{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Estabilidad y control din\u00e1micos longitudinales en cadena abierta"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "An\u00e1lisis de la estabilidad longitudinal de un B747-100"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Los datos se han obtenido del libro Dynamics of Flight Stability and Control, B. Etkin & L.D. Reid pag 165 y corresponden a un Boeing 747-100. La condici\u00f3n de referencia tambi\u00e9n se ha tomado del *Etkin*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import *\n",
      "init_printing()\n",
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#se crean los s\u00edmbolos para todas las variables:\n",
      "u, alfa, tetha, de, q = symbols('\\\\Delta\\hat{u}, \\\\Delta\\\\alpha, \\\\Delta\\\\theta, \\\\Delta\\\\delta_e, \\\\Delta\\hat{q}')\n",
      "mu, Iy, D, landa = symbols('mu, \\hat{I}_y, D, \\hat{\\\\lambda}')\n",
      "\n",
      "C_Xu, C_Xalfa, C_Xde = symbols('C_X_\\hat{u}, C_X_alpha, C_X_\\\\delta_e')\n",
      "C_Zs, C_Zu, C_Zalfap, C_Zalfa, C_Zq, C_Zde = symbols(\"C_Z_s, C_Z_\\\\hat{u}, C_Z_\\hat{\\dot{\\\\alpha}}, C_Z_alpha, C_Z_\\hat{q}, C_Z_\\\\delta_e\")\n",
      "C_mu, C_malfap, C_malfa, C_mq, C_mde, C_mdep = symbols(\"C_m_\\hat{u}, C_m_\\hat{\\dot{\\\\alpha}}, C_m_alpha, C_m_\\hat{q}, C_m_\\\\delta_e, C_m_\\hat{\\dot{\\\\delta_e}}\")\n",
      "\n",
      "C_mu, C_malfap, C_malfa, C_mq, C_mde, C_mdep, C_Zs, C_Zu, C_Zalfap, C_Zalfa, C_Zq, C_Zde, C_Xu, C_Xalfa, C_Xde, u, alfa, tetha, de, q, mu, Iy, D, landa"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\begin{pmatrix}C_{m \\hat{u}}, & C_{m \\hat{\\dot{\\alpha}}}, & C_{m \\alpha}, & C_{m \\hat{q}}, & C_{m \\delta e}, & C_{m \\hat{\\dot{\\delta e}}}, & C_{Z s}, & C_{Z \\hat{u}}, & C_{Z \\hat{\\dot{\\alpha}}}, & C_{Z \\alpha}, & C_{Z \\hat{q}}, & C_{Z \\delta e}, & C_{X \\hat{u}}, & C_{X \\alpha}, & C_{X \\delta e}, & \\Delta\\hat{u}, & \\Delta\\alpha, & \\Delta\\theta, & \\Delta\\delta_{e}, & \\Delta\\hat{q}, & \\mu, & \\hat{I}_{y}, & D, & \\hat{\\lambda}\\end{pmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "(C_m_\\hat{u}, C_m_\\hat{\\dot{\\alpha}}, C_m_alpha, C_m_\\hat{q}, C_m_\\delta_e, C_\n",
        "m_\\hat{\\dot{\\delta_e}}, C_Z_s, C_Z_\\hat{u}, C_Z_\\hat{\\dot{\\alpha}}, C_Z_alpha,\n",
        " C_Z_\\hat{q}, C_Z_\\delta_e, C_X_\\hat{u}, C_X_alpha, C_X_\\delta_e, \\Delta\\hat{u\n",
        "}, \\Delta\\alpha, \\Delta\\theta, \\Delta\\delta\u2091, \\Delta\\hat{q}, \u03bc, \\hat{I}_y, D, \n",
        "\\hat{\\lambda})"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W = 2.83176e6 #N\n",
      "Sup_alar = 511. #m^2\n",
      "cuerda = 8.324 #m\n",
      "Inercia_y = 0.449e8 #kg*m^2\n",
      "\n",
      "rho = 0.3045 #Kg/m^3\n",
      "us = 235.9 #m/s\n",
      "\n",
      "masa_adim = W/9.81/(rho*Sup_alar*cuerda/2)\n",
      "Inercia_y_adim = 8.*Inercia_y / (rho*Sup_alar*cuerda**3)\n",
      "coef_fuerza_zs = -W / (1./2.*rho*us**2*Sup_alar) \n",
      "\n",
      "num_vals = {C_mu:0.1043, C_malfap:-6.314, C_malfa:-1.023, C_mq:-23.92, C_mde:-1.444, C_mdep:0,\\\n",
      "            C_Zs:coef_fuerza_zs, C_Zu: -0.106, C_Zalfap:5.9, C_Zalfa:-4.92, C_Zq:-5.92, C_Zde:-0.3648,\\\n",
      "            C_Xu: -0.1080, C_Xalfa: 0.2193, C_Xde:0,\\\n",
      "            mu: masa_adim, Iy:Inercia_y_adim }"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#se ha tenido en cuenta theta_s=0\n",
      "#se ha cambiado \u00bfuna errata en el libro? en los t\u00e9rminos F_3i\n",
      "F = Matrix([[(C_Xu) / (2*mu), C_Xalfa/(2*mu), 0, C_Zs/(2*mu)],\n",
      "            [(C_Zu + 2*C_Zs) / (2*mu - C_Zalfap), C_Zalfa / (2*mu - C_Zalfap), (2*mu + C_Zq) / (2*mu - C_Zalfap), 0],\n",
      "            [C_mu/Iy + C_malfap/Iy * (C_Zu + 2*C_Zs)/(2*mu - C_Zalfap), C_malfa/Iy + C_malfap/Iy * C_Zalfa/(2*mu - C_Zalfap), C_mq/Iy + C_malfap/Iy * (2*mu + C_Zq)/(2*mu - C_Zalfap), 0],\n",
      "            [0,0,1,0]])\n",
      "F"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{smallmatrix}{}\\frac{C_{X \\hat{u}}}{2 \\mu} & \\frac{C_{X \\alpha}}{2 \\mu} & 0 & \\frac{C_{Z s}}{2 \\mu}\\\\\\frac{C_{Z \\hat{u}} + 2 C_{Z s}}{- C_{Z \\hat{\\dot{\\alpha}}} + 2 \\mu} & \\frac{C_{Z \\alpha}}{- C_{Z \\hat{\\dot{\\alpha}}} + 2 \\mu} & \\frac{C_{Z \\hat{q}} + 2 \\mu}{- C_{Z \\hat{\\dot{\\alpha}}} + 2 \\mu} & 0\\\\\\frac{C_{m \\hat{\\dot{\\alpha}}} \\left(C_{Z \\hat{u}} + 2 C_{Z s}\\right)}{\\hat{I}_{y} \\left(- C_{Z \\hat{\\dot{\\alpha}}} + 2 \\mu\\right)} + \\frac{C_{m \\hat{u}}}{\\hat{I}_{y}} & \\frac{C_{Z \\alpha} C_{m \\hat{\\dot{\\alpha}}}}{\\hat{I}_{y} \\left(- C_{Z \\hat{\\dot{\\alpha}}} + 2 \\mu\\right)} + \\frac{C_{m \\alpha}}{\\hat{I}_{y}} & \\frac{C_{m \\hat{\\dot{\\alpha}}} \\left(C_{Z \\hat{q}} + 2 \\mu\\right)}{\\hat{I}_{y} \\left(- C_{Z \\hat{\\dot{\\alpha}}} + 2 \\mu\\right)} + \\frac{C_{m \\hat{q}}}{\\hat{I}_{y}} & 0\\\\0 & 0 & 1 & 0\\end{smallmatrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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lo55JEzAlhPgWp443uNmTiUm08XQSMAcZpgVvOIEcw9XFID4msmaaPOsBviyTNy+llYs2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\n5wBon/3jrdLu8untSwpYAlwc5Sb+A/tI4hJw+oymAAAAAElFTkSuQmCC\n",
       "prompt_number": 4,
       "text": [
        "\u23a1                        C_X_\\hat{u}                                          \n",
        "\u23a2                        \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                                          \n",
        "\u23a2                            2\u22c5\u03bc                                              \n",
        "\u23a2                                                                             \n",
        "\u23a2                   C_Z_\\hat{u} + 2\u22c5C_Z_s                                     \n",
        "\u23a2               \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                              \u2500\u2500\u2500\n",
        "\u23a2               -C_Z_\\hat{\\dot{\\alpha}} + 2\u22c5\u03bc                              -C_\n",
        "\u23a2                                                                             \n",
        "\u23a2C_m_\\hat{\\dot{\\alpha}}\u22c5(C_Z_\\hat{u} + 2\u22c5C_Z_s)   C_m_\\hat{u}       C_Z_alpha\u22c5\n",
        "\u23a2\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "\u23a2  \\hat{I}_y\u22c5(-C_Z_\\hat{\\dot{\\alpha}} + 2\u22c5\u03bc)       \\hat{I}_y   \\hat{I}_y\u22c5(-C_Z\n",
        "\u23a2                                                                             \n",
        "\u23a3                             0                                               \n",
        "\n",
        "       C_X_alpha                                                              \n",
        "       \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                                                   0          \n",
        "          2\u22c5\u03bc                                                                 \n",
        "                                                                              \n",
        "       C_Z_alpha                                           C_Z_\\hat{q} + 2\u22c5\u03bc  \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                           \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "Z_\\hat{\\dot{\\alpha}} + 2\u22c5\u03bc                           -C_Z_\\hat{\\dot{\\alpha}} +\n",
        "                                                                              \n",
