03 Sistemas_lineares.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Sistemas Lineares\n",
    "\n",
    " _Prof. Dr. Tito Dias Júnior_"
   ]
  },
  {
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"
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "## **Módulo Scipy**\n",
    "O módulo _scipy_ possui implementados vários algoritmos para solução de sistemas de equações lineares. \n",
    "Nesse exemplo, utilizaremos a bilioteca _linalg_ .\n",
    "\n",
    "Considerando o exemplo mostrado na aula, as equações resultantes da modelagem matemática da queda dos \n",
    "paraquedistas, temos:\n",
    "\n",
    "$$\n",
    "m_1g − T − c_1v     = m_1a \\\\\n",
    "m_2g + T − c_2v − R = m_2a \\\\\n",
    "m_3g − c_3v + R = m_3a\n",
    "$$\n",
    "\n",
    "\n",
    "com os seguintes dados:\n",
    "\n",
    "| Páraquedista      | Massa, kg     | Coeficiente de Arrasto, kg/s    |\n",
    "| :------------- | :----------: | -----------: |\n",
    "| 1 | 70   | 10    |\n",
    "| 2   | 60 |14  |\n",
    "| 3   | 40 | 17  |\n",
    "\n",
    "Obtemos o sistema \n",
    "\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{*{3}{rR}l}\n",
    "   70a & + &  T & + & 0 R & = & 636 \\\\\n",
    "    60a & - &  T & + &  R & = &  518 \\\\\n",
    "    40a & + & 0 T & - & R & = & 307\n",
    "\\end{array}\n",
    "\\right.\n",
    "$$\n",
    "E na forma matricial,\n",
    "\n",
    "![image.png](attachment:09044b6b-857e-44ea-a716-e33c4567028a.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[70  1  0]\n",
      " [70 -1  1]\n",
      " [70  0 -1]]\n",
      "[[636.7]\n",
      " [636.7]\n",
      " [636.7]]\n",
      "x =  [[ 9.09571429]\n",
      " [-0.        ]\n",
      " [-0.        ]]\n"
     ]
    }
   ],
   "source": [
    "#Solução do sistema linear\n",
    "import numpy as np            # Importa módulo numpy para criação das matrizes e vetores\n",
    "from scipy import linalg      # Importa linalg de scipy para solução sistemas de equações lineares\n",
    "\n",
    "# Coeficientes de Arrasto\n",
    "c1 = 10\n",
    "c2 = 14\n",
    "c3 = 17\n",
    "# Massas dos paraquedistas\n",
    "m1 = 70\n",
    "m2 = 60\n",
    "m3 = 40\n",
    "\n",
    "v = 5   # Velocidade\n",
    "g = 9.81\n",
    "\n",
    "A = np.array([[m1,1,0],[m2,-1,1],[m3,0,-1]])   # Cria a matriz A\n",
    "print(A)\n",
    "\n",
    "b = np.array([[m1*g - c1*v], [m2*g - c2*v], [m3*g - c3*v]])            # Cria o vetor b\n",
    "print(b)\n",
    "\n",
    "x = linalg.solve(A, b)                      # Resolve o sistema utilizando linalg.solve\n",
    "print('x = ',x)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Após a solução numérica, o resultado obtido deve ser \n",
    "a = 8,5941 m/s2; T=34,4118 N e R = 36,7647 N.\n",
    "\n"
   ]
  },
  {
   "attachments": {
    "e973e84d-989e-4357-98cf-11f6d3ef7c92.png": {
     "image/png": 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"
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     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Exercício - Aula 31/08/2020\n",
    "Utilizando o notebook do exemplo anterior, encontre a solução para o problema a seguir. Quatro blocos de diferentes massas ($m_i$) estão conectados por cabos inelásticos e com massa desprezível. Como mostrado na figura, os blocos estão apoiados em um plano inclinado, com coeficientes de atrito entre os blocos e o plano iguais a $μ_i$ . Pode-se mostrar que as equações do movimento para os blocos são\n",
    "\n",
    "![image.png](attachment:e973e84d-989e-4357-98cf-11f6d3ef7c92.png)\n",
    "\n",
    "Onde $T_i$  são as forças de tensão nos cabos e $a$ é a aceleração do sistema. \n",
    "Determine $a$ and $T_i$  se θ = 45° (Check1) ou θ = 75° (Check2), $g = 9.82 m/s^2$ e  \n",
    "\n",
    "![image.png](attachment:f5fbdcb5-19b3-448b-8180-ab0546df457a.png)\n",
    "\n",
    "Para a solução, procure a forma matricial do sistema de equações e insira no modelo, lembrando do uso das funções seno e cosseno da aula anterior.\n",
