOejAB75Jz2HWAi57Smt8nFichRE/Vp06bj1q2bKF26NFen2gR5+23CRM5+2PPOzo0Ae+Sc1P4qRI7mnDt3Dr6+vmahdOPGdTRo0ECusXTpUiRMmNCs9fhh7SPg5eUtpExWoXjxYkInrpL2D8wnNBsB+t1etGiRlJQZP36C2euFtEDq1KkQLVp0q+4RuDhVWPNgBLSMABM5LVvHimdTIXJfv36VemLUUJ0HI2AMAunTp0fmzJmlNh0PRsDSCJCWYdmy5Sy9bLDrMZGzCcy8iRkIMJEzAzxHfpSJnCNbj8/OCDg3AkzknNv+fPufEWAi56RvhAqRozlPnz6Bv79/sChR2LVNmzY4duyYFHhVGUWLFsWYMWOQJ08elemykXuqVKlkSyiVsXTpMuzfvw8LFy5UmY4rV66gXr16QjvtKCJGjKD0TJkyZdC3b18UKVJEaX7v3r0RJ04cdOvWTWn+mjVrQEUCnp6eSvPv3LmLihUriL6nR4Ssh1q4icKdJOhLuWsqY9CgQVL/je6tMjZv3iw7RKxdu0ZluvD6PhHFELlw4sRJ0cM1vtIzNWvWQqNGDVG5cmWl+SNHjgR5mYcMGaI0f/fu3SLHbxq2bNmiNP/16zcoVKggtm7dhqRJkyg9U79+fVStWhW1atVSmj9hwgQ8f/5cdtZQGYcOHQLde9euXSrThfzMZxEaLYDly5cjbdq0Ss80bdpUhNBLoGHD7+kThgblTl6/fh2TJ082NFX+3NvbG7169RI9gA8GzY8VK7Z8H20xVP9ts8VZeA9GIDgEmMg56XuhQuRCgubQoYOYPn0G+vXrh6xZsxpE8e3bN/IDl0hNoUKFRfViZIPPUHcBkquoWbMm4sdPYHA+9QolDbTWrdsgderUBucfP34cY8eOwYABA+UdXF1dQ3zmy5cvMt+rfft2KFasuNRUMzS6du0iGtH/jTp1aovcwL8MTRc5Rgtx+vRpsUcHpEmTxuB8EugdMKC/ICdDkSVLFiHeGzrEZ4iUV6pUEc2aNUOJEiWUpEB69+6FmDFjCcLrhkSJEhs80/Llnvjnn8Po1KmTtJ+hcfHiRRBOw4ePkHcgrTlDo3r1apL8EKmmsxkagwYNlMUWRDb+/tswyVq3bi127NiBLl26IkOGDIaWx40bN2Tf2aFDh8m2ZSoko27dOqhQoQLKly8PIiaGxogRI0S+qg+aNGkitfwMjS1bNgsivRY9evRExowZDU2XcjNELIcNGyZIdR5EiGD4iw0RafpyRr8XceLENbjHuHHj8ObNa7i7uwtJm+QG5+/Zs1t+Kevdu48M1dtjMJGzB+q8pzEIMJEzBi0dzTWXyFGbJvIKHD/upYTKy5cvpGft5MlTUhBWZZC3qEGD+sLr0lhlOujDmvTPZs+erTR/166dkliePXtOaT6J5aZMmQK7d+9R+mCkRatUqSw/qFu1aq20x6hRo0QHhSuC0C1Wmv/PP4fk2pcvX1aaT0SO8h7XrFkrCYfKqF27lujyUEAQs84q0zFp0iThRfES+XGrlOafOHECRGpu3bqtNJ8mpU2bBh4e88SXgkJKzzRu3Ejq4JG9VQZ9Kdi5c6fwjG5SmY7//vtP5GyVEYTuphIBokWzZs0CIjalSql5RVu2bCl1/AYNGqx0JvpSQDmKO3eqeePIS5YvX17pLVMVbM6TJzf69+8viJyaV7Rjxw7C8x1R/NsxRukO1PuXevoePHhIab41JjGRswaqvKYlEWAiZ0k0HWgtc4gckYft27dLIkDhLUPj4cMHkvRRqKZhw0ZKniwKf5FHoEqVKkqeqWXLluLmzZvSO1CkSFFDR5Lh4I0bNyB79uyCRLgZnP/s2VMZkqM7kNdCxQtEIa1QoUKJsGdFJa8OfWiR5lrhwoWFt6ykwTORyC49Q97E+vUNh7Vev34lPah0Bzc3N2UPClUtk+dIxSNCsiMUcqfKxdKlyxi8A81dunSJXLtx4yYG53/48EGEd/vIFmJ16tQRYVjDFdCTJ0+SIcOyZctKexsa5MmicF7+/PkFCa9gaLq02bx5HpLc05cOQ17Rb9++oU+f3tK7WatWTSUv54wZ00GhW/JA5sqVy+CZdu7cIULth5E3b14lkkWe7JkzZ4CKVMgOhjyK9IWA7EBeuJo1ayh5COfOnSO/aFF7t3z58hm8w969e7Bv3z6pP1itWnWD8601gYmctZDldS2FABM5SyHpYOuYQ+RmzZopvFK7sWHDRqVbU//O8uXLSW9F+PDhlZ7JkiUzKB+oZMlSSvNbtGghPhATCW/FIKX5CxcuwOrVq0X4bKfSfPqgy58/n9W9FZEiRcKoUWr5TytXrsCcOXNw4MBBpTs8eHBfekVv3bqlRIBo0cKFC8lculq1aivt0bNnD9naa9IktfwnItNjx44VxPq40vovXjyXdzhz5oxSaI4WLVWqlAypWtez20f2oVUZHz9+lJ7dvXv3KRF8WrNy5UryC0HLlq1UtpB5cdevXxNhyUVK8ylVgvJdL11S8+xSlw7y7K5btx45cuRQ2oNC4ZRD2LFjJ6X5EydOFDmT3sqeXaVFTZjERM4E0PgRmyLARM6mcGtnM1OJHOVvUcgpSpTISv8