{"nbformat":4,"nbformat_minor":0,"metadata":{"anaconda-cloud":{},"colab":{"name":"mac0209-movimento-1D-stateSpace.ipynb","provenance":[]},"kernelspec":{"display_name":"Python [default]","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":"3.5.2"},"toc":{"base_numbering":1,"nav_menu":{},"number_sections":true,"sideBar":true,"skip_h1_title":false,"title_cell":"Table of Contents","title_sidebar":"Contents","toc_cell":false,"toc_position":{},"toc_section_display":true,"toc_window_display":true}},"cells":[{"cell_type":"markdown","metadata":{"id":"JAcSMzHxSxR5","colab_type":"text"},"source":[" MAC0209 - Modelagem e Simulação \n","\n","Roberto M. Cesar Jr. (IME-USP)\n","\n","Roberto Hirata Jr. (IME-USP)\n","***\n"," Movimento 1D usando Sistemas dinâmicos, State Vectors e State Space\n","***"]},{"cell_type":"markdown","metadata":{"id":"uEcmOVX9SxR7","colab_type":"text"},"source":["# Introdução: modelagem por sistemas dinâmicos e vetores de estado"]},{"cell_type":"markdown","metadata":{"id":"MhfLFFY0SxR8","colab_type":"text"},"source":["Equações diferenciais do movimento:\n","\n","$$\\frac{d^2x}{dt^2} = \\frac{dv}{dt} = a(t)$$\n","\n","$$\\frac{dx}{dt} = v(t)$$\n","\n","\n","\n","Euler:\n","\n","$$x(t+\\Delta t) = x(t) + v(t) \\; \\Delta t $$\n","\n","$$v(t+\\Delta t) = v(t) + a(t) \\; \\Delta t $$\n","\n","Assim, o movimento 1D da partícula pode ser representado por um vetor de estados \n","\n","$$\\vec{s} = (x,v)$$ \n","\n","O vetor de estados \n","\n","$$\\vec{s}(t) = (x(t),v(t))$$\n","\n","define a posição e a velocidade da partícula no instante de tempo $t$. \n","\n","A implementação do modelo de movimento da partícula com vetor de estados em uma modelagem por sistemas dinâmicos usando o algoritmo de Euler pode ser definida como:\n","\n","$$\\vec{s}(t+\\Delta t) = \\vec{s}(t) + \\vec{r}(t) \\; \\Delta t $$\n","\n","em que $\\vec{s}$ é o vetor de estados e $\\vec{r}$ é o vetor de taxas de variação."]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"XgnSRpe2jwdo"},"source":["## Exercício: $\\frac{dx}{dt} = 2t+1$"]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"11OVI5qe4BVs"},"source":["A partícula se movimenta segundo a equação:\n","\n","$$\n","v(t) = \\frac{dx}{dt} = 2 t + 1\n","$$\n","\n","$$ x(0) = 0$$\n","\n","**Solução analítica:**\n","\n","$$ x(t) = t^2 + t + c$$\n","\n","Como $ x(0) = 0 \\implies c = 0$\n","\n","**Solução de Euler:**\n","\n","$$\n","x(t + \\Delta t) = x(t) + (2 t + 1) \\Delta t\n","$$\n","\n","$$\n","v(t + \\Delta t) = 2 (t + \\Delta t) + 1 = (2 t + 1) + 2 \\Delta t = v(t) + 2 \\Delta t \n","$$\n","\n"," "]},{"cell_type":"markdown","metadata":{"id":"lECKyNJvSxR-","colab_type":"text"},"source":["### Exercício: Resolva na célula abaixo antes de olhar a solução"]},{"cell_type":"markdown","metadata":{"id":"q3VM_CJzSxR_","colab_type":"text"},"source":["O programa abaixo implementa a solucão desse problema **sem** usar a modelagem por sistemas dinâmicos e vetores de estado."]