        "C_m_\\hat{\\dot{\\alpha}}       C_m_alpha  C_m_\\hat{\\dot{\\alpha}}\u22c5(C_Z_\\hat{q} + \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "_\\hat{\\dot{\\alpha}} + 2\u22c5\u03bc)   \\hat{I}_y  \\hat{I}_y\u22c5(-C_Z_\\hat{\\dot{\\alpha}} + 2\n",
        "                                                                              \n",
        "           0                                                       1          \n",
        "\n",
        "                    C_Z_s\u23a4\n",
        "                    \u2500\u2500\u2500\u2500\u2500\u23a5\n",
        "                     2\u22c5\u03bc \u23a5\n",
        "                         \u23a5\n",
        "                         \u23a5\n",
        "\u2500\u2500\u2500\u2500                  0  \u23a5\n",
        " 2\u22c5\u03bc                     \u23a5\n",
        "                         \u23a5\n",
        "2\u22c5\u03bc)   C_m_\\hat{q}       \u23a5\n",
        "\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500    0  \u23a5\n",
        "\u22c5\u03bc)     \\hat{I}_y        \u23a5\n",
        "                         \u23a5\n",
        "                      0  \u23a6"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "F_num = F.subs(num_vals)\n",
      "F_num.evalf()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{smallmatrix}{}-0.000121148097204233 & 0.000245997941823041 & 0 & -0.000733694395262001\\\\-0.00159686187656966 & -0.00555573828018484 & 0.999977415698048 & 0\\\\2.85777474748945 \\cdot 10^{-5} & -0.00024682567369277 & -0.00755373324823986 & 0\\\\0 & 0 & 1.0 & 0\\end{smallmatrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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ESKj5TqUjgdv0mLDRG1xadZqZ37COUjSQUeHinkhyh37kilhRTTujaCiPOj0rLWNixuwo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\n",
       "prompt_number": 5,
       "text": [
        "\u23a1-0.000121148097204233  0.000245997941823041           0            -0.0007336\n",
        "\u23a2                                                                             \n",
        "\u23a2-0.00159686187656966   -0.00555573828018484   0.999977415698048              \n",
        "\u23a2                                                                             \n",
        "\u23a2 2.85777474748945e-5   -0.00024682567369277  -0.00755373324823986            \n",
        "\u23a2                                                                             \n",
        "\u23a3          0                     0                    1.0                     \n",
        "\n",
        "94395262001\u23a4\n",
        "           \u23a5\n",
        "0          \u23a5\n",
        "           \u23a5\n",
        "0          \u23a5\n",
        "           \u23a5\n",
        "0          \u23a6"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(F - landa * eye(4))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{smallmatrix}{}\\frac{C_{X \\hat{u}}}{2 \\mu} - \\hat{\\lambda} & \\frac{C_{X \\alpha}}{2 \\mu} & 0 & \\frac{C_{Z s}}{2 \\mu}\\\\\\frac{C_{Z \\hat{u}} + 2 C_{Z s}}{- C_{Z \\hat{\\dot{\\alpha}}} + 2 \\mu} & \\frac{C_{Z \\alpha}}{- C_{Z \\hat{\\dot{\\alpha}}} + 2 \\mu} - \\hat{\\lambda} & \\frac{C_{Z \\hat{q}} + 2 \\mu}{- C_{Z \\hat{\\dot{\\alpha}}} + 2 \\mu} & 0\\\\\\frac{C_{m \\hat{\\dot{\\alpha}}} \\left(C_{Z \\hat{u}} + 2 C_{Z s}\\right)}{\\hat{I}_{y} \\left(- C_{Z \\hat{\\dot{\\alpha}}} + 2 \\mu\\right)} + \\frac{C_{m \\hat{u}}}{\\hat{I}_{y}} & \\frac{C_{Z \\alpha} C_{m \\hat{\\dot{\\alpha}}}}{\\hat{I}_{y} \\left(- C_{Z \\hat{\\dot{\\alpha}}} + 2 \\mu\\right)} + \\frac{C_{m \\alpha}}{\\hat{I}_{y}} & \\frac{C_{m \\hat{\\dot{\\alpha}}} \\left(C_{Z \\hat{q}} + 2 \\mu\\right)}{\\hat{I}_{y} \\left(- C_{Z \\hat{\\dot{\\alpha}}} + 2 \\mu\\right)} + \\frac{C_{m \\hat{q}}}{\\hat{I}_{y}} - \\hat{\\lambda} & 0\\\\0 & 0 & 1 & - \\hat{\\lambda}\\end{smallmatrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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CUX1nh2ckmXUvQz9lzNonMuIHyTe79/GH1f3RiQvxTDAlbAa1RhuBUILd2KSRKJFZk3ZD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\n+cdCKz7d+zt/cCZD2ewqfBbO/wMBlOlokhnjOQAAAABJRU5ErkJggg==\n",
       "prompt_number": 6,
       "text": [
        "\u23a1                C_X_\\hat{u}                                                  \n",
        "\u23a2                \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \\hat{\\lambda}                                  \n",
        "\u23a2                    2\u22c5\u03bc                                                      \n",
        "\u23a2                                                                             \n",
        "\u23a2                   C_Z_\\hat{u} + 2\u22c5C_Z_s                                    C\n",
        "\u23a2               \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                      \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "\u23a2               -C_Z_\\hat{\\dot{\\alpha}} + 2\u22c5\u03bc                      -C_Z_\\hat{\\\n",
        "\u23a2                                                                             \n",
        "\u23a2C_m_\\hat{\\dot{\\alpha}}\u22c5(C_Z_\\hat{u} + 2\u22c5C_Z_s)   C_m_\\hat{u}       C_Z_alpha\u22c5\n",
        "\u23a2\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "\u23a2  \\hat{I}_y\u22c5(-C_Z_\\hat{\\dot{\\alpha}} + 2\u22c5\u03bc)       \\hat{I}_y   \\hat{I}_y\u22c5(-C_Z\n",
        "\u23a2                                                                             \n",
        "\u23a3                             0                                               \n",
        "\n",
        "       C_X_alpha                                                              \n",
        "       \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                                                           0  \n",
        "          2\u22c5\u03bc                                                                 \n",
        "                                                                              \n",
        "_Z_alpha                                                           C_Z_\\hat{q}\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \\hat{\\lambda}                           \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "dot{\\alpha}} + 2\u22c5\u03bc                                           -C_Z_\\hat{\\dot{\\a\n",
        "                                                                              \n",
        "C_m_\\hat{\\dot{\\alpha}}       C_m_alpha  C_m_\\hat{\\dot{\\alpha}}\u22c5(C_Z_\\hat{q} + \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "_\\hat{\\dot{\\alpha}} + 2\u22c5\u03bc)   \\hat{I}_y  \\hat{I}_y\u22c5(-C_Z_\\hat{\\dot{\\alpha}} + 2\n",
        "                                                                              \n",
        "           0                                                               1  \n",
        "\n",
        "                                        C_Z_s     \u23a4\n",
        "                                        \u2500\u2500\u2500\u2500\u2500     \u23a5\n",
        "                                         2\u22c5\u03bc      \u23a5\n",
        "                                                  \u23a5\n",
        " + 2\u22c5\u03bc                                            \u23a5\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                              0       \u23a5\n",
        "lpha}} + 2\u22c5\u03bc                                      \u23a5\n",
        "                                                  \u23a5\n",
        "2\u22c5\u03bc)   C_m_\\hat{q}                                \u23a5\n",