gkzdu/fr1MoeItKXChAkTIghEAoigULitTZu20kNgaFCIlJK6qYCiSpWqhqZLjxHlP1EulkoBwpMnj2Wu0cWLlyS5pNBQSIO8FXQH8uo0bdpMKYdw3769gpAdkHNVvJwXLlwAVe6RHVXChc+fPxPh1DWSbIwfP15Jg4u8fZRHSN4+FS/QwYMHRKHJfpkX5+ZWz6AdKBy8detWUO7hgAEDDM5/9eqlJN+nT58RZHckYseOY/AZKrYg7ythSh42Q4O8WGQLakmm4iEkgk/FEJQDSvlxhgb1raV3g+5AqQAqeZNEdo8cOSLz0FS9zXv27BFfbP5C8+buho4kPdlUnEJeZ5UvEUREV6xYLu9A+ZOq+XqELaVLqHw5o99/KtCIHTuW/HfAnoOJnD3R571VEGAip4KSDueYSuQGDhwgquZeyLwVlUEhHqp0pJ6dKoNCZ+St2L//gBKJozUpeZ8KKVq0aKmyBShp/ObNG1iwQK2ylQgKVc0SkVMZFIqkO1jbW3Hy5Anxgaqm00akkooVbt68pXIFOSdNmtQSI8qPUxnk9cqUKTN69uypMl2G8vbu3SuI/gal+efPnxch3vLyDoZCf4ELZs6cSebsqYSq6ZkWLdxlqNOant0CBfJLz2706DGU7k3VvAMHDhQeOTVh5Q4d2osvWlGEV26U0vpEyjw8POTvnMqgoggKzxMBVClCojXJE0fFLypfUmh+jx7dZW/eiRMnqRzJqnOYyFkVXl7cAggwkbMAiI64hClEjkJz9A9+6NBhlDwolJNFXqNNmzZLb5ChQdIQ9GHdpUsXIV2xRKkogjwiI0YMl0SuRo2ahrYAeQiJnPj4fFPyoFCFHXkGSI6B7mFokEeRvGVUhTljxkwlMkof6lQ9W6xYMUG26hvaQkh1PJLSHlRAMnbsOIPzyQtEXiYKw6okvhMRpbwv8lZS2DNbtmwG96APdfL0EekgL6ShQV7O5ctX4N69u0KGYoqh6Xj//r3wuh4UH+wT5R0MVbaSV5TuQKFeKg5Qkbu5ffuWJH3kBabKZ0ODPFjkIbxw4aJSgQ15so4ePSIrjL97taOEuAX9jtId+vXrK38nVLxxd+/ekZIpiRMnVipOoVD1unXrpAd8/vwFhq4scg0/yUIWIuvk1VbxipLnlTyuVNWrUthB7wR9UaSCC9UvBQYPbsYEJnJmgMeP2gQBJnI2gVl7m5hC5MhbQVIa5B1QGQsWzJchye3bd6hMF9WaV2WSPLX0Um2/kytXTgwePFh4aioq7UHSIdGiRRPkb6TSfJLSmD9/viBC+5Xm04cQyVUQOdOKt2LDhvWiOnK8DDGqDArDUh4ahaCTJk2m8oj4gC4pQpGNRZVxQ6X5JJny8uVL4ZVT8+zu2LFdVkdSOE9lEPEjryhVO6pIoNCapMVHmm7u7i1UthByKcNlH1lrenYpD41yUVWKNOjQJNVTpEhhkdfYUekOlCpw+vQpSapVhpeXl6wkp3xX1UHttKgKWyW0TWvS+lmyZBVeuR6qW1h1HhM5q8LLi1sAASZyFgDREZdgIsdE7k/vLRM5JnJ/ejeYyDniv/Z8Zr0jwERO7xb+w/2MJXLNmjWV1WkkvaGS2zN9+jQZFiLvnYpnipLqSc6Amm6T18+QOC+F/yjvZujQocKLV0hJu6t169ZSyqRJk8ZKOlkeHnNlyIn2UJG5oEpKqvD09Fwm70DSI4YGeU/I80ACw1Sxamh07txJ4tmyZQslCRSS9qDEd5J/UUmsJ5uR5pqn53Ip8WFISoPOSwnsrVu3knIjKkLPvXr1FHeNLPIO2yoJ4a5evUoWzJD36K+/EhmCSOZu1ahRHcuWeUp7GyqwoQUpz5LebfLsGgp50nzKFaXfIcr7Ugkvku4ipQtMmTJFSW7k0aOHUqaDOpVkypTJYCiZzkTeOLoHSXWoiFVTrigVadD7pyLmS/mu1JVh5syZ8v02NCj0T1I68+bNlx5FlbxGyuOkFIPatWsre+UNncPcn7NHzlwE+XlrI8BEztoIa3R9Y4mcKWEnyjlSybshiA4c2C9JEOUbqQzKRaOwE+WtqeRw0Zo1atQQHxJFZdcElUE5X2fPnpGkRmUQGSWl++vXb6hMl3NSpUqJxYuXWC3sRPpjVElKhRcqg8KpRAaooMBQHlrgepkyZZQEhdo0qQx39+ay0lGlUpXWmz9/niRy27ZtV1letl0j2RQK/6kQGlo0Z84ckrCr6MbRfCKhMWLEkN0oVAaR+wULFhgdoqdq73jx1FqWUWstyqVTyRWlM3fv3k2S0QkTJqpcQdhgnZx79OhRpfmUQ0ghepIfUqlspUVLliwhciybKukiKh3CApOYyFkARF7CqggwkbMqvNpd3BgiRxVklDxN8gcqbXVIHPX+/fvSu0FinoYGyRKQJAPpZJUrV97QdFE1+0xIn3SUHRPoTCoeQkoYJ88J7UEfLobG4sWLZJ4bVQqSqKqhQSGnxYsXy6pKlepC8oSQbhd5s+gOKi2aBg8eJDxeUeQdVPpgUjUifYjSeVQqT8mjSF0x6A6k1G/IK/r582dxh9ayuwLdIW7ceIZgkhXD5OWj+SrSMiQfcvLkSSlIXLiw4d62VGhCAsDf343KBr1x5NmlO5C8ChXMqHiPqQCEKirJDuQtMzQ2b94kWpb9I+9AnldDg3JFR48eFXQHFe3Ftm3byLPQHVS8loTRhw8f5R1UWuyRN46KfugOKvIhd+7clt54skPlylUMSvYQJp06dZSt9ejdUGmjZghHS/2ciZylkOR1rIUAEzlrIavxdY0hcrbwVlA/RRJIVRlUmUedAIhoqZAHWpOITLduXVG9eg2VLeRc+gectO9UBvXmpIrHI0fUvBVPnz4RyfgphaTJReUPrRIlisseqSpdHOjM/fv3E90AXsvqWZWxffs2+eF76tRplemgalgqKKC+qirEkhYlkli9enUlfTOaT30/yd4UnlMZ+/fvk+HO//67oDId1GWBPLtbtmxVIjS0KIVtixcvLrxy7ZX2oDZc58+fk6FelUFFKRTeNtazS5XMKh0T6Az169cTnuzswivXXeVIoq/yNCk8TRWuKoP0Cqk9HXl2VULbtGbGjBlkxa0K2VU5g6XmMJGzFJK8jrUQYCJnLWQ1vq4KkSOvA2l9PX78WKriq3xYU/iFJEToA6Vs2XIGUSB9M/qmHzduHCXJB8odolDku3dvhSxDf6WcLOpE8eDBA9mKS9WDQsLH5KVR8a7RXGpZFiNGdKWwLZE4UtwneZY+ffooeRSpvdG9e/dk2EwllEykjPL7qAm9SnsjshkJ21KeHoXnDA0S550710M2QCeZEpUcK+qmQflr5KFR8dTu3r1LChJT1Wnt2nUMHUmS4g0bNshcLJWKR/KKzp49R9qByJ9KHuSSJYvlFwjyHKtUYZLsC4n5khdYRVqGvHFU6U3kgfQXDQ10vWhWAAACz0lEQVSSNKGcNbIHeXhVPFlUiU3h5xIlSihJmlBLPiJxSZMmURJJJhuvWrUK5O2klnCGckVJdojuQJ52EjBW7cVsCBtL/ZyJnKWQ5HWshQATOWshq/F1VYgc/QNL3oqtW7dpyltBxQrXrl1XRpi8RuQNUQmR0qKUcJ0jR06lrg80f9q0qULj7B/5AawyKIRZrVpV6a1QKSagNTNkSC8TzYsWLaayhfDcNRXFCimkZIfKoHD4xo0bpa1VBmmDFS1aROahqRQH0Jo5cmSXkh0q4XOaT+HCWLFiCa/ccJUjCRsvleHtPXv2Ks2n8B+FFYmYqRBRWpTIG6UaqJBjmk96gkRkSP5FZVAomfINDx8+ojIdpMdHJNFYz27z5s2ViCUdgtIS3r59K7xyM5TOtG3bVikJdPLkKaX5RKhTpkwlCS8Vp2htMJHTmkX4PL8iwETOSd8JFSJHBQV169bBmDFjZRhQZVA1H1WoVa1aTWW6bPpOISRVwkEfWCQArKp7RYdwc6srEusHKuVk0XwK51FXAxUvEM0nnTYqEiChV5VBxIE8ceS1MOStCFyPQm1dunRVJtRjxowRuVIJlXXd6MOXPkhVWjTRmUgvj4pTqLOEoZZlgXegfrju7u5K4rz0DIWqo0WLKkhpcxVYBYHbLYV2VZP3iQRRYv2KFSuUvKJ0CCpyoPZjpHeoMqjYhGysIjBM65HoMX0hmDZtusry0hPn5uYmqluXKqcZdOnSWebGqXa7IJJPnr9OnTornYnyRamwY+7cuUrzaW36d4ZEgKmrhtYGEzmtWYTP8ysCTOSc9J1QIXJOCg1fmxFgBBiBIASYyPHLoHUEmMhp3UJWOh8TOSsBy8syAoyArhBgIqcrc+ryMkzkdGlWvhQjwAgwAowAI8AIOAMCTOScwcp8R0aAEWAEGAFGgBHQJQJM5HRpVr4UI8AIMAKMACPACDgDAv8H+NexhTbevoYAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "a11c29f1-85b3-42c7-8a10-2c7f58e15fe2",
   "metadata": {},
   "source": [
    "![image.png](attachment:98b68228-379f-481d-9846-8f3e2f48d514.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "a2e9bf92-d760-4c7b-a6ca-18d9136583a7",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "P=phybody()\n",
    "tetha=pi/2-alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "627d059b-548a-4214-b8ca-5665e91fa601",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "P.add_weight()\n",