},{"cell_type":"code","metadata":{"id":"uZZq4c6NSxSA","colab_type":"code","colab":{}},"source":["# Escreva sua solucao aqui."],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"05WAdxBTSxSD","colab_type":"text"},"source":["### Resolução: Compare sua solução"]},{"cell_type":"code","metadata":{"colab_type":"code","id":"zqAj0xhX4BVu","colab":{}},"source":["# funcoes genericas que podem ser re-usadas em outros problemas\n","\n","import math\n","import matplotlib.pyplot as pyplot\n","import numpy as np\n","\n","# funcoes base para implementar o Euler. \n","# Deve-se implementar a funcao rates, que depende de cada modelo.\n","\n","def initStateVector(s):\n"," return(np.array(s))\n","\n","def updateStateVectorEuler(s,dt):\n"," return(s + rates(s,dt))\n","\n","# State Vector Trajectories store state space evolution. Uses list to init empty.\n","\n","def initSVTrajectory():\n"," return([])\n","\n","# append s a svt\n","def updateSVTrajectory(svt,s):\n"," svt.append(s)\n"," return(svt)\n","\n","def extractSVTrajectory(svt,i): # returns the trajectory as numpy array\n"," foo = np.array(svt)\n"," return(foo[:,i])\n"," \n","def plotCompareAnalyticalEuler(vxa, vva, vxe, vve, vtime):\n","\n"," fig, ax = pyplot.subplots()\n"," pyplot.plot(vtime, vxe, label='Euler',linestyle='',marker='o') \n"," pyplot.plot(vtime, vxa, label='Analytical') \n"," pyplot.title('Posição')\n"," ax.set_xlabel('Tempo (segundos)')\n"," ax.set_ylabel('Posição (metros)')\n"," pyplot.show(block=False)\n"," \n"," fig, ax = pyplot.subplots()\n"," pyplot.plot(vtime, vve,label='Euler',linestyle='',marker='o')\n"," pyplot.plot(vtime, vva,label='Analytical')\n"," pyplot.title('Velocidade')\n"," ax.set_xlabel('Tempo (segundos)')\n"," ax.set_ylabel('Velocidade (metros / segundo)')\n"," pyplot.show()\n","\n"," fig, ax = pyplot.subplots()\n"," pyplot.plot(vxe, vve,label='Euler',linestyle='',marker='o')\n"," pyplot.plot(vxa, vva,label='Analytical')\n"," pyplot.title('Dynamical System Trajectory')\n"," ax.set_xlabel('Posição (metros)')\n"," ax.set_ylabel('Velocidade (metros / segundo)')\n"," pyplot.show()\n","\n","\n","def erroTrajetorias(v1,v2,tipoErro):\n"," if (tipoErro == 0): # erro com sinal\n"," return(np.array(v1) - np.array(v2))\n"," elif (tipoErro == 1): # erro quadratico\n"," return((np.array(v1) - np.array(v2))**2)\n"," elif (tipoErro == 2): # erro em modulo\n"," return(fabs((np.array(v1) - np.array(v2))))\n"," \n","\n","def easyPlot(v,title):\n"," pyplot.figure()\n"," pyplot.plot(v)\n"," pyplot.title(title)\n"," pyplot.show()\n"," "],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"8WXAo3Z2SxSH","colab_type":"code","outputId":"0e08c789-27a8-4aa9-9bfb-91c419da6076","colab":{"base_uri":"https://localhost:8080/","height":1000},"executionInfo":{"status":"ok","timestamp":1588009788936,"user_tz":180,"elapsed":1973,"user":{"displayName":"Roberto M Cesar-Jr","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhGz-__eofJQcn1KDxeHHo4TBBV_Y3cg_tX79E4_g=s64","userId":"07799089339871026779"}}},"source":["# solucao sem modelagem por sistemas dinamicos e vetor de estados\n","\n","# dx / dt = 2t + 1\n","\n","import math\n","import matplotlib.pyplot as pyplot\n","\n","def nextXeuler(x,t,dt):\n"," return (x + (2*t+1) * dt)\n","\n","def nextVeuler(v,dt):\n"," return (v + 2*dt)\n","\n","def nextVa(t):\n"," return (2*t + 1)\n","\n","def nextXa(t):\n"," return (t**2 + t)\n","\n","def main():\n"," t=0\n"," tf = 1\n"," dt=0.1\n"," x=0\n"," v=1\n"," vva=[]\n"," vxa=[]\n"," vve=[]\n"," vxe=[]\n"," vtime = []\n"," while 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\n","text/plain":["