        "\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \\hat{\\lambda}        0       \u23a5\n",
        "\u22c5\u03bc)     \\hat{I}_y                                 \u23a5\n",
        "                                                  \u23a5\n",
        "                                    -\\hat{\\lambda}\u23a6"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(F - landa * eye(4)).det()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{C_{X \\hat{u}} C_{Z \\hat{\\dot{\\alpha}}} C_{m \\hat{q}} \\hat{\\lambda}^{2}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{C_{X \\hat{u}} C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\hat{\\lambda}^{3}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{C_{X \\hat{u}} C_{Z \\hat{q}} C_{m \\hat{\\dot{\\alpha}}} \\hat{\\lambda}^{2}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{C_{X \\hat{u}} C_{Z \\hat{q}} C_{m \\alpha} \\hat{\\lambda}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{C_{X \\hat{u}} C_{Z \\alpha} C_{m \\hat{q}} \\hat{\\lambda}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{C_{X \\hat{u}} C_{Z \\alpha} \\hat{I}_{y} \\hat{\\lambda}^{2}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{2 C_{X \\hat{u}} C_{m \\hat{\\dot{\\alpha}}} \\hat{\\lambda}^{2} \\mu}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{2 C_{X \\hat{u}} C_{m \\hat{q}} \\hat{\\lambda}^{2} \\mu}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{2 C_{X \\hat{u}} C_{m \\alpha} \\hat{\\lambda} \\mu}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{2 C_{X \\hat{u}} \\hat{I}_{y} \\hat{\\lambda}^{3} \\mu}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{C_{X \\alpha} C_{Z \\hat{q}} C_{m \\hat{u}} \\hat{\\lambda}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{C_{X \\alpha} C_{Z \\hat{u}} C_{m \\hat{q}} \\hat{\\lambda}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{C_{X \\alpha} C_{Z \\hat{u}} \\hat{I}_{y} \\hat{\\lambda}^{2}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{2 C_{X \\alpha} C_{Z s} C_{m \\hat{q}} \\hat{\\lambda}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{2 C_{X \\alpha} C_{Z s} \\hat{I}_{y} \\hat{\\lambda}^{2}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{2 C_{X \\alpha} C_{m \\hat{u}} \\hat{\\lambda} \\mu}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{C_{Z \\hat{\\dot{\\alpha}}} C_{Z s} C_{m \\hat{u}} \\hat{\\lambda}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{2 C_{Z \\hat{\\dot{\\alpha}}} C_{m \\hat{q}} \\hat{\\lambda}^{3} \\mu}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\hat{\\lambda}^{4} \\mu}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{2 C_{Z \\hat{q}} C_{m \\hat{\\dot{\\alpha}}} \\hat{\\lambda}^{3} \\mu}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{2 C_{Z \\hat{q}} C_{m \\alpha} \\hat{\\lambda}^{2} \\mu}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{C_{Z \\hat{u}} C_{Z s} C_{m \\hat{\\dot{\\alpha}}} \\hat{\\lambda}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{C_{Z \\hat{u}} C_{Z s} C_{m \\alpha}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{C_{Z \\alpha} C_{Z s} C_{m \\hat{u}}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{2 C_{Z \\alpha} C_{m \\hat{q}} \\hat{\\lambda}^{2} \\mu}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{2 C_{Z \\alpha} \\hat{I}_{y} \\hat{\\lambda}^{3} \\mu}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{2 C_{Z s}^{2} C_{m \\hat{\\dot{\\alpha}}} \\hat{\\lambda}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{2 C_{Z s}^{2} C_{m \\alpha}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{2 C_{Z s} C_{m \\hat{u}} \\hat{\\lambda} \\mu}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{4 C_{m \\hat{\\dot{\\alpha}}} \\hat{\\lambda}^{3} \\mu^{2}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{4 C_{m \\hat{q}} \\hat{\\lambda}^{3} \\mu^{2}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} + \\frac{4 C_{m \\alpha} \\hat{\\lambda}^{2} \\mu^{2}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}} - \\frac{4 \\hat{I}_{y} \\hat{\\lambda}^{4} \\mu^{2}}{2 C_{Z \\hat{\\dot{\\alpha}}} \\hat{I}_{y} \\mu - 4 \\hat{I}_{y} \\mu^{2}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
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SFE3lsivPXCkv72J58aKmtKA/XCHFZYAZfCF2leIocgk64Iv7Y0OQSUBHJiEb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\n",
       "prompt_number": 7,
       "text": [
        "                                                            2                 \n",
        "C_X_\\hat{u}\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5C_m_\\hat{q}\u22c5\\hat{\\lambda}    C_X_\\hat{u}\u22c5C_\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                        2                     \n",
        "    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc           2\u22c5C_Z_\\hat{\n",
        "\n",
        "                                            3                                 \n",
        "Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\\hat{\\lambda}    C_X_\\hat{u}\u22c5C_Z_\\hat{q}\u22c5C_m_\\h\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                         2                                    \n",
        "\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc           2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\\n",
        "\n",
        "                              2                                               \n",
        "at{\\dot{\\alpha}}\u22c5\\hat{\\lambda}       C_X_\\hat{u}\u22c5C_Z_\\hat{q}\u22c5C_m_alpha\u22c5\\hat{\\l\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                          2                                                   \n",
        "hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc        2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\ha\n",
        "\n",
        "                                                                              \n",
        "ambda}         C_X_\\hat{u}\u22c5C_Z_alpha\u22c5C_m_\\hat{q}\u22c5\\hat{\\lambda}          C_X_\\h\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "        2                                                       2             \n",
        "t{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat\n",
        "\n",
        "                                       2                                      \n",
        "at{u}\u22c5C_Z_alpha\u22c5\\hat{I}_y\u22c5\\hat{\\lambda}       2\u22c5C_X_\\hat{u}\u22c5C_m_\\hat{\\dot{\\alp\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                          2                                   \n",
        "{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}\n",
        "\n",
        "                  2                                                  2        \n",
        "ha}}\u22c5\\hat{\\lambda} \u22c5\u03bc         2\u22c5C_X_\\hat{u}\u22c5C_m_\\hat{q}\u22c5\\hat{\\lambda} \u22c5\u03bc      \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \n",
        "                    2                                                       2 \n",
        "_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc  \n",
        "\n",
        "                                                                              \n",
        "         2\u22c5C_X_\\hat{u}\u22c5C_m_alpha\u22c5\\hat{\\lambda}\u22c5\u03bc                 2\u22c5C_X_\\hat{u}\n",
        "- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                      2                       \n",
        "  2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alp\n",
        "\n",