    "P.add_forza(N1,tetha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "42ceaf9f-5415-4473-8144-070581e3ac4f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{m v^{2}}{R} = \\left(2 N_{1} \\cos{\\left(\\alpha \\right)} - g m\\right) \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1=MQ(m*v*v/R,P.fyrelative(-tetha))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "3b35d9bc-6acc-46f1-bf76-ee330f7b2684",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def eQtangencial(self,ang=alpha):\n",
    "    QQ=MQ(self.fxrelative(-pi/2+ang),self.m*self.at)\n",
    "    return QQ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "5163e467-2299-4a58-bbd7-e8cc9f308e90",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle g m \\sin{\\left(\\alpha \\right)} = a_{t} m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qt=eQtangencial(P,ang=tetha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "f7c09990-4189-47c4-b3c6-ed6ad7ebef86",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def eQnormal(self,ang=alpha):\n",
    "    QQ=MQ(self.fyrelative(-pi/2+ang),-1*self.m*self.an)\n",
    "    return QQ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "a32acc53-8f97-41f6-bb65-37d255cbdcb6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle N_{1} - g m \\cos{\\left(\\alpha \\right)} = - a_{n} m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qn=eQnormal(P,ang=tetha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "d0c808ba-b8be-4657-bd08-edef8d33018c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle g \\sin{\\left(\\alpha \\right)} = a_{t}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qt.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "d831d590-0c21-4d41-a741-d1d1d3624bdd",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a_{t} = g \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qt.swap()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "91f2e689-5396-413f-9587-bd268aad43d7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{dv}{dt} = g \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qt.set(at=dv/dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "01895384-9f53-475b-81a2-72a30936b573",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{ds dv}{dt} = ds g \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qt.Mul(ds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "b04c0ce3-3c1a-4103-bc33-de5cfb8ae9f6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle dv v = ds g \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qt.subs(ds/dt,v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "e26ef55b-5153-43f1-8cba-70f18e2b989c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle dv v = R d𝛼 g \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qt.subs(ds,R*dalpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "afce6ab3-6801-42ff-9c3c-2a71b69f7f31",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int