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\n","text/plain":["
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\n","text/plain":["
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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"ByTpW_R3SxSK","colab_type":"text"},"source":["### Exercício: Resolva na célula abaixo antes de olhar a solução"]},{"cell_type":"markdown","metadata":{"id":"7QF3oENhSxSL","colab_type":"text"},"source":["Dado que temos a equação analítica da velocidade, vamos usá-la na atualização da coordenada da velocidade no vetor de estados. O programa abaixo implementa a solucão desse problema **com** a modelagem por sistemas dinâmicos e vetores de estado."]},{"cell_type":"code","metadata":{"id":"C32m3tPMSxSM","colab_type":"code","colab":{}},"source":["# Escreva sua solucao aqui."],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"qBSedGTiSxSP","colab_type":"text"},"source":["### Resolução: Compare sua solução"]},{"cell_type":"code","metadata":{"colab_type":"code","executionInfo":{"elapsed":699,"status":"ok","timestamp":1549217274797,"user":{"displayName":"Roberto M Cesar-Jr","photoUrl":"https://lh3.googleusercontent.com/-Nzs7M_4iTwE/AAAAAAAAAAI/AAAAAAAABoc/ml4PaW0NzG0/s64/photo.jpg","userId":"07799089339871026779"},"user_tz":120},"id":"dI_Ps3ixlezb","outputId":"0c5f77c9-f97d-4d73-d055-92f4cc43f9a9","colab":{"base_uri":"https://localhost:8080/","height":362}},"source":["# solucao com a modelagem por sistemas dinamicos e vetor de estados\n","# Implementa o exercício da integração de Euler de dx(t)/dt = 2t + 1\n","# compara com o resultado analítico\n","\n","# Com o uso das funcoes acima e Euler, rates eh a unica funcao a ser\n","# re-programada na maioria dos problemas\n","\n","def rates(s,dt):\n"," r0 = (2 * s[2] + 1) * dt\n"," r1 = 2 * dt\n"," r2 = dt\n"," return(np.array([r0,r1,r2]))\n","\n","# analitica:\n","def velocity(t):\n"," return(2*t + 1)\n","\n","def updateStateVectorAnalytical(s,dt):\n"," t = s[2] + dt\n"," x = t*t + t\n"," v = velocity(t)\n"," return(np.array([x,v,t]))\n","\n","def main():\n"," t=0\n"," tf = 1\n"," dt=0.1\n"," x=0\n"," \n"," # state vector: [position x, velocity v, time t]\n"," stateVectorEuler = initStateVector([x,velocity(t),t])\n"," stateVectorAnalytical = initStateVector([x,velocity(t),t])\n"," \n"," svtEuler = initSVTrajectory() \n"," svtAnalytical = initSVTrajectory() \n"," \n"," while (stateVectorEuler[2]"]},"metadata":{"tags":[]}},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAYwAAAEWCAYAAAB1xKBvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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RVG\ntwfggEshJcq8EecqhihXGDcCe5jZsmQH41yZtOyHoK/2L19CmyPg+EehwQ5xR+VcqYuSMH4kmMHk\nXOWSnQlf/Bc+vQ/SasCJT8M+Z3r9J1dpRUkYfYEvwjGMjbkLzezqpEXlXNwWT4cProTfvoHdusOx\nD0KdbeOOyrlYRUkYzwKfADMIxjCcq7gyN8DYB2Dco1CzIZw+CHbvEXdUzpUJURJGlpldn/RInIvb\nLxOCq4rlP8C+Z8Mx/4aa28QdlXNlRpSE8b+wIuxQ/npLyqfVuoph41r4+G74qj/UawHnvAs7HRl3\nVM6VOVESxlnh974Jy3xarasY5n4EQ6+FVQvgwH8ED+FVqx13VM6VSVGe9PZmw67iWb8CRt0C01+F\nRjvDRSOh5UFxR+VcmVZYx72OYT2ogtbXBVqa2cykROZcCUrsrX1WnWnclvIC1TethENvhMN6by4W\n6JwrWGFXGKdIegAYCUwBlgLVgZ2AzsAOwA1Jj9C5YsrtrV07cxlPpQ2kW+YkvrVW/N65P507HRV3\neM6VGwUmDDO7LuxFcSpwGrA9QXmQ2cCzhV19OFeW9Bv5HcflfMJt1V6mOpncl9mT57KPY7sJKYzv\nFHd0zpUfhY5hmNkfBKXMiyxn7lyZ9MfP3Lf+Dg5Nm8HEnF3pm3kJ86wpAItWZsQcnHPlS6Rqtc6V\nOznZMOl5+Ogu9k/N5tbMCxmcfSSW0GTSe2s7t2WSljAkDQCOB5aY2Z75rO8NnJ0Qx25A47Db3nxg\nDZBN8OBgerLidBXQ0jlBscBfJ8JOR/F56z68M3I5lp29eRPvre3clktmbeaBQNeCVppZPzPb18z2\nJXjG47M8DwN2Dtd7snDRZGfC2H7wTEdY9j2c9Cyc/TZdOhzAvSfv5b21nSumKP0wahLMhmppZpdK\nagvsYmbDCtvPzMZKahUxjjOB1yJu69zfLZoWlPX4fQbscVLQr6J2k82rvbe2c8UX5QrjRYKSIAeH\n7xcA/y6pAMKE1BV4J2GxAaMlTQnLkhS2fy9JkyVNXrp0aUmF5cqLzAwYcwc8dwSsWwJnDIbTBv4l\nWTjnSkaUMYw2ZnaGpDMBzCxDKtGGACcA4/PcjupgZoskNQHGSPrOzMbmt7OZ9Qf6A6Snp1sJxuXK\nup+/CMYqls+FdufCMfdAjQZxR+VchRUlYWySVIPgt34ktSGhCGEJ6Eme21Fmtij8vkTSe0B7IN+E\n4SqhjWuCVqmTnof6O8B5H8COnWIOyrmKL0rCuIPgae8WkgYDHYALSuLgkuoBhwPnJCyrBaSY2Zrw\n9TEEPcWdgx/GBMUCVy+Egy6HI26FqrXijsq5SiFK8cExkqYCBwECronS31vSa0AnoJGkBQSJJy38\nzGfCzU4CRpvZuoRdtwXeC+96VQFeNbORkc/IVUzrV8DIvvDN69B4V7h4DLQ4IO6onKtUZJb/bX9J\n+xW2o5lNTUpExZCenm6TJ09srH+jAAAWDUlEQVSOOwxXksxg1nswvDdsWAmH3hB8VakWd2TOVQiS\npkR9fKGwK4yHwu/VgXRgOsEVxt7ARKBjcYJ0rkirF8PwG+G7YdC0HXT/ALb72zOgzrlSUljxwc4A\nkl4HepnZjPD9nsCNpROeq5TM4OuXYdStkL0Rjr4nGK9I9Uo2zsUpyv/AXXOTBYCZzZS0bxJjcpXZ\nip9g6DXw02ewQ0fo/jg0bBN3VM45oiWM2ZKeB14hmFp7DkGJc+dKTk42THwWPrkHlArHPwL7XQAp\nyaxe45zbElESxoXAZcA14fuxwNNJi8hVPktmB2U9Fk6Gtl2CZFHPy3g4V9ZEmVa7AXgk/HKu5GRt\ngvGPwmcPQLU6cPLzsNepUKKFBJxzJSVK8cG2wL3A7gQzpgAwsx2TGJergBL7ah9RdwEPV3+eequ/\nhz1PhW73Q61GcYfonCtElFtSLxI8dPcIQS/vCwmm1zoXWW5fbctcT58qb3PJxuEs3diA2Qc9yUHd\nzin6A5xzsYsyoljDzD4meMjvZzO7EzgiuWG5iqbfqDnskz2DEVX78I8qH/JGdmeO3vgAN0xvGndo\nzrmIolxhbJCUAvwg6UpgIeC1o110G1Zx+donOLvqx8zP2ZYzN93Clzl7ALDW+2o7V25ESRjXAjWB\nq4F7CK4uzk9mUK4C+X4UDL2WnlV+o3/WcTycdSob+LOsh/fVdq78iDJLalL4ci3B+IVzRVu3DEb2\ngRlvQZPd+bzdwzzyP7EB76vtXHlVYMKQNJSwB0Z+zKx7UiJy5ZsZzHwHRtwEG1ZDp5uh43V0qlKV\nexv8OUuqaf0a9O6yi7dNda4cKewK48Hw+8nAdgRPekPQf3t+EmNy5dWqhfDh9fD9SGi2P3R/Arbd\nffNq76vtXPlWWPHBzwAk3WNmhyWsGirJu9+5P+XkwNSXYMztkJ0JXf4DB/4TUlLjjsw5V4KiTKtt\nLGnzQ3qSWgONi9pJ0gBJSyTNLGB9J0mrJE0Lv25PWNdV0hxJcyX1iXIiLibLf4RB3WHYtbD9PnD5\nF3DwFZ4snKuAosySug74VNK88H0r4B8R9hsIPAEMKmSbz83s+MQFklKBJ4GjgQXAJElDzOzbCMd0\npSU7CyY+DZ/8H6SmwQmPw37neVkP5yqwKLOkRoblQXYNF31nZhsj7DdWUqutiKk9MNfM5sHmfhw9\nAE8YZcXvs4JigYumwi7HwnEPQV1/AM+5iq6wWVJHmNknkk7Os6qNJMzs3RI4/sGSpgOLgBvNbBbQ\nDPg1YZsFwIGFxNkL6AXQsmXLEgjJFShrI3z+UPBVvT6cOgD2ONmvKpyrJAq7wjgc+AQ4IZ91BhQ3\nYUwFdjCztZKOBd4H2pJ/narCpvf2B/pD0NO7mDG5giyYHFxVLJ0Ne58BXe6FWg3jjso5V4oKmyV1\nR/g9KQ/rmdnqhNfDJT0lqRHBFUWLhE2bE1yBuDhsWheMU0x4KrjtdNabsHOXuKNyzsWgyFlSkv4j\nqX7C+waS/l3cA0vaTgruZUhqH8ayHJgEtJXUWlJVoCcwpLjHc1th3mfw9CEw4UlIvwgun+DJwrlK\nLMosqW5mdnPuGzP7I7yFdGthO0l6DegENJK0gKBEelr4Gc8ApwKXScoCMoCeZmZAVljkcBSQCgwI\nxzZcaclYCWNug6mDYJsd4YIPoVXHuKNyzsUsSsJIlVQtd2aUpBqQUD2uAGZ2ZhHrnyCYdpvfuuHA\n8AixuZL23Ycw7HpYtwQ6XAOd+kKaFwh0zkVLGK8AH0t6kWDw+SLgpaRG5Urf2qVB/adZ78K2e8KZ\nr0Gz/eKOyjlXhkR5DuMBSd8AR4WL7jGzUckNyyVTYqvUpvWq89ge35M++/5ggLvzrdDx2uBhPOec\nSxDlCgPga4LxBwtfu3Iqt1VqRmY227Oce9a/QPrUaaxosA/bXNgfmuxa9Ic45yqlKLOkTge+Ihik\nPh2YKOnUZAfmkqPfqDlsyMzknNQxjK52EwelzOauzHPpsf42TxbOuUJFucK4BTjAzJYASGoMfAS8\nnczAXHJUWzWP16s+x4Ep3/F59p70zbqEBdYErdoUd2jOuTIuSsJIyU0WoeVEq3LrypLsLPjyCUZU\n+z82WBV6Z/birezDyX2w3lulOueKEiVhjJQ0CngtfH8GPuW1fPltBnxwBSyezvLtj6LnglP5Jbvu\n5tXeKtU5F0WUWVK9JZ0CdCD4dbS/mb2X9Mhc8WVthLH9YNwjUKMBnPYSTXfvwfXTFnmrVOfcFlPw\ncHXFkJ6ebpMnT447jLLh16+CYoHL5sA+ZwZd8GpuE3dUzrkyRtIUM0uPsm1h5c3XkH+VWAFmZnXz\nWefitnEtfPJvmPgM1GsOZ78DbY8qej/nnCtCYdVq65RmIK4E/PgJDL0GVv4CB1wKR90B1fyv0TlX\nMiI9uCepI9DWzF4MS5DXMbOfkhuaiyzjDxh1K0x7BRruBBeOgB0OiTsq51wFU2TCkHQHkA7sArwI\nVCWoL9UhuaG5SGYPhQ9vgHXLoOP1cPi/IK163FE55yqgKFcYJwHtCDrkYWaLJPl9jrit+R1G9IZv\nP4Dt9goaGzXdN+6onHMVWJSEscnMTJIBSKqV5JhcYcxg+uswsg9kZsCRt8MhV3uxQOdc0kVJGG9K\nehaoL+lSgvLmzyU3LJevlb/A0Gvhx4+hxYHQ/QlovHPcUTnnKokoD+49KOloYDXBOMbtZjamqP0k\nDQCOB5aY2Z75rD8b+Ff4di1wmZlND9fNB9YA2UBW1DnCFVZODkx6Hj66M3jfrR8ccAmkeIUW51zp\nKew5jCeAV83sizBBFJkk8hhI0FFvUAHrfwIOD1u+dgP6AwcmrO9sZsu28JgVz7Ifggfwfp0AbY6E\nEx6F+i3jjso5VwkVdoXxA/CQpO2BN4DXzGxa1A82s7GSWhWy/ouEtxOA5lE/u1LIzoQvHodP7w9a\npPZ4CvY9C6S4I3POVVIF3tMws8fM7GDgcGAF8KKk2ZJul1TSN84vBkYkHh4YLWmKpF6F7Sipl6TJ\nkiYvXbq0hMOKyeLp8NwR8PHdsEtXuOIraHe2JwvnXKy2qJaUpHbAAGBvM0uNsH0rYFh+YxgJ23QG\nngI6mtnycFnTcPpuE4JbYVeZ2diijlfua0llboDP7ofxj0HNhnDcQ7B797ijcs5VYCVSSyrhw9KA\nrkBP4EjgM+CuYkX452fvDTwPdMtNFhA86xF+XyLpPaA9UGTCKE/+0le7fg3uTV/LYbPvhuU/wL7n\nQJd/BxVmnXOujChs0Pto4EzgOIIWra8DvcxsXUkcWFJL4F3gXDP7PmF5LYKmTWvC18cAd5fEMcuK\nxL7atcig19oXOWzcGNbVbEatc9+DNkfEHaJzzv1NYVcYNwOvAjea2Yot/WBJrwGdgEaSFgB3AGkA\nZvYMcDvQEHhKwb353Omz2wLvhcuqEMzUGrmlxy/L+o2aQ0ZmNoelTOc/aS/QlOW8mNWFwdnn85En\nC+dcGVVYtdrOxflgMzuziPWXAJfks3wesE9xjl3WrVu5lIfSXuaU1M+Zm9OUUzPvYKrtjFbFHZlz\nzhUsUrVaV4Jmvc8n1XtTx9by36wTeSLrRDZSFfC+2s65ss0TRmlZ8xsMvxFmDyWl3u6cvuJ8vs5q\nsXm199V2zpV1njCSzQymDYZRNwc9to+6i/oHX8n53/zOEu+r7ZwrRzxhJNMf84MOePM+hZaHQPf/\nQqOdADixXTNPEM65csUTRjLkZMNXz8HHd4FSggfw9r/IiwU658o1TxglbemcoFjggq9gp6Ph+Eeg\nfoui93POuTLOE0ZJyc6E8Y/CZw9A1VpwUn/Y+3Sv/+ScqzA8YZSERV8HVxW/z4Q9Tgr6VdRuHHdU\nzjlXojxhFEdmBnx6L3zxX6jVBM4YDLsdH3dUzjmXFJ4wttb88TDkKljxI+x3Hhx9D9SoH3dUzjmX\nNJ4wttSG1UGr1MkvQP0d4LwPYMdOMQflnHPJ5wljS3w/GoZdB6sXwkFXwBG3BAPczjlXCXjCiGLd\nchjVF755AxrvChePgRYHxB2Vc86VKk8YhTGDWe/C8Jtgw0o4/F9w6A1QpVrckTnnXKnzhFGQ1Yvh\nw+thznBo2g66fwDbFdhp1jnnKjxPGHmZwdRBMPo2yN4YzH466HJI9T8q51zlltSfgpIGAMcDS8zs\nb7+eK2ir9xhwLLAeuMDMpobrzgduDTf9t5m9lIwYE3trp9ddxVN1B9J42UTYoSN0fxwatknGYZ1z\nrtxJdjW8gUDXQtZ3A9qGX72ApwEkbUPQ0vVAoD1wh6QGJR1cbm/txSvXcVHqcAZtvIYaS7/h633u\nhPOHerJwzrkESb3CMLOxkloVskkPYJCZGTBBUn1J2xP0Ah+T20tc0hiCxPNaScbXb9Qc0jJX8WrV\nB2iXMpePs9txS+ZFpM5pznivLOucc38R9435ZsCvCe8XhMsKWv43knoRXJ3QsmXLLTr4opUZGLX4\n2Zrw4qYuDMk5BBBambFFn+Occ5VB3Akjv1KuVsjyvy806w/0B0hPT893m4I0rV+DhSszuDbzyr8t\nd84591dx33dZACQ2i2gOLCpkeYnq3WUXaqSl/mWZ99Z2zrn8xZ0whgDnKXAQsMrMFgOjgGMkNQgH\nu48Jl5