        "                        3                                                     \n",
        "\u22c5\\hat{I}_y\u22c5\\hat{\\lambda} \u22c5\u03bc            C_X_alpha\u22c5C_Z_\\hat{q}\u22c5C_m_\\hat{u}\u22c5\\hat{\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                2                                             \n",
        "ha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\\n",
        "\n",
        "                                                                              \n",
        "\\lambda}         C_X_alpha\u22c5C_Z_\\hat{u}\u22c5C_m_\\hat{q}\u22c5\\hat{\\lambda}          C_X_\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "          2                                                       2           \n",
        "hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\h\n",
        "\n",
        "                                         2                                    \n",
        "alpha\u22c5C_Z_\\hat{u}\u22c5\\hat{I}_y\u22c5\\hat{\\lambda}            2\u22c5C_X_alpha\u22c5C_Z_s\u22c5C_m_\\ha\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                            2                                 \n",
        "at{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{\n",
        "\n",
        "                                                                         2    \n",
        "t{q}\u22c5\\hat{\\lambda}              2\u22c5C_X_alpha\u22c5C_Z_s\u22c5\\hat{I}_y\u22c5\\hat{\\lambda}     \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                      2                                                       \n",
        "I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc\n",
        "\n",
        "                                                                              \n",
        "           2\u22c5C_X_alpha\u22c5C_m_\\hat{u}\u22c5\\hat{\\lambda}\u22c5\u03bc          C_Z_\\hat{\\dot{\\alp\n",
        "\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "2                                                       2                     \n",
        "    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\a\n",
        "\n",
        "                                                                              \n",
        "ha}}\u22c5C_Z_s\u22c5C_m_\\hat{u}\u22c5\\hat{\\lambda}   2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5C_m_\\hat{q}\u22c5\\h\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                  2                                           \n",
        "lpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc     2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - \n",
        "\n",
        "           3                                                      4           \n",
        "at{\\lambda} \u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\\hat{\\lambda} \u22c5\u03bc    2\u22c5C_Z\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\n",
        "             2                                                       2        \n",
        "4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z\n",
        "\n",
        "                                             3                                \n",
        "_\\hat{q}\u22c5C_m_\\hat{\\dot{\\alpha}}\u22c5\\hat{\\lambda} \u22c5\u03bc          2\u22c5C_Z_\\hat{q}\u22c5C_m_al\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                               2                              \n",
        "_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\h\n",
        "\n",
        "                 2                                                            \n",
        "pha\u22c5\\hat{\\lambda} \u22c5\u03bc         C_Z_\\hat{u}\u22c5C_Z_s\u22c5C_m_\\hat{\\dot{\\alpha}}\u22c5\\hat{\\la\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                         2                                                    \n",
        "at{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_\n",
        "\n",
        "                                                                              \n",
        "mbda}                C_Z_\\hat{u}\u22c5C_Z_s\u22c5C_m_alpha                             C\n",
        "\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "   2                                                        2                 \n",
        "y\u22c5\u03bc     2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\do\n",
        "\n",
        "                                                                              \n",
        "_Z_alpha\u22c5C_Z_s\u22c5C_m_\\hat{u}                       2\u22c5C_Z_alpha\u22c5C_m_\\hat{q}\u22c5\\hat{\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                      2                                       \n",
        "t{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc\n",
        "\n",
        "        2                                                      3              \n",
        "\\lambda} \u22c5\u03bc                 2\u22c5C_Z_alpha\u22c5\\hat{I}_y\u22c5\\hat{\\lambda} \u22c5\u03bc            \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\n",
        "                2                                                       2     \n",
        " - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5\n",
        "\n",
        "         2                                                                    \n",
        "  2\u22c5C_Z_s \u22c5C_m_\\hat{\\dot{\\alpha}}\u22c5\\hat{\\lambda}                         2\u22c5C_Z_\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                  2                           \n",
        "C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\n",
        "\n",
        " 2                                                                            \n",
        "s \u22c5C_m_alpha                             2\u22c5C_Z_s\u22c5C_m_\\hat{u}\u22c5\\hat{\\lambda}\u22c5\u03bc  \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                            2                                                 \n",
        "\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{\n",
        "\n",
        "                                                      3  2                    \n",
        "                4\u22c5C_m_\\hat{\\dot{\\alpha}}\u22c5\\hat{\\lambda} \u22c5\u03bc                    4\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "      2                                                       2               \n",
        "I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\\n",
        "\n",
        "                          3  2                                                \n",
        "\u22c5C_m_\\hat{q}\u22c5\\hat{\\lambda} \u22c5\u03bc                           4\u22c5C_m_alpha\u22c5\\hat{\\lamb\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                        2                                     \n",
        "dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\n",
        "\n",
        "   2  2                                                    4  2            \n",
        "da} \u22c5\u03bc                            4\u22c5\\hat{I}_y\u22c5\\hat{\\lambda} \u22c5\u03bc             \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                  2                                                       2\n",
        "\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc    2\u22c5C_Z_\\hat{\\dot{\\alpha}}\u22c5\\hat{I}_y\u22c5\u03bc - 4\u22c5\\hat{I}_y\u22c5\u03bc "
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "polinomio = (F-landa * eye(4)).det().subs(num_vals).evalf()\n",
