├── README.md
├── razones_python.ipynb
└── Ejercicio_1_Circulo_Inversion.ipynb


/README.md:
--------------------------------------------------------------------------------
 1 | # Python_HA
 2 | 
 3 | ## Juan Luis Cano (@Pybonacci) y Álex Sáez (@Alex__S12)
 4 | 
 5 | <a rel="license" 
 6 | href="http://creativecommons.org/licenses/by/4.0/deed.es"><img 
 7 | alt="Licencia Creative Commons" style="border-width:0" 
 8 | src="http://i.creativecommons.org/l/by/4.0/88x31.png" /></a><br /><span 
 9 | xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Curso 
10 | AeroPython</span> por <span xmlns:cc="http://creativecommons.org/ns#" 
11 | property="cc:attributionName">Juan Luis Cano Rodriguez y Alejandro Sáez 
12 | Mollejo</span> se distribuye bajo una <a rel="license" 
13 | href="http://creativecommons.org/licenses/by/4.0/deed.es">Licencia 
14 | Creative Commons Atribución 4.0 Internacional</a>.
15 | 
16 | Python para las asignaturas de Helicópteros y Aeronaves diversas.
17 | 
18 | Los notebooks se pueden previsualizar a través de
19 | http://nbviewer.ipython.org/github/AeroPython/Python_HA/tree/master/
20 | 


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/razones_python.ipynb:
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  1 | {
  2 |  "metadata": {
  3 |   "celltoolbar": "Slideshow",
  4 |   "name": "",
  5 |   "signature": "sha256:61df5e633b537aa1e6e331db529124f78211447cc3a352d58854bff78516363d"
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  7 |  "nbformat": 3,
  8 |  "nbformat_minor": 0,
  9 |  "worksheets": [
 10 |   {
 11 |    "cells": [
 12 |     {
 13 |      "cell_type": "markdown",
 14 |      "metadata": {
 15 |       "slideshow": {
 16 |        "slide_type": "slide"
 17 |       }
 18 |      },
 19 |      "source": [
 20 |       "# \u00bfPor qu\u00e9 Python?\n",
 21 |       "\n",
 22 |       "### Juan Luis Cano y Alejandro S\u00e1ez, 2014-03-17"
 23 |      ]
 24 |     },
 25 |     {
 26 |      "cell_type": "markdown",
 27 |      "metadata": {
 28 |       "slideshow": {
 29 |        "slide_type": "slide"
 30 |       }
 31 |      },
 32 |      "source": [
 33 |       "## Python y nosotros\n",
 34 |       "\n",
 35 |       "* Formaci\u00f3n autodidacta\n",
 36 |       "* Uso creciente en muchas asignaturas de la carrera\n",
 37 |       "* \u00abCurso de Python aplicado a la Ingenier\u00eda Aeron\u00e1utica\u00bb organizado por Ongawa"
 38 |      ]
 39 |     },
 40 |     {
 41 |      "cell_type": "markdown",
 42 |      "metadata": {
 43 |       "slideshow": {
 44 |        "slide_type": "slide"
 45 |       }
 46 |      },
 47 |      "source": [
 48 |       "## Ventajas de Python frente a MATLAB y Maple"
 49 |      ]
 50 |     },
 51 |     {
 52 |      "cell_type": "markdown",
 53 |      "metadata": {
 54 |       "slideshow": {
 55 |        "slide_type": "fragment"
 56 |       }
 57 |      },
 58 |      "source": [
 59 |       "Inspiraci\u00f3n:\n",
 60 |       "\n",
 61 |       "* Experiencia propia\n",
 62 |       "* http://metarabbit.wordpress.com/2013/10/18/why-python-is-better-than-matlab-for-scientific-software/\n",
 63 |       "* http://lugtigheid.ca/2013/08/matlab-vs-python/\n",
 64 |       "* http://www.pyzo.org/python_vs_matlab.html\n",
 65 |       "* http://www.stat.washington.edu/~hoytak/blog/whypython.html\n",
 66 |       "* http://phillipmfeldman.org/Python/Advantages_of_Python_Over_Matlab.html\n",
 67 |       "* http://picachu.dmt.upm.es/iimyo/inconsistencias.html\n"