WoE9s1496T96JZ/RoIaFa/BveevJe3TnXOuXwke1rtawQD2I0kLSCY+ZQGYGbPAMMJptTO\nJZhWe2G4boWke4BJ4UfdnTsAXtK8t7ZzzkWT7FlSZxax3oArClg3ABiQjLicc85tubhvSTnnnCsn\nPGE455yLxBOGc865SDxhOOeci0TBuHPFIGkp8PNW7t4IWFaC4ZQHfs4VX2U7X/Bz3lI7mFnjKBtW\nqIRRHJImm1l63HGUJj/niq+ynS/4OSeT35JyzjkXiScM55xzkXjC+FP/uAOIgZ9zxVfZzhf8nJPG\nxzCcc85F4lcYzjnnIvGE4ZxzLpJKlzAkdZU0R9JcSX3yWV9N0hvh+olFtJgt8yKc7/WSvpX0jaSP\nJe0QR5wlqahzTtjuVEkmqdxPwYxyzpJOD/+uZ0l6tbRjLGkR/m23lPQ/SV+H/76PjSPOkiJpgKQl\nkmYWsF6SHg//PL6RtF+JB2FmleYLSAV+BHYEqgLTgd3zbHM58Ez4uifwRtxxJ/l8OwM1w9eXlefz\njXrO4XZ1gLHABCA97rhL4e+5LfA10CB83yTuuEvhnPsDl4Wvdwfmxx13Mc/5MGA/YGYB648FRhB0\nLD0ImFjSMVS2K4z2wFwzm2dmm4DXgR55tukBvBS+fhs4UlJ+LWPLgyLP18z+Z2brw7cTCLoblmdR\n/o4B7gEeADaUZnBJEuWcLwWeNLM/AMxsSSnHWNKinLMBdcPX9UhC187SZGZjgcL6AvUABllgAlBf\n0vYlGUNlSxjNgF8T3i8Il+W7jZllAauAhqUSXcmLcr6JLib4DaU8K/KcJbUDWpjZsNIMLImi/D3v\nDOwsabykCZK6llp0yRHlnO8Ezgmbtw0Hriqd0GKzpf/ft1hSGyiVQfldKeSdVxxlm/Ii8rlIOgdI\nBw5PakTJV+g5S0oBHgEuKK2ASkGUv+cqBLelOhFcRX4uaU8zW5nk2JIlyjmfCQw0s4ckHQy8HJ5z\nTvLDi0XSf3ZVtiuMBUCLhPfN+ftl6uZtJFUhuJRNSnvYUhDlfJF0FHAL0N3MNpZSbMlS1DnXAfYE\nPpU0n+Be75ByPvAd9d/1B2aWaWY/AXMIEkh5FeWcLwbeBDCzL4HqBEX6KqpI/9+Lo7IljElAW0mt\nJVUlGNQekmebIcD54etTgU8sHFEqh4o83/D2zLMEyaK839eGIs7ZzFaZWSMza2VmrQjGbbqb2eR4\nwi0RUf5dv08wwQFJjQhuUc0r1ShLVpRz/gU4EkDSbgQJY2mpRlm6hgDnhbOlDgJWmdnikjxApbol\nZWZZkq4ERhHMshhgZrMk3Q1MNrMhwAsEl65zCa4sesYXcfFEPN9+QG3grXBs/xcz6x5b0MUU8Zwr\nlIjnPAo4RtK3QDbQ28yWxxd18UQ85xuA5yRdR3Br5oJy/Msfkl4juKXYKByXuQNIAzCzZwjGaY4F\n5gLrgQtLPIZy/OfnnHOuFFW2W1LOOee2kicM55xzkXjCcM45F4knDOecc5F4wnDOOReJJwxXbkhq\nKGla+PWbpIUJ76vGGFdKWBW1dlwx5CWpiqSteoo7rFpcr6RjcuVfpXoOw5Vv4XMD+wJIuhNYa2YP\nxhpU4ASCuf9r4w6khLwK/BO4P+5AXNniVxiuQpB0vqSvwquNp8Lf+qtIWimpn6SpkkZJOlDSZ5Lm\n5fZHkHSJpPfC9XMk3ZrwuTdJmhl+FVS87mzgg3D7OpJGSJoe7nNquPyA8LhTwvXbhssPCnsXfBHG\nOS0hpkcT4hgpqWPCOd0XHuNLSU3Cbdoo6OEyiaDwXu6+KZIeDuOZkRBTM0njwj+zmZIOCXf5ADir\nJP5eXMXiCcOVe5L2BE4CDjGzfQmunHOf0K8HjDaz/YBNBD9IjwROA+5O+Jj24T77AWdJ2ldSe4Jk\n0B44GLhc0t75hNABmBq+Ppag78I+ZrYnMEZSNeAx4BQz2x94haC8OsCLwCVmdgj5F4/LTz3gMzPb\nB/gSuChc/l/gMTM7gL+WwDiNoB/EPsDRwCNhkjkHGBr+me0DfANgZsuAOpLqR4zHVRJ+S8pVBEcB\nBwCTw/ImNfizzHOGmY0JX88gqK+TJWkG0CrhM0bl9oqQ9D7QEagGvJPbLyRh+Td5jl8noafIN8B9\nku4j+GE8XtK+wB7AR2F8qcCCsKZTVTP7Ktz31fBcipJhZrll6KcAh4avDya4PQbwMnBX+Loj8KqZ\nZQO/SRpHUJl4EvCspOrA+2Y2PeEYS4HtgfJazdYlgScMVxGIoJbQbX9ZGFQb3pSwKAfYmPA68d9/\n3ho5RvTf+DeXyzaz2Qoq3x4L9JM0jKDHyDdmdmjiTpIaF/KZWfz1DkD1hNeJ55TNn+dh5F/OOt/z\nMLNPJHUCjgMGS7rXzAYnHC+jkPhcJeS3pFxF8BFwevgbe+5sqpZb+BnHSKovqSZB57LxBC1cT5JU\nI5wB1QP4PJ995yrs/S6pGcFg/MvAwwS3uL4FmoW3uJBUVdIeZrYUyNSfpdUTC13OB9op0ArYP8I5\nTABOD1+fnbB8LNBTUmo4dtKB4GpsB+A3M+sPDATahfGlEJQBT2zG45xfYbjyz8xmSLqL4JZPCpBJ\nMMtnS3oBjCO4JdQGeNnMcgefXyO4dQPwtJnNyGffDwmqiA4kGAu4T1IOwZXAP81sYzjQ/LikOgT/\n7x4CZhGMP7woaQ3BD/ZV4Wd+BiwkuI02E5gW4RyuJrhSuB54L2H52wR9P6YTXIFcb2ZLJF0EXC8p\nE1hLMKYBwZjNuPAWlnObebVaV+lJugTY08yu3cr9mwPPm9kWtz2VVDt3Oq6kW4BtzOyGrYmjpEh6\nEnjTzD6LMw5X9vgVhnPFZGYLJA1M/OG/BbpLuong/+J8ykbr2K89Wbj8+BWGc865SHzQ2znnXCSe\nMJxzzkXiCcM551wknjCcc85F4gnDOedcJP8Pc6N2ACIuM8YAAAAASUVORK5CYII=\n","text/plain":["