      "polinomio.evalf(5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$1.0 \\hat{\\lambda}^{4} + 0.013231 \\hat{\\lambda}^{3} + 0.00029077 \\hat{\\lambda}^{2} + 5.1891 \\cdot 10^{-8} \\hat{\\lambda} + 4.0567 \\cdot 10^{-10}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAmoAAAAVBAMAAAAEF99xAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nefSvjeFtMD3e/LoBEbJYj3GvdfR/S+wO2kFDV1YAAAAASUVORK5CYII=\n",
       "prompt_number": 8,
       "text": [
        "                 4                         3                           2      \n",
        "1.0\u22c5\\hat{\\lambda}  + 0.013231\u22c5\\hat{\\lambda}  + 0.00029077\u22c5\\hat{\\lambda}  + 5.1\n",
        "\n",
        "                                 \n",
        "891e-8\u22c5\\hat{\\lambda} + 4.0567e-10"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "roots(polinomio)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\begin{Bmatrix}-0.00655727817554652 - 0.0156473088968295 i : 1, & -0.00655727817554652 + 0.0156473088968295 i : 1, & -5.8031637267945 \\cdot 10^{-5} - 0.00118575618463337 i : 1, & -5.8031637267945 \\cdot 10^{-5} + 0.00118575618463337 i : 1\\end{Bmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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7qsDyT3EKMJnIToieUyS41I7zfNF0nB9ZFLxFx4hOXwaHFof0lM/KjMjv9cVDB/2HtZGW\nDOjr83hL9Gc5PgltBXu4XeRW+7F7aJGTtJGkZWDwAUPaqOs2wW4VubeFvQAj4h2tgYfst+XXOYNj\nRd4/cYsc3yLY/HQzAUIYk/vq8oNi/4imP+zbiG6HuQQNFxHl2lUi19QTTOc1LpVcGiZyPcEZGM4C\nDINclQmXkIu9US6Vgdst+lm/Zf+iSbkEW6fcQBQ+AAEwcAENDfkW/bxRaQYiaJGBaaRm04tmhQRX\nYaJ7zLLsN5eXuks7hnOmqitceUCqZVTCDqTa6IFjQjTXvuaZJohI1O4+FIeIjEWlnZNICYoNNIIX\nYVPbIM9nfPCUh0WMXdrJZKbSjky6dlPBRNspwGQiOxItHqwluNR+YFKnxtrJ/O9kz6T+i4fYyO7L\nsmd6eEbuaMn5opmVHTMi753a9kWRQa3qxtkyMedn2lawh9tFHhExa07SJoEiSAVmOaYhbPT9f5tg\nd8rgIe4FGBEvLa/syFizuJkMhn87dfr+kbMLfc8BBgeGO4a0Z9Z682wwvW3LdHGT/ZcFRnRwCRou\nIsq1q0SuqScY41LJpWEiN7xop2A4RzR0uRosuIRccIlyqQzc/lrK7RLlEmydcoGncuEDEIwtisFo\nTHRkh2az0gxE0CIDaAxyGU6zhave6PpMb0lZQpAVhpMOq+phzdgej7ZVApiAXuxINNdudPhBv4tP\nr3YXa1yQAsai0s5JpATFhoLMtUMHTkoXWPjeGyeoqnDuDNqZhaidmWQxmAokiaegSg0pR6KNBy40\n5N7vvUdZ+KR1xe5P4ecujOhqp+rM+S94rX6btvOqUuSCaf1mf2Xlcb2/WW2O23mmyOk/vrvDFe7B\ndjlpZa/AGpO0IYr3GRh8wBA2Urvx4Q7AGqeesaQ/QxoxgKGrnfptdbLt9ElO1vV/z/fLNtsIsLHd\ngNiyYAM831tiJu+KEz4wKboJIzq6BA2KiHLtKpEL9QCj5igXholcP9MZ2NAXHt/rAaVcCxZcQi65\nRLlQBm4DV21bkkQuwNYpF0RVLnwAAmDgwkzdh7BGzQgwaJEBWKIMPJCwJds8tPEuyzJukBB0UMj4\nGSivEJC4zEoAE9CLHcoj0w46W/RE9LRe7QJHwAEi6yxqxyS0s9isIEkwOIctFIWZMHrKWbV3C8cu\n7chC1M4zBlCowDK1YzLKjkTl63NAVAT92tRKCt9J4MM5Fo7urtE6YvpCgjeSwBGUu5EyV8f62+rT\nGzh7JFLu8j5jY/ac3kDdGws1sbFwKdo/05sNuj6CcjdI4ZPAdJ5kbWOWjkTKXdkmOtOf2JhkPlVQ\nNpncLOxFJ7vdZDeb6ExvsjxvMrnZud3U71HsN/7N8t47y3r/ph+BozUCXzVhtcWjVV5fVz8Cmy4C\nd0HxOeWmE94X3I/A0RmB0T9C1+C1R6e8vqp+BDZbBBrf3GyK+3r7EdgEEfgfTg1E8J/XGesAAAAA\nSUVORK5CYII=\n",
       "prompt_number": 9,
       "text": [
        "{-0.00655727817554652 - 0.0156473088968295\u22c5\u2148: 1, -0.00655727817554652 + 0.0156\n",
        "473088968295\u22c5\u2148: 1, -5.8031637267945e-5 - 0.00118575618463337\u22c5\u2148: 1, -5.80316372\n",
        "67945e-5 + 0.00118575618463337\u22c5\u2148: 1}"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "F_num = np.array(np.array(F_num), np.float)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "autovalores, autovectores = np.linalg.eig(F_num)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "autovalores #son los mismos que se han sacado del pol caracter\u00edstico para comprobar\n",
      "            # Adem\u00e1s salen los mismos (l\u00f3gico) que cuando hab\u00eda puesto la matriz caracter\u00edstica."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "array([ -6.55727818e-03+0.01564731j,  -6.55727818e-03-0.01564731j,\n",
        "        -5.80316373e-05+0.00118576j,  -5.80316373e-05-0.00118576j])"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Se observa que se han obtenidos dos pares de *autovalores complejos conjugados* (sistema oscilante). Todos con *parte real negativa*, lo que indica que el sistema va a ser estable. La parte real de una pareja de autovalores es apreciablemente menor que la de la otra. Esto nos indica que ese modo va a estar d\u00e9bilmente amortiguado y corresponder\u00e1 al **fugoide**. La otra pareja corresponder\u00e1 al **corto periodo**."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Se reordenan los autovalores y sus autovectores de forma que $\\lambda_1$ y $\\lambda_2$ correspondan al fugoide y $\\lambda_3$ y $\\lambda_4$ al corto periodo:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "landa = np.zeros([4],dtype=complex)\n",
      "modos = np.zeros([4,4],dtype=complex)\n",
      "\n",
      "for i in range(4):\n",
      "    j = argmax(autovalores)\n",
      "    landa[i] = autovalores[j]\n",
      "    modos[i] = autovectores[:,j]\n",
      "    autovalores[j] = -100    #esto de quitar los que ya he cogido deber\u00eda hacerlo m\u00e1s elegante\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Fugoide."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Se trabajar\u00e1 ahora s\u00f3lo con la primera pareja de autovalores y sus atovectores asociados.\n",
      "\n",
      "Los autovalores se pueden caracterizar por su parte real $\\hat{n}$ e imaginaria $\\omega$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = np.zeros(4)\n",
      "w = np.zeros(4)\n",
      "for i in range(4):\n",
      "    n[i] = np.real(landa[i])\n",
      "    w[i] = np.imag(landa[i])\n",
      "print('n1 = %g \\n'\n",
      "      'w1 = %g' %(n[0], w[0]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "n1 = -5.80316e-05 \n",
        "w1 = 0.00118576\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "En lugar de caracterizar la raiz por su parte real $n$ e imaginaria $\\omega$, puede resultar m\u00e1s interesante dar el **tiempo para que la perturbaci\u00f3n se reduzca a la mitad:** $\\hat{t}_{1/2}$ y el **periodo del modo oscilatorio** $T$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t05 = np.zeros(4)\n",
      "T   = np.zeros(4)\n",
      "\n",
      "for i in range(4):\n",
      "    t05[i] = -0.693/n[i]\n",
      "    T[i]   = abs(2*np.pi/w[i])\n",
      "print('t0.5 = %g \\n'\n",
      "      'T = %g' %(t05[0], T[0]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "t0.5 = 11941.8 \n",
        "T = 5298.88\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Estos tiempos son adimensionales, si se quiere recuperar las unidades, no hay m\u00e1s que multiplicar por el adimensionalizador de tiempos:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t05_d = np.zeros(4)\n",
      "T_d   = np.zeros(4)\n",
      "\n",
      "tc = cuerda/(2*us)\n",
      "for i in range(4):\n",
      "    t05_d[i] = t05[i] * tc\n",
      "    T_d[i]   = T[i] * tc\n",
      "    \n",
      "print('t0.5 = %g s\\n'\n",
      "      'T = %g s' %(t05_d[0], T_d[0]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "t0.5 = 210.689 s\n",
        "T = 93.4886 s\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Una \u00faltima forma de expresar los autovalores ser\u00eda mediante su **amortiguamiento** $\\xi$ y **frecuencia natural** $\\hat{\\omega}_n$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xi = np.zeros(4)\n",
      "wn = np.zeros(4)\n",
      "\n",
      "for i in range(4):\n",
      "    xi[i] = -n[i] /(np.sqrt(n[i]**2 + w[i]**2))\n",
      "    wn[i] = np.sqrt(n[i]**2 + w[i]**2)\n",
      "print('xi = %g \\n'\n",
      "      'wn = %g' %(xi[0], wn[0]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "xi = 0.0488821 \n",