 68 |      ]
 69 |     },
 70 |     {
 71 |      "cell_type": "markdown",
 72 |      "metadata": {
 73 |       "slideshow": {
 74 |        "slide_type": "slide"
 75 |       }
 76 |      },
 77 |      "source": [
 78 |       "### Software libre"
 79 |      ]
 80 |     },
 81 |     {
 82 |      "cell_type": "markdown",
 83 |      "metadata": {
 84 |       "slideshow": {
 85 |        "slide_type": "fragment"
 86 |       }
 87 |      },
 88 |      "source": [
 89 |       "* Posibilidad de estudiar su funcionamiento y corregirlo o mejorarlo"
 90 |      ]
 91 |     },
 92 |     {
 93 |      "cell_type": "markdown",
 94 |      "metadata": {
 95 |       "slideshow": {
 96 |        "slide_type": "fragment"
 97 |       }
 98 |      },
 99 |      "source": [
100 |       "* Sin restricciones para su uso o distribuci\u00f3n, incluso para uso comercial"
101 |      ]
102 |     },
103 |     {
104 |      "cell_type": "markdown",
105 |      "metadata": {
106 |       "slideshow": {
107 |        "slide_type": "fragment"
108 |       }
109 |      },
110 |      "source": [
111 |       "* Historial de cambios completo"
112 |      ]
113 |     },
114 |     {
115 |      "cell_type": "markdown",
116 |      "metadata": {
117 |       "slideshow": {
118 |        "slide_type": "fragment"
119 |       }
120 |      },
121 |      "source": [
122 |       "### Portable"
123 |      ]
124 |     },
125 |     {
126 |      "cell_type": "markdown",
127 |      "metadata": {
128 |       "slideshow": {
129 |        "slide_type": "fragment"
130 |       }
131 |      },
132 |      "source": [
133 |       "### Coste total de propiedad = cero"
134 |      ]
135 |     },
136 |     {
137 |      "cell_type": "markdown",
138 |      "metadata": {
139 |       "slideshow": {
140 |        "slide_type": "slide"
141 |       }
142 |      },
143 |      "source": [
144 |       "### El lenguaje Python\n",
145 |       "\n",
146 |       "* Prop\u00f3sito general, mucho mejor dise\u00f1ado\n",
147 |       "* Orientaci\u00f3n a objetos real y muy potente\n",
148 |       "* Paradigma extendido, m\u00e1s apropiado para equipos interdisciplinares\n",
149 |       "* Sin restricciones para la definici\u00f3n de funciones"
150 |      ]
151 |     },
152 |     {
153 |      "cell_type": "markdown",
154 |      "metadata": {
155 |       "slideshow": {
156 |        "slide_type": "subslide"
157 |       }
158 |      },
159 |      "source": [
160 |       "### Mejor organizado\n",
161 |       "\n",
162 |       "Separaci\u00f3n de funcionalidad en paquetes y bibliotecas reusables"
163 |      ]
164 |     },
165 |     {
166 |      "cell_type": "code",
167 |      "collapsed": false,
168 |      "input": [
169 |       "import numpy  # Manejo de arrays\n",
170 |       "import matplotlib  # Representaci\u00f3n gr\u00e1fica"
171 |      ],
172 |      "language": "python",
173 |      "metadata": {
174 |       "slideshow": {
175 |        "slide_type": "fragment"
176 |       }
177 |      },
178 |      "outputs": [],
179 |      "prompt_number": 1
180 |     },
181 |     {
182 |      "cell_type": "markdown",
183 |      "metadata": {
184 |       "slideshow": {
185 |        "slide_type": "subslide"
186 |       }
187 |      },
188 |      "source": [
189 |       "### M\u00e1s did\u00e1ctico\n",
190 |       "\n",
191 |       "Delimitaci\u00f3n de bloques por sangrado"
192 |      ]
193 |     },
194 |     {
195 |      "cell_type": "code",
196 |      "collapsed": false,
197 |      "input": [
198 |       "if 1 > 0:\n",