v\\, dv = \\int R g \\sin{\\left(\\alpha \\right)}\\, d\\alpha$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qt.integral(v,alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "eff62338-589a-45a8-a744-c5023804772b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{v^{2}}{2} = - R g \\cos{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qt.doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "a1c81504-87b6-4959-b1b0-e84e98bbdb5b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{v^{2}}{2} = - R g \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qt.subs(cos(alpha),cos(pi/2-alpha))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "8d42a9f8-8659-4f0e-bbed-c159bcc89593",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-R*g*cos(alpha)'"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(Qt.R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a622a0ba-0049-43e3-91ec-2c0cd145278f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb37139d-7c9d-4ba8-a05d-fed9ceb9bf37",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "84125a0f-d18a-4c43-907e-658c156bd552",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "737caf63-6377-4006-8bf3-4d2fe842a8ae",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb711d29-0e77-467e-a1fb-2085584e63fb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2a8795b4-42f4-4abc-a2ac-de5c6e3b7d0b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "1968f0c2-f819-4f45-913b-afab9d97cb1f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle d𝜃$"
      ],
      "text/plain": [
       "d𝜃"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dtetha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "260d9069-4036-448b-a4b7-8d6796aa0c41",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "fd611213-d65f-46cf-821a-044ebf076dfc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{v^{2}}{2} = R g \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qt.doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f08159b2-0617-4cf0-9c31-bcb2bfba6c89",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle v =\\sqrt{2} \\sqrt{R g \\sin{\\left(\\alpha \\right)}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v=Qt.solve('v','pos')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "a0305c20-6357-4d0f-8ae4-439fb686ef15",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle N_{1} - g m \\sin{\\left(\\alpha \\right)} = - a_{n} m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qn=eQnormal(P,ang=alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "5e9adb8b-f863-4c88-b9c4-9bc7cff8c25b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{m