        "wn = 0.00118718\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "la frecuencia natural dimensional, $\\omega_n$, es:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wn_d = wn * 1./tc\n",
      "print('wn = %g s^-1' %(wn_d[0]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "wn = 0.0672885 s^-1\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Se pasa a analizar ahora la forma del modo asociado a esta pareja de autovalores complejos:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "modos[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "array([ -2.16226620e-02+0.5243972j ,   3.84126916e-03+0.03032094j,\n",
        "        -4.93645945e-05+0.00100866j,   8.50649694e-01+0.j        ])"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "modos[1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "array([ -2.16226620e-02-0.5243972j ,   3.84126916e-03-0.03032094j,\n",
        "        -4.93645945e-05-0.00100866j,   8.50649694e-01+0.j        ])"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Se puede observar que como los autovalores son conjugados, sus modos tambi\u00e9n lo son.\n",
      "\n",
      "Estos autovectores est\u00e1n expresados en la forma:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u, alfa, q, tetha"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\begin{pmatrix}\\Delta\\hat{u}, & \\Delta\\alpha, & \\Delta\\hat{q}, & \\Delta\\theta\\end{pmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAANAAAAAaBAMAAAA0+c+VAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nNXBBVH6UWn2/8KSP0gf/AI4r46Q3pL+rAAAAAElFTkSuQmCC\n",
       "prompt_number": 21,
       "text": [
        "(\\Delta\\hat{u}, \\Delta\\alpha, \\Delta\\hat{q}, \\Delta\\theta)"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Si se referencian a $\\Delta\\theta$ todos los valores y mostramos s\u00f3lo los m\u00f3dulos:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "amplitud_1 = abs(modos[0]) / abs(modos[0][3])\n",
      "amplitud_1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "array([ 0.61699052,  0.03592935,  0.00118718,  1.        ])"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "se observa que:\n",
      "\n",
      "- las variaciones en velocidad adimensional son del orden del 60 % de las variaciones de \u00e1ngulo de cabeceo.\n",
      "- las variaciones de \u00e1ngulo de ataque son del orden del 4 % de las variaciones del \u00e1ngulo de cabeceo.\n",
      "- la velocidad de cabeceo adimensional es del orden del 0.1 % de las variaciones del \u00e1ngulo de cabeceo."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Referenciando tambi\u00e9n la fase a $\\Delta\\theta$ se obtiene:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# np.angle da el argumento del vector en sentido antihorario\n",
      "desfase_1 = np.angle(modos[0], deg=True) - np.angle(modos[0][3], deg=True)\n",
      "desfase_1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "array([ 92.36116035,  82.77983289,  92.80185514,   0.        ])"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "se observa que:\n",
      "\n",
      "- la velocidad adimensional est\u00e1 adelantada unos 90\u00ba al \u00e1ngulo de cabeceo (retrasada unos 270\u00ba seg\u00fan el resultado).\n",
      "- el \u00e1ngulo de ataque est\u00e1 adelantado unos 80\u00ba al \u00e1ngulo de cabeceo. **esto no es lo que esperaba**, esperaba que saliese en torno a 180\u00ba\n",
      "- la velocidad de cabeceo adimensional va casi en fase con la velocidad adimensional."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "plt.figure()\n",
      "\n",
      "#me gustar\u00eda ponerle nombre a cada fasor\n",
      "for i in range(4):\n",
      "    dx = amplitud_1[i]*np.cos(np.deg2rad(desfase_1[i]))\n",
      "    dy = amplitud_1[i]*np.sin(np.deg2rad(desfase_1[i]))\n",
      "    plt.arrow(0,0,dx,dy, length_includes_head = True, width = 0.0015)\n",
      "    plt.xlim(-0.1,1)\n",
      "    plt.ylim(-0.11,1)\n",
      "    plt.xlabel(r'$Re$', fontsize=18)\n",
      "    plt.ylabel(r'$Im$', fontsize=18)\n",
      "    plt.grid(color='g', alpha=0.5, linestyle='dashed', linewidth=0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GZGSk5XERpyhgz2Jgz2Jwdt/pljXHASAyMhKTJk1yeHxMTAxqampgNBrR3t6OrVu3WgVC\n10d9a2trkZycjHfeecdqjBJ6muhQxEnR2LMY2DPZI3uuKnvS09Md37BGg5ycHCQmJsJsNmPhwoWI\niIhAbm4uAOvvj6iJU6sTEX3HrcExZcoUWeNnzZqFWbNmdXusp8DYtGmT03W5isFBRPQdt52qupMx\nOIiIvsPgcICPjw8A22tyEBGJhsHhgJ7W5BDtExgAexYFeyZ73PZxXDX19cdxu7YxZcrD2L//7326\nHSIipaj+cVwRnD5tVLsEIiLV8YhDxjYAzldFRHcOHnH0sZ7W5CAiEg2Dw0H3369XuwQion6BweGg\n4GC91WMiTlHAnsXAnskeBoeDbK3JIeIbjT2LgT2TPQwOB92+JgcRkcgYHA7itCNERLcwOBzE4CAi\nuoXB4SAGBxHRLQwOB9kKDhHntmHPYmDPZA+Dw0FdwXH58mXLYyK+0dizGNgz2cPgcBBPVRER3cLg\ncFDXmhznzzeqXAkRkboYHA7qaU0OIiLRMDhkOnnSqHYJRESqYnDIdOaM0XJbxCkK2LMY2DPZw+CQ\n6dy5M5bbIr7R2LMY2DPZw+CQgWtyEBExOGThmhxERAwOWWytyUFEJBoGhwy21uQgIhINg0OGrjU5\nWltbAYg5RQF7FgN7JnsYHDJ8f9oREd9o7FkM7JnsYXDIwPmqiIgYHLIwOIiIGByyMDiIiPpBcBgM\nBoSHhyM0NBTZ2dlWz3/44YeIiorChAkTMG3aNFRUVKhQ5S0MDiIilYPDbDZjyZIlMBgMqKqqQl5e\nHqqrq7uNGTduHPbu3YuKigr87ne/wwsvvKBStdbBIeIUBexZDOyZ7FE1OEpLSxESEgK9Xg8vLy+k\npKQgPz+/25i4uDgMGzYMADB16lTU19erUSoA6zU5RHyjsWcxsGeyR9XgaGhoQFBQkOW+TqdDQ0ND\nj+M3bNiA2bNnK1GaTVyTg4gI0Ki58a4dsSP27NmDjRs34quvvrL5/Pz0+Zbb0bHRiI6Nht5fb/Oz\n2cYWo82/LhwarwcONpejyFiE89fO26zFpdfv5+NtGUj1czzHizzeWG5EUVGR1XOySSrat2+flJiY\naLm/evVqKSsry2rcoUOHpODgYKmmpsbm6yjZBgBp1Kj7JUmSpD21exTbbn/BnsXAnsXg7L5T1VNV\nMTExqKmpgdFoRHt7O7Zu3YqkpKRuY86cOYM5c+Zgy5YtCAkJUanS7m5fk4OISDSqnqrSaDTIyclB\nYmIizGYzFi5ciIiICOTm5gIA0tLSsHLlSjQ3N2PRokUAAC8vL5SWlqpWs1arR0ODEYCYUxSwZzGw\nZ7LH45+HKwOah4eHYjPW/uAHCdi3r4gz5BLRgOfsvlP1LwAONFyTg4hEx+CQiWtyEJHoGBwyfX9N\nDiIi0TA4ZOJ8VUQkOgaHTLcHh4hTFLBnMbBnsofBIRODw6h2CYpjz2IQsWdnMThk4qkqIhIdg0Om\nrpl6GRxEJCoGh0w84iAi0TE4ZPL19QXw3ZocRESiYXDIdPuaHCLObcOexcCeyR7OVeXk9mJjp2Pf\nvmLFtklE5G6cq0php08b1S6BiEgVPOJwcnsA56siooGNRxwKGjXqfrVLICJSDYPDCWPG6NUugYhI\nNQwOJ4wbpwcg5hQF7FkM7JnsYXA4oWtNjtrmWpUrUZ6I/7nYsxhE7NlZDA4n3HdfIACgra1N5UqI\niJTH4HBC17Qj165dU7kSIiLlMTicwOAgIpExOJzQFRzXr19XuRIiIuUxOJzQFRx+Jj+VK1GeiPP5\nsGcxiNizsxgcTugKjiE3hqhcifJE/M/FnsUgYs/OYnA4gWtyEJHIGBxO6FqTo7HxW5UrISJSHoPD\nCbevyUFEJBoGhwtOnjSqXQIRkeIYHC44efE4Jk9+GH//+9/VLkUxIk7LwJ7FIGLPzmJwuODb9gs4\ncKAKf/jDVrVLUYyI/7nYsxhE7NlZDA4n+fuPAOCHzs4d+PzzHVzUiYiEoWpwGAwGhIeHIzQ0FNnZ\n2TbHLF26FKGhoYiKisLBgwcVrtC2+vp6XLnSBuA1AD9AW5snjhw5onZZRESKUC04zGYzlixZAoPB\ngKqqKuTl5aG6urrbmIKCApw4cQI1NTV49913sWjRIpWq/Y7ZbMaTTz4DSfp3AJEAPGAyPY7PP9+h\ndmlEJKA///nPeOihBPzmNy/j888/x/nz5/t8m6oFR2lpKUJCQqDX6+Hl5YWUlBTk5+d3G7N9+3bM\nmzcPADB16lS0tLSgsbFRjXItVq5cg6oqD0jSMstj7e2PIy+PwUFEyjt+/DgOHfLFf/+3L+bNy4Ve\nPx4BAWPxk5/Mxbp1/4PS0lK0t7e7dZsat76aDA0NDQgKCrLc1+l02L9/f69j6uvrERgYqFidt/vq\nq6/wxhs5uHHjGwCDgJautcdn4OTJanz77bcYOXKkKrUpRcRpGdizGAZyz56eYTCbf48rVwCgEzdv\n1mDnzn3YvbsEgwdvxI0bNfiXf4lGQkIspk+PRVxcHHQ6ndPbUy04ur5E15vvX3R29Pfcrbm5GU8+\n+XPcuPEeAC2AfwNacizPt7dDtUAjIrF5eMTcds8TQBiAMLS1zcet9eauorKyDJWVH+Ptt+dBkm5g\n1KgBGBxarRZ1dXWW+3V1dVYJ+P0x9fX10Gq1Nl9vfvp8y+3o2GhEx0ZD76+3+VeEscVo86N39sb/\nv8XP4eJQP8DvNIAPAbwLtABoCQeQCeBLPPDAN8jI+BUumC6gqaPJ6nVGaEYgwCvA6nGO53iO53hn\nx+/YsQOff66FyfTPJ/yNt37QBuA4gCr4+FSi89IxeF4xITDwfowbp8P99wdh8+bNVq/rCA9Jpc+R\ndnR0ICwsDLt378bo0aMxZcoU5OXlISIiwjKmoKAAOTk5KCgoQElJCdLT01FSUmL1Wh4eHn3+cdgX\nX8zEN98cwbffXkBT0zk0NX033YifXxg8PO6ByXQY169fxqBBg/q0FiKiLmvXrsXLL9fBZFoCoASD\nB++Dt3cJbtyoxtixDyAhIQ4zZsQiNjYWer2+21kbZ/edqh1xaDQa5OTkIDExEWazGQsXLkRERARy\nc3MBAGlpaZg9ezYKCgoQEhICPz8/bNq0Sa1ysXbtasvtVauysHKlASZTMYAfYsyYa3jzzd/DZDIx\nNIhIUV5eXujo+B/4+3+MKVPi8OijcYiLm4tJkybBx8enT7ap2hGHOylxxNGlo6MD9903Dhcv/hFA\nAoD/hZ/f/8eGDcvw9NP/qkgNRERdbty4gYsXLzp1sdvZfSe/OS7