199 |       "    print(\"Uno es mayor que cero\")\n",
200 |       "else:\n",
201 |       "    print(\"Algo fue mal\")"
202 |      ],
203 |      "language": "python",
204 |      "metadata": {
205 |       "slideshow": {
206 |        "slide_type": "fragment"
207 |       }
208 |      },
209 |      "outputs": [
210 |       {
211 |        "output_type": "stream",
212 |        "stream": "stdout",
213 |        "text": [
214 |         "Uno es mayor que cero\n"
215 |        ]
216 |       }
217 |      ],
218 |      "prompt_number": 2
219 |     },
220 |     {
221 |      "cell_type": "markdown",
222 |      "metadata": {
223 |       "slideshow": {
224 |        "slide_type": "subslide"
225 |       }
226 |      },
227 |      "source": [
228 |       "### M\u00e1s consistente\n",
229 |       "\n",
230 |       "* Diferencia clara entre operaciones elemento a elemento y de \u00e1lgebra lineal"
231 |      ]
232 |     },
233 |     {
234 |      "cell_type": "code",
235 |      "collapsed": false,
236 |      "input": [
237 |       "a = numpy.array([1, 2, 3])\n",
238 |       "b = numpy.array([4, 5, 6])"
239 |      ],
240 |      "language": "python",
241 |      "metadata": {
242 |       "slideshow": {
243 |        "slide_type": "fragment"
244 |       }
245 |      },
246 |      "outputs": [],
247 |      "prompt_number": 3
248 |     },
249 |     {
250 |      "cell_type": "code",
251 |      "collapsed": false,
252 |      "input": [
253 |       "a * b  # Elemento a elemento"
254 |      ],
255 |      "language": "python",
256 |      "metadata": {
257 |       "slideshow": {
258 |        "slide_type": "fragment"
259 |       }
260 |      },
261 |      "outputs": [
262 |       {
263 |        "metadata": {},
264 |        "output_type": "pyout",
265 |        "prompt_number": 4,
266 |        "text": [
267 |         "array([ 4, 10, 18])"
268 |        ]
269 |       }
270 |      ],
271 |      "prompt_number": 4
272 |     },
273 |     {
274 |      "cell_type": "code",
275 |      "collapsed": false,
276 |      "input": [
277 |       "numpy.dot(a, b)  # Producto escalar"
278 |      ],
279 |      "language": "python",
280 |      "metadata": {
281 |       "slideshow": {
282 |        "slide_type": "fragment"
283 |       }
284 |      },
285 |      "outputs": [
286 |       {
287 |        "metadata": {},
288 |        "output_type": "pyout",
289 |        "prompt_number": 5,
290 |        "text": [
291 |         "32"
292 |        ]
293 |       }
294 |      ],
295 |      "prompt_number": 5
296 |     },
297 |     {
298 |      "cell_type": "markdown",
299 |      "metadata": {
300 |       "slideshow": {
301 |        "slide_type": "fragment"
302 |       }
303 |      },
304 |      "source": [
305 |       "* Diferencia clara entre indexaci\u00f3n (corchetes) y llamada a funciones (par\u00e9ntesis)"
306 |      ]
307 |     },
308 |     {
309 |      "cell_type": "code",
310 |      "collapsed": false,
311 |      "input": [
312 |       "a[2]"
313 |      ],
314 |      "language": "python",
315 |      "metadata": {
316 |       "slideshow": {
317 |        "slide_type": "fragment"
318 |       }
319 |      },
320 |      "outputs": [
321 |       {
322 |        "metadata": {},
323 |        "output_type": "pyout",
324 |        "prompt_number": 6,
325 |        "text": [
326 |         "3"
327 |        ]
328 |       }
329 |      ],
330 |      "prompt_number": 6
331 |     },
332 |     {
333 |      "cell_type": "markdown",
334 |      "metadata": {
335 |       "slideshow": {