    "E responda os checks de verificação no AVA:\n",
    "\n",
    "1. Check: Qual a solução para $\\theta = 45°$?\n",
    "2. Check: Qual a solução para $\\theta = 75°$?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  0  0 10]\n",
      " [-1  1  0  4]\n",
      " [ 0 -1  1  5]\n",
      " [ 0  0 -1  6]]\n",
      "[[ 88.40978648]\n",
      " [ 34.85611162]\n",
      " [ 44.83964695]\n",
      " [-58.86      ]]\n",
      "x =  [[44.71156846]\n",
      " [62.08839287]\n",
      " [85.07893081]\n",
      " [ 4.3698218 ]]\n"
     ]
    }
   ],
   "source": [
    "#Solução do sistema linear\n",
    "import numpy as np            # Importa módulo numpy para criação das matrizes e vetores\n",
    "from scipy import linalg      # Importa linalg de scipy para solução sistemas de equações lineares\n",
    "\n",
    "# Coeficientes de Atrito\n",
    "mu1 = 0.25\n",
    "mu2 = 0.3\n",
    "mu3 = 0.2\n",
    "# Massas dos paraquedistas\n",
    "m1 = 10\n",
    "m2 = 4\n",
    "m3 = 5\n",
    "m4 = 6\n",
    "\n",
    "g = 9.81\n",
    "theta = 75*np.pi/180\n",
    "\n",
    "A = np.array([[1,0,0,m1],[-1,1,0,m2],[0,-1,1,m3],[0,0,-1,m4]])   # Cria a matriz A\n",
    "print(A)\n",
    "sinT = np.sin(theta)\n",
    "cosT = np.cos(theta)\n",
    "\n",
    "b = np.array([[m1*g*(sinT - mu1*cosT)], [m2*g*(sinT - mu2*cosT)], [m3*g*(sinT - mu3*cosT)] , [-m4*g]])            # Cria o vetor b\n",
    "print(b)\n",
    "\n",
    "x = linalg.solve(A, b)                      # Resolve o sistema utilizando linalg.solve\n",
    "print('x = ',x)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Treliça"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.8660254  0.         0.5        0.         0.         0.       ]\n",
      " [-0.5        0.        -0.8660254  0.         0.         0.       ]\n",
      " [ 0.8660254  1.         0.         1.         0.         0.       ]\n",
      " [ 0.5        0.         0.         0.         1.         0.       ]\n",
      " [ 0.        -1.        -0.5        0.         0.         0.       ]\n",
      " [ 0.         0.         0.8660254  0.         0.         1.       ]]\n",
      "[[2000]\n",
      " [1000]\n",
      " [   0]\n",
      " [   0]\n",
      " [   0]\n",
      " [   0]]\n",
      "x =  [[-2232.05080757]\n",
      " [  -66.98729811]\n",
      " [  133.97459622]\n",
      " [ 2000.        ]\n",
      " [ 1116.02540378]\n",
      " [ -116.02540378]]\n"
     ]
    }
   ],
   "source": [
    "#Solução do sistema linear\n",
    "import numpy as np            # Importa módulo numpy para criação das matrizes e vetores\n",
    "from scipy import linalg      # Importa linalg de scipy para solução sistemas de equações lineares\n",
    "\n",
    "# F1, F2, F3, H2, V2, V3\n",
    "\n",
    "sin30 = np.sin(30*np.pi/180)\n",
    "cos30 = np.cos(30*np.pi/180)\n",
    "\n",
    "sin60 = np.sin(60*np.pi/180)\n",
    "cos60 = np.cos(60*np.pi/180)\n",
    "\n",
    "\n",
    "A = np.array([[-cos30,0,cos60,0,0,0],[-sin30,0,-sin60,0,0,0],[cos30,1,0,1,0,0],[sin30,0,0,0,1,0],[0,-1,-cos60,0,0,0],[0,0,sin60,0,0,1]])   # Cria a matriz A\n",
    "print(A)\n",
    "\n",
    "\n",
    "b = np.array([[0], [1000], [0], [0], [0], [0]])            # Cria o vetor b\n",
    "print(b)\n",
    "\n",
    "x = linalg.solve(A, b)                      # Resolve o sistema utilizando linalg.solve\n",
    "print('x = ',x)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "## Referências"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Kiusalaas, J. (2013). **Numerical Methods in Engineering With Python 3**. Cambridge: Cambridge.<br>\n",
    "Brasil, R.M.L.R.F, Balthazar, J.M., Góis, W. (2015) **Métodos Numéricos e Computacionais na Prática de Engenharias e Ciências**, São Paulo: Edgar Blucher"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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