Tjh070N5+P4AZgD8ANOH69fVY\nvPi3QiwlK+K0DOxZDAO1Zx8fH5c+IeUMBodMq1evx9WrSwB4AP7AoEE1AKajtXUaVq7MUru8PjdQ\n/3O5gj2LQcSencXgkKGyshKVlUcBzLE8NmjQcQDAjRtvYP36/8WpU6dUqo6ISBkMDhnefPNttLen\nARhseayjowrAJQCeuHlzLtLSXlSrPCIiRaj2qaqB6LPP/oRBg0wYNGgtzOY2mAF0dl6Fj08wBg/2\nweDB3jh37l6YTCZ4eXmpXS4RUZ9gcMhw4kQ1Ojo64O3tDW9vb+w7tw8JYxPULouISFEMDhlGjBjR\n7f7Ye8aqVIl6BvJ8Ps5iz2IQsWdn8XscRESC4vc4iIhIEQwOIiKShcFBRESyMDiIiEgWBocLRJyi\ngD2LgT2TPQwOF4j4RmPPYmDPZA+DwwXlJeVql6A49iwG9kz2MDhcIOIbjT2LgT2TPQwOIiKShcFB\nRESy3BFTjsTHx6O4uFjtMoiIBpQZM2agqKhI9u/dEcFBRETK4akqIiKShcFBRESyMDgcYDAYEB4e\njtDQUGRnZ9scs3TpUoSGhiIqKgoHDx5UuEL3663nDz/8EFFRUZgwYQKmTZuGiooKFap0L0f+nQGg\nrKwMGo0Gn376qYLV9Q1Hei4qKsLEiRMRGRmJ+Ph4ZQvsA7313NTUhJkzZyI6OhqRkZHYvHmz8kW6\n0XPPPYfAwEA8+OCDPY6Rvf+SyK6Ojg4pODhYqq2tldrb26WoqCipqqqq25idO3dKs2bNkiRJkkpK\nSqSpU6eqUarbONLz119/LbW0tEiSJEm7du0SoueucQkJCdJjjz0mbdu2TYVK3ceRnpubm6Xx48dL\ndXV1kiRJ0oULF9Qo1W0c6Xn58uXSyy+/LEnSrX6HDx8umUwmNcp1i71790oHDhyQIiMjbT7vzP6L\nRxy9KC0tRUhICPR6Pby8vJCSkoL8/PxuY7Zv34558+YBAKZOnYqWlhY0NjaqUa5bONJzXFwchg0b\nBuBWz/X19WqU6jaO9AwA69evR3JyMgICAlSo0r0c6fmjjz7CU089BZ1OB8B6FcyBxpGeR40ahStX\nrgAArly5gnvvvRcazcBdLPWRRx7BPffc0+Pzzuy/GBy9aGhoQFBQkOW+TqdDQ0NDr2MG8o7UkZ5v\nt2HDBsyePVuJ0vqMo//O+fn5WLRoEYBbq6cNZI70XFNTg0uXLiEhIQExMTH44IMPlC7TrRzpOTU1\nFZWVlRg9ejSioqKwbt06pctUlDP7r4EbowpxdOcgfe9TzQN5pyKn9j179mDjxo346quv+rCivudI\nz+np6cjKyrIst/n9f/OBxpGeTSYTDhw4gN27d6O1tRVxcXGIjY1FaGioAhW6nyM9r169GtHR0Sgq\nKsLJkyfx6KOP4tChQxg6dKgCFapD7v6LwdELrVaLuro6y/26ujrLYXtPY+rr66HVahWr0d0c6RkA\nKioqkJqaCoPBYPdQeCBwpOdvvvkGKSkpAG5dQN21axe8vLyQlJSkaK3u4kjPQUFBGDFiBHx8fODj\n44Pp06fj0KFDAzY4HOn566+/xrJlywAAwcHBGDt2LI4dO4aYmBhFa1WKU/svt12BuUOZTCZp3Lhx\nUm1trXTz5s1eL47v27dvwF8odqTn06dPS8HBwdK+fftUqtK9HOn5dvPnz5c++eQTBSt0P0d6rq6u\nln70ox9JHR0d0vXr16XIyEipsrJSpYpd50jPv/71r6UVK1ZIkiRJ58+fl7RarXTx4kU1ynWb2tpa\nhy6OO7r/4hFHLzQaDXJycpCYmAiz2YyFCxciIiICubm5AIC0tDTMnj0bBQUFCAkJgZ+fHzZt2qRy\n1a5xpOeVK1eiubnZcr7fy8sLpaWlapbtEkd6vtM40nN4eDhmzpyJCRMmwNPTE6mpqRg/frzKlTvP\nkZ4zMzOxYMECREVFobOzE6+//jqGDx+ucuXOmzt3LoqLi9HU1ISgoCC8+uqrMJlMAJzff3HKESIi\nkoWfqiIiIlkYHEREJAuDg4iIZGFwEBGRLAwOIiKShcFBRESyMDiIiEgWBgcREcnCb44TuaiyshIr\nV67E7t270dzcjDlz5sDb2xttbW24ePEiQkNDkZmZiTFjxqhdKpFb8JvjRG4ybdo0+Pr64m9/+5vl\nsc7OTqSmpiI/Px/l5eU2J4skGmh4qorIDa5du4aysjKrdUk8PT0xceJEXLp0CWVlZSpVR+ReDA4i\nN9i7dy86OjqsgkOSJPzpT3/C8OHD8fDDD6tUHZF78RoHkRsUFhZCr9cjLCzM8tilS5eQmZmJ1tZW\nFBcXW5abbWtrwxtvvIFLly5h5MiRqKurw5o1ayxL8RL1d7zGQeQGkyZNwuDBg/Hkk0/CbDajqKgI\n586dw9tvv43p06dbxl29ehUJCQlISUnBb3/7WwDAp59+Ck9PT/z0pz9Vq3wiWRgcRC5qbm5GQEAA\nNm/ejGeeeQYA0NHRgYSEBEybNg1ZWVmWsS+88AKKi4tx7NgxAMC5c+fwyiuvIDs7G4GBgarUTyQX\ng4PIRZ999hmeeuop1NbWdvvI7UsvvYTc3FxcvnwZAHD58mUEBgYiPj4eP/zhD2EymTB06FA888wz\nA3qhIBIPr3EQuaiwsBA6nc7qexrl5eUwm82W+8ePH0d7ezsyMjKQkJCgdJlEbsNPVRG5qLCwENOm\nTbN6vKysDHfddZfl/tChQwEAo0aNshp79OjRviuQyM0YHEQuOH/+PKqrq20Gh7e3NwYPHgwAaGpq\nQkFBASZNmoTDhw9bxphMJqxatQp1dXWK1UzkKl7jIHJCbW0tMjMzceTIEVRVVSEqKgqTJ09Gbm6u\nZcyuXbuPrBo0AAAAb0lEQVSQkZGBOXPmwGQyITMzExcuXEBGRgYiIiKg0WjQ3t6OefPmITg4WMVu\niORhcBARkSw8VUVERLIwOIiISBYGBxERycLgICIiWRgcREQkC4ODiIhkYXAQEZEsDA4iIpKFwUFE\nRLIwOIiISJb/A3anxwg7RVAFAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7cd2070>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Corto Periodo"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Se proceder\u00e1 ahroa de manera an\u00e1loga al fugoide, pero trabajando con la segunda pareja de autovalores y autovectores:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "landa[2]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "(-0.0065572781755465171+0.01564730889682945j)"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "landa[3]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "(-0.0065572781755465171-0.01564730889682945j)"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Los autovalores se pueden caracterizar por su parte real $\\hat{n}$ e imaginaria $\\omega$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('n3 = %g \\n'\n",
      "      'w3 = %g' %(n[2], w[2]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "n3 = -0.00655728 \n",
        "w3 = 0.0156473\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**tiempo para que la perturbaci\u00f3n se reduzca a la mitad:** $\\hat{t}_{1/2}$ y el **periodo del modo oscilatorio** $T$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('t0.5 = %g \\n'\n",
      "      'T = %g' %(t05[2], T[2]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "t0.5 = 105.684 \n",
        "T = 401.551\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('t0.5 = %g s\\n'\n",
      "      'T = %g s' %(t05_d[2], T_d[2]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "t0.5 = 1.86459 s\n",
        "T = 7.08458 s\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**amortiguamiento** $\\xi$ y **frecuencia natural** $\\hat{\\omega}_n$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('xi = %g \\n'\n",
      "      'wn = %g' %(xi[2], wn[2]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "xi = 0.386501 \n",
        "wn = 0.0169657\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('wn = %g s^-1' %(wn_d[0]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "wn = 0.0672885 s^-1\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Se pasa a analizar ahora la forma del modo asociado a esta pareja de autovalores complejos:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "modos[2]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "array([  1.54797745e-02+0.01216979j,   7.33677679e-01+0.j        ,\n",
        "        -7.10104441e-04+0.01149977j,   6.41326188e-01-0.22337705j])"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "modos[3]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "array([  1.54797745e-02-0.01216979j,   7.33677679e-01+0.j        ,\n",
        "        -7.10104441e-04-0.01149977j,   6.41326188e-01+0.22337705j])"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Si se referencian a $\\Delta\\theta$ todos los valores y mostramos s\u00f3lo los m\u00f3dulos:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "amplitud_2 = abs(modos[2]) / abs(modos[2][3])\n",
      "amplitud_2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "array([ 0.02899479,  1.0803445 ,  0.01696574,  1.        ])"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "se observa que:\n",
      "\n",
      "- las variaciones en velocidad adimensional son del orden del 4 % de las variaciones de \u00e1ngulo de cabeceo.\n",
      "- las variaciones de \u00e1ngulo de ataque son del orden de las variaciones del \u00e1ngulo de cabeceo.\n",
      "- la velocidad de cabeceo adimensional es del orden del 1 % de las variaciones del \u00e1ngulo de cabeceo."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Referenciando tambi\u00e9n la fase a $\\Delta\\theta$ se obtiene:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "desfase_2 = np.angle(modos[2], deg=True) - np.angle(modos[2][3], deg=True)\n",
      "desfase_2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "array([  57.376961  ,   19.20347759,  112.73697243,    0.        ])"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "se observa que:\n",
      "\n",
      "- las variaciones en velocidad adimensional est\u00e1n adelantadas unos 60\u00ba al \u00e1ngulo de cabeceo.\n",
      "- las variaciones de \u00e1ngulo de ataque est\u00e1n adelantas 16\u00ba a las variaciones del \u00e1ngulo de cabeceo.\n",
      "- la velocidad de cabeceo adimensional est\u00e1 adelantada m\u00e1s de 90\u00ba al \u00e1ngulo de cabeceo."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(4):\n",