336 |        "slide_type": "slide"
337 |       }
338 |      },
339 |      "source": [
340 |       "### Ecosistema con multitud de bibliotecas para m\u00faltiples prop\u00f3sitos\n",
341 |       "\n",
342 |       "* Bibliotecas cient\u00edficas gen\u00e9ricos o muy espec\u00edficas\n",
343 |       "* C\u00e1lculo num\u00e9rico y c\u00e1lculo simb\u00f3lico en el mismo lenguaje\n",
344 |       "* Scripts de sistema operativo\n",
345 |       "* Interfaces gr\u00e1ficas de usuario (GUIs)\n",
346 |       "* Servicios web"
347 |      ]
348 |     },
349 |     {
350 |      "cell_type": "markdown",
351 |      "metadata": {
352 |       "slideshow": {
353 |        "slide_type": "slide"
354 |       }
355 |      },
356 |      "source": [
357 |       "### Interfaz con otros lenguajes\n",
358 |       "\n",
359 |       "* Comunicaci\u00f3n con otros procesos (*glue language*)\n",
360 |       "* Integraci\u00f3n de c\u00f3digo legado\n",
361 |       "* Reescritura de partes cr\u00edticas en lenguajes compilados"
362 |      ]
363 |     },
364 |     {
365 |      "cell_type": "markdown",
366 |      "metadata": {
367 |       "slideshow": {
368 |        "slide_type": "slide"
369 |       }
370 |      },
371 |      "source": [
372 |       "## Desventajas de Python\n",
373 |       "\n",
374 |       "* C\u00f3digo accesible no significa c\u00f3digo f\u00e1cil de entender o arreglar\n",
375 |       "* Algunas bibliotecas son mantenidas por equipos muy reducidos de voluntarios\n",
376 |       "* M\u00e1s verborreico como contrapartida a su sintaxis m\u00e1s gen\u00e9rica\n",
377 |       "* *Paradoja de la elecci\u00f3n*: muchas opciones disponibles, documentaci\u00f3n y recursos dispersos\n",
378 |       "* Poco material de aprendizaje en espa\u00f1ol (*estamos trabajando en ello*)\n",
379 |       "* Debilidad en \u00e1reas como teor\u00eda de control\n"
380 |      ]
381 |     }
382 |    ],
383 |    "metadata": {}
384 |   }
385 |  ]
386 | }


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/Ejercicio_1_Circulo_Inversion.ipynb:
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  1 | {
  2 |  "metadata": {
  3 |   "name": "",
  4 |   "signature": "sha256:c37f1b9c0c65093e47d103be436cdaae692ae45020073c3e649e76807ad9fd09"
  5 |  },
  6 |  "nbformat": 3,
  7 |  "nbformat_minor": 0,
  8 |  "worksheets": [
  9 |   {
 10 |    "cells": [
 11 |     {
 12 |      "cell_type": "code",
 13 |      "collapsed": false,
 14 |      "input": [
 15 |       "from sympy import *\n",
 16 |       "init_printing(use_latex=True)\n",
 17 |       "\n",
 18 |       "from sympy.physics.mechanics import *"
 19 |      ],
 20 |      "language": "python",
 21 |      "metadata": {},
 22 |      "outputs": [],
 23 |      "prompt_number": 1
 24 |     },
 25 |     {
 26 |      "cell_type": "code",
 27 |      "collapsed": false,
 28 |      "input": [
 29 |       "# Definimos nuestra propia clase para que los versores sean IJK\n",
 30 |       "# Por Juan Luis Cano \n",
 31 |       "class IJKReferenceFrame(ReferenceFrame):\n",
 32 |       "    def __init__(self, name):\n",
 33 |       "        super().__init__(name, latexs=['\\mathbf{%s}_{%s}' % (idx, name) for idx in (\"i\", \"j\", \"k\")])"
 34 |      ],
 35 |      "language": "python",
 36 |      "metadata": {},
 37 |      "outputs": [],
 38 |      "prompt_number": 2
 39 |     },
 40 |     {
 41 |      "cell_type": "markdown",
 42 |      "metadata": {},
 43 |      "source": [
 44 |       "En primer lugar se crean los sistemas de referencia:\n",