v^{2}}{R} = \\frac{m v^{2}}{R}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "39f9aac9-72c5-420a-bdb6-a58325216add",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 g m \\sin{\\left(\\alpha \\right)} = \\left(2 N_{1} \\sin{\\left(\\alpha \\right)} - g m\\right) \\cos{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1=MQ(m*v*v/R,P.fyrelative(-alpha))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "be49f172-c40a-4892-9304-d7bb77fd4814",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "60730acd-ac3e-4869-9eda-267fa1ff10f1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle N1=g m \\left(1 - 2 m\\right) \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N1=Qn.solve(N1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6c1f924d-baba-4b7a-9129-7935735c2217",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9457983f-7889-425d-9ad2-3956720eb5af",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cb8482d2-d16b-4f14-ad7a-b9fd1c582bc0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8ab3c3ee-66f3-4f43-ba19-93384db44f17",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAAJCAYAAADpeqZqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVQYGXWR3Q2CQBCEDyogsQNKQFuwA2MJWoKv90akA6jBDqQDfzoQKyChg/ObC2suJGyy7OzMLHsHWQjBpeG9vyZ9Ca7h3gnnMhtCkOFOnsG9TNSC8iW34IGUp8p5WLwALUIcEAmeKE/yop44kH0cQmxpCmojZRED/W7mNnqRbTpC/jcshrStxKy71tJyGp1bqfushfSHtsigoQjW3DM/4buZx47XQeyNtIrxBNYWpaOvVNNPbv/nI4GQscOoLfpQOtEIbn6C60qF/XOl+wAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle \\alpha$"
      ],
      "text/plain": [
       "α"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0ca0c7e9-0c9d-4625-a5f0-fbd5ac7fda2c",
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  },
  {
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   "execution_count": null,
   "id": "56593f1b-49c4-486f-af22-fe5ab6e590cb",
   "metadata": {},
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   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d41347c8-8405-4cbd-a49f-abc0f41d7724",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2fa4430f-c320-4167-b159-d1612a275d9e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4708883c-a08a-49ca-bd27-c7dc9a20b206",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5a6944f6-5ad2-4731-8d4d-b13f0a7c1a77",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bc1bbb43-e47b-4fc4-b481-f870821e4708",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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