      "    dx = amplitud_2[i]*np.cos(np.deg2rad(desfase_2[i]))\n",
      "    dy = amplitud_2[i]*np.sin(np.deg2rad(desfase_2[i]))\n",
      "    plt.arrow(0,0,dx,dy, length_includes_head = True, width = 0.0015)\n",
      "    plt.xlim(-0.1,1.1)\n",
      "    plt.ylim(-0.11,1)\n",
      "    plt.xlabel(r'$Re$', fontsize=18)\n",
      "    plt.ylabel(r'$Im$', fontsize=18)\n",
      "    plt.grid(color='g', alpha=0.5, linestyle='dashed', linewidth=0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7JubNixUAav158823RF5entDr9Raf2VyZRZlyj2Axas4mBPMpxdmzZ0VAwBPi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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7d7a430>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Evoluci\u00f3n en funci\u00f3n del tiempo"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "S\u00f3lo corto periodo"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class Modos:\n",
      "    ''' n, w son las partes re e im del autovalor\n",
      "        phi_u, phi_alfa son los desfases en grados con respecto a theta del modo\n",
      "        u, alfa son los m\u00f3dulos de las dos primeras componentes del modo referidas a theta'''\n",
      "    def __init__(self, n, w, phi_u, phi_alfa, u, alfa):\n",
      "        self.n = n\n",
      "        self.w = w\n",
      "        self.phi_u = phi_u / 180. * 3.14159\n",
      "        self.phi_alfa = phi_alfa / 180. * 3.14159\n",
      "        self.u = abs(u)\n",
      "        self.alfa = abs(alfa)\n",
      "    \n",
      "    def du(self,t):\n",
      "        n = self.n\n",
      "        w = self.w\n",
      "        phi = self.phi_u\n",
      "        u = self.u\n",
      "        return 2 * np.real(u * np.exp(n*t) * np.exp(1j*(phi+w*t)))\n",
      "    \n",
      "    def dalfa(self,t):\n",
      "        n = self.n\n",
      "        w = self.w\n",
      "        phi = self.phi_alfa\n",
      "        alfa = self.alfa\n",
      "        return 2 * np.real(alfa * np.exp(n*t) * np.exp(1j*(phi+w*t)))\n",
      "    \n",
      "    def dtheta(self,t):\n",
      "        n = self.n\n",
      "        w = self.w\n",
      "        return 2 * np.real(np.exp(n*t) * np.exp(1j*(w*t)))\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fugoide = Modos(n[0], w[0], desfase_1[0], desfase_1[1], amplitud_1[0], amplitud_1[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t_adim = np.linspace(0,40000,1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure()\n",
      "plt.plot(t_adim * tc, fugoide.du(t_adim))\n",
      "plt.xlabel('tiempo(s)', fontsize=18)\n",
      "plt.ylabel(r'$\\Delta u/us$', fontsize=18)\n",
      "plt.grid()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gThfAK/lMJudPrlvr/OYbcVVo1bFUpckxhr//DiQmmjF+vHhdAK9Mmz8fmD3b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\nEITq/D92DYCGGHOwqgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7d74f10>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "La variaci\u00f3n de la velocidad es muy alta porque se ha tomado $\\theta=2$ **RADIAN**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure()\n",
      "plt.plot(t_adim * tc, fugoide.dalfa(t_adim))\n",
      "plt.xlabel('tiempo(s)', fontsize=18)\n",
      "plt.ylabel(r'$\\alpha$', fontsize=18)\n",
      "plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IDrZuftNjDw/gzz/VaPp3bcv9KiuBkhJ+P2ufT3Ps7R2L0lL967m5uVbd78yZ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\nEARBEJJChocgCIKQlP8HiVttKA+RdEAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7d05d10>"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Casi constante"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure()\n",
      "plt.plot(t_adim * tc, fugoide.dtheta(t_adim))\n",
      "plt.xlabel('tiempo(s)', fontsize=18)\n",
      "plt.ylabel(r'$\\theta$', fontsize=18)\n",
      "plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PpcPREmRDoqN59ZNIr2/3br6uxZGFp/qMGsVfs5MnxegCeNnxv/9tufTYFl59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\nBQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7d836b0>"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "S\u00f3lo corto Fugoide"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cortoper = Modos(n[2], w[2], desfase_2[0], desfase_2[1], amplitud_2[0], amplitud_2[1])\n",
      "t_adim = np.linspace(0,1000,200)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure()\n",
      "plt.plot(t_adim * tc, cortoper.du(t_adim))\n",
      "plt.xlabel('tiempo(s)', fontsize=18)\n",
      "plt.ylabel(r'$\\Delta u/us$', fontsize=18)\n",
      "plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QIQBuuOEG2rdv36Rj9+ihrV5QU9O89yCEEMKB1/F888037Nixg7vuustRu6ynuLiYgIAA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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7cfe970>"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure()\n",
      "plt.plot(t_adim * tc, cortoper.dalfa(t_adim))\n",
      "plt.xlabel('tiempo(s)', fontsize=18)\n",
      "plt.ylabel(r'$\\Delta \\alpha$', fontsize=18)\n",
      "plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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EpIiOJOP7BMiZi5nUYSbtsKBoYPhwMQ2Js/jpJ3Ftkw0b2DchoppxyEsDOTli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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd1f70>"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure()\n",
      "plt.plot(t_adim * tc, cortoper.dtheta(t_adim))\n",
      "plt.xlabel('tiempo(s)', fontsize=18)\n",
      "plt.ylabel(r'$\\Delta \\theta$', fontsize=18)\n",
      "plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aibl53OvXgVGjgAUL1CkmWp1b1mIuZpKHmZTDgqIinQ545hnp4ECtmj5dOuFj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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7d591f0>"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Movimiento longitudinal completo"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t_adim = np.linspace(0,40000,1000)\n",
      "plt.figure()\n",
      "plt.plot(t_adim * tc, cortoper.du(t_adim)+fugoide.du(t_adim))\n",
      "plt.xlabel('tiempo(s)', fontsize=18)\n",
      "plt.ylabel(r'$\\Delta u/us$', fontsize=18)\n",
      "plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1nTridAG8ks9gcPzkurnOH34QV4VWGVNVmhRjeOYMEBdnxLhx4nUBvDJtwQJg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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff5d50>"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure()\n",
      "plt.plot(t_adim * tc, cortoper.dalfa(t_adim)+fugoide.dalfa(t_adim))\n",
      "plt.xlabel('tiempo(s)', fontsize=18)\n",
      "plt.ylabel(r'$\\Delta \\alpha$', fontsize=18)\n",
      "plt.xlim(0,100)\n",
      "plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KEBoaipCQEKxatcrkcZ1Oh549eyI6OhrR0dF46623Wtweey5ERNahyLXF7t27h/fffx8r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\nkwsRESmOyYWIiBT3f2CzReX0YtV3AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fdbe70>"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure()\n",
      "plt.plot(t_adim * tc, cortoper.dtheta(t_adim)+fugoide.dtheta(t_adim))\n",
      "plt.xlabel('tiempo(s)', fontsize=18)\n",
      "plt.ylabel(r'$\\Delta \\theta$', fontsize=18)\n",
      "plt.xlim(0,200)\n",
      "plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lPG2MHu1++22MGyeHc7dsqToSc2FNw4XefVeuszRpkupI1DlzRm6tmZgIlC2r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\ntiycEALR0dEIDg7GsGHDbO9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       "text": [
        "<matplotlib.figure.Figure at 0x81176f0>"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}