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8maRpQHNCne50TgIGZioe51zVsUGdbDOY+TY8eRZ8+xHUawIH/iPUyK7VILuBVjCFJgxJ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\nFprD1TWv9GThnCtXknzwD5M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IPLFGn8XA9cDbwJXAEnd3M1sMPG5mvyEyqDwAWB6ML8wE8tz9N/WzKSK127L3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\n","text/plain":["
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VTuAfgIPAYSCjqj/2t1Vlc7aqHgancwcsLsWbRKXwF7ype9SISCPw\nPeDPVfWY3+0pJRG5DuhS1V1+t6WMaoDXAf+iqpcB/ZTo1/+gcMe1NwHnAkuBBhH5PX9bFS1RKfwV\nuam7iNTiFP1vqup9frenDK4CrheR/TjDeW8Rkf/0t0kllwJSqur9NvddnB8EUfY24GVVTavqEHAf\n8Aaf21Qur4rIEgD3z65SvElUCn8hG8JHiogIzrjvc6r6eb/bUw6q+jFVXa6qq3D+jX+iqpHuCarq\nK0CHiKx2D70VZw/rKDsIXCki9e73+VuJ+IR2jm3Aze7nNwPfL8WbTLrZehiMtyG8z80qtauA9wLt\nIvKMe+z/qOp2H9tkSuPDwDfdTk0S+AOf21NSqvq0iHwX+CXO6rVfEcH4BhG5B9gANIlICrgd+Fvg\nOyLyfpwfgO8uyXtbZIMxxlSWqAz1GGOMKZAVfmOMqTBW+I0xpsJY4TfGmApjhd8YYyqMFX5jjKkw\nVviNMabC/H9dA71iy2GzlAAAAABJRU5ErkJggg==\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"ZzsRkUuw4BV1"},"source":["## Exercício: $\\frac{d^2x}{dt^2} = 6t$"]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"0yvVlvmZ4BV2"},"source":["Escreva a solução para a EDO:\n","\n","$ \\frac{d^2x}{dt^2} = 6t$"]},{"cell_type":"markdown","metadata":{"id":"zM2UjLv9SxSU","colab_type":"text"},"source":["### Exercício: Resolva na célula abaixo antes de olhar a solução"]},{"cell_type":"markdown","metadata":{"id":"gz7XjMFeSxSV","colab_type":"text"},"source":["O programa abaixo implementa a solucão desse problema **sem** usar a modelagem por sistemas dinâmicos e vetores de estado."]},{"cell_type":"code","metadata":{"code_folding":[],"id":"0fMHEa4pSxSV","colab_type":"code","colab":{}},"source":["# Escreva sua solucao aqui."],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"EEMA66WjSxSY","colab_type":"text"},"source":["### Resolução: Compare sua solução"]},{"cell_type":"markdown","metadata":{"id":"4oNc0of6SxSZ","colab_type":"text"},"source":["Depois de ter escrito sua solução, compare com a resolução abaixo:\n"]},{"cell_type":"code","metadata":{"colab_type":"code","executionInfo":{"elapsed":1465,"status":"ok","timestamp":1549219896679,"user":{"displayName":"Roberto M Cesar-Jr","photoUrl":"https://lh3.googleusercontent.com/-Nzs7M_4iTwE/AAAAAAAAAAI/AAAAAAAABoc/ml4PaW0NzG0/s64/photo.jpg","userId":"07799089339871026779"},"user_tz":120},"id":"HuRRZz6Z4BV3","outputId":"1c60de0c-c024-4422-f9a7-f77c6d5e033e","colab":{"base_uri":"https://localhost:8080/","height":894}},"source":["# d2x / dt2 = 6t\n","\n","import math\n","import matplotlib.pyplot as pyplot\n","\n","def nextXeuler(x,v,dt):\n"," return x+v*dt\n","\n","def nextVeuler(v,t,dt):\n"," return v + (6*t*dt)\n","\n","def nextVa(t):\n"," return 3*(t**2)\n","\n","def nextXa(t):\n"," return t**3\n","\n","def main():\n"," t=0\n"," tf = 1\n"," dt=0.1\n"," x=0\n"," v=0\n"," vva=[]\n"," vxa=[]\n"," vve=[]\n"," vxe=[]\n"," vtime = []\n"," while (t"]},"metadata":{"tags":[]}},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAYUAAAEWCAYAAACJ0YulAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nec3hmdPj2gNPAy8CfQodd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BEUDXZAea2WBgMEBhYaGlIBZXk49HwbMXQPlqOPJ/sFs/nxHNuSYqTlIYCLwZ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\nbbPGduecc0FKk4KkQyXNkjR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V8XqR+kalL58pLi3ng3U7eXV5Hm+u3E5hcRlNGyVx7kntGTWwA+ec2JYmjfQt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\nRUQSiEpfRCSBqPRFRBLI/wEvQw+uaUWyfwAAAABJRU5ErkJggg==\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"H5aEXF0MSxSc","colab_type":"text"},"source":["### Exercício: Resolva na célula abaixo antes de olhar a solução"]},{"cell_type":"markdown","metadata":{"id":"NOsdjhKiSxSd","colab_type":"text"},"source":["O programa abaixo implementa a solucão desse problema **com** a modelagem por sistemas dinâmicos e vetores de estado."]},{"cell_type":"code","metadata":{"code_folding":[],"id":"Odk1OQRiSxSd","colab_type":"code","colab":{}},"source":["# Escreva sua solucao aqui."],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"n4iKEtZDSxSf","colab_type":"text"},"source":["### Resolução: Compare sua solução"]},{"cell_type":"code","metadata":{"colab_type":"code","executionInfo":{"elapsed":1792,"status":"ok","timestamp":1549219182393,"user":{"displayName":"Roberto M Cesar-Jr","photoUrl":"https://lh3.googleusercontent.com/-Nzs7M_4iTwE/AAAAAAAAAAI/AAAAAAAABoc/ml4PaW0NzG0/s64/photo.jpg","userId":"07799089339871026779"},"user_tz":120},"id":"xDtL5OZS4BV6","outputId":"0475eca1-a4f2-4c7e-8944-eac8197b618b","colab":{"base_uri":"https://localhost:8080/","height":707}},"source":["# Implementa o exercício da integração de Euler de d2x/dt2 = 6t\n","# compara com o resultado analítico\n","\n","# Euler:\n","def rates(s,dt):\n"," r0 = s[1] * dt\n"," r1 = 6 * s[2] * dt\n"," r2 = dt\n"," return(np.array([r0,r1,r2]))\n","\n","# analitica:\n","\n","def updateStateVectorAnalytical(s,dt):\n"," t = s[2] + dt\n"," x = t**3\n"," v = 3*(t**2)\n"," return(np.array([x,v,t]))\n","\n","def main():\n"," t=0\n"," tf = 1\n"," dt=0.1\n"," x=0\n"," v=0\n"," \n"," # state vector: [position x, velocity v, time t]\n"," stateVectorEuler = initStateVector([x,v,t])\n"," stateVectorAnalytical = initStateVector([x,v,t])\n"," \n"," svtEuler = initSVTrajectory() \n"," svtAnalytical = initSVTrajectory() \n"," \n"," while (stateVectorEuler[2]"]},"metadata":{"tags":[]}},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAYUAAAEWCAYAAACJ0YulAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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IHsVMcwp9kRR06Ggd3/njOp55bQsjT+3Bo1PGMLx/97DLknZAoS+SYl4v38vX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\niKQRhb6ISBpR6IuIpJH/D+ncIa1+DnXCAAAAAElFTkSuQmCC\n","text/plain":["
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V8XqR+kalL58pLi3ng3U7eXV5Hm+u3E5hcRlNGyVx7kntGTWwA+ec2JYmjfQt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\nRUQSiEpfRCSBqPRFRBLI/wEvQw+uaUWyfwAAAABJRU5ErkJggg==\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"code","metadata":{"id":"52fbwAPYSxSj","colab_type":"code","colab":{}},"source":[""],"execution_count":0,"outputs":[]}]}