 45 |       "\n",
 46 |       "* Tierra (0)\n",
 47 |       "* Arbol (A)\n",
 48 |       "* Auxiliar 1 (A1)"
 49 |      ]
 50 |     },
 51 |     {
 52 |      "cell_type": "code",
 53 |      "collapsed": false,
 54 |      "input": [
 55 |       "Tierra = IJKReferenceFrame('0')\n",
 56 |       "Arbol = IJKReferenceFrame('A')\n",
 57 |       "A1 = IJKReferenceFrame('A1')"
 58 |      ],
 59 |      "language": "python",
 60 |      "metadata": {},
 61 |      "outputs": [],
 62 |      "prompt_number": 3
 63 |     },
 64 |     {
 65 |      "cell_type": "markdown",
 66 |      "metadata": {},
 67 |      "source": [
 68 |       "Se orienta el sistema $A$ con respecto al $0$ y $A1$ con respecto al sistema $A$"
 69 |      ]
 70 |     },
 71 |     {
 72 |      "cell_type": "code",
 73 |      "collapsed": false,
 74 |      "input": [
 75 |       "Arbol.orient(Tierra, 'body', (pi,0,pi), 'zyx')\n",
 76 |       "\n",
 77 |       "psi = dynamicsymbols('\\psi')\n",
 78 |       "A1.orient(Arbol, 'body', (psi, 0, 0), 'zyx')"
 79 |      ],
 80 |      "language": "python",
 81 |      "metadata": {},
 82 |      "outputs": [],
 83 |      "prompt_number": 4
 84 |     },
 85 |     {
 86 |      "cell_type": "code",
 87 |      "collapsed": false,
 88 |      "input": [
 89 |       "Arbol.dcm(Tierra)"
 90 |      ],
 91 |      "language": "python",
 92 |      "metadata": {},
 93 |      "outputs": [
 94 |       {
 95 |        "latex": [
 96 |         "$$\\left[\\begin{matrix}-1 & 0 & 0\\\\0 & 1 & 0\\\\0 & 0 & -1\\end{matrix}\\right]$$"
 97 |        ],
 98 |        "metadata": {},
 99 |        "output_type": "pyout",
100 |        "png": "iVBORw0KGgoAAAANSUhEUgAAAHkAAABLCAMAAABjltjdAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\ni5TiB99WKvy9ytOqAAAAAElFTkSuQmCC\n",
101 |        "prompt_number": 5,
102 |        "text": [
103 |         "\u23a1-1  0  0 \u23a4\n",
104 |         "\u23a2         \u23a5\n",
105 |         "\u23a20   1  0 \u23a5\n",
106 |         "\u23a2         \u23a5\n",
107 |         "\u23a30   0  -1\u23a6"
108 |        ]
109 |       }
110 |      ],
111 |      "prompt_number": 5
112 |     },
113 |     {
114 |      "cell_type": "code",
115 |      "collapsed": false,
116 |      "input": [
117 |       "Arbol.dcm(A1)"
118 |      ],
119 |      "language": "python",
120 |      "metadata": {},
121 |      "outputs": [
122 |       {
123 |        "latex": [
124 |         "$$\\left[\\begin{matrix}\\cos{\\left (\\psi{\\left (t \\right )} \\right )} & - \\sin{\\left (\\psi{\\left (t \\right )} \\right )} & 0\\\\\\sin{\\left (\\psi{\\left (t \\right )} \\right )} & \\cos{\\left (\\psi{\\left (t \\right )} \\right )} & 0\\\\0 & 0 & 1\\end{matrix}\\right]$$"
125 |        ],
126 |        "metadata": {},
127 |        "output_type": "pyout",
128 |        "png": "iVBORw0KGgoAAAANSUhEUgAAAQAAAABLCAMAAACoRKlPAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nob4v+Mzzo5NeBk//SAk+d/0f13xgVuFjXusAAAAASUVORK5CYII=\n",
129 |        "prompt_number": 6,
130 |        "text": [
131 |         "\u23a1cos(\\psi(t))  -sin(\\psi(t))  0\u23a4\n",
132 |         "\u23a2                              \u23a5\n",
133 |         "\u23a2sin(\\psi(t))  cos(\\psi(t))   0\u23a5\n",
134 |         "\u23a2                              \u23a5\n",
135 |         "\u23a3     0              0        1\u23a6"
136 |        ]
137 |       }
138 |      ],
139 |      "prompt_number": 6
140 |     },
141 |     {
142 |      "cell_type": "markdown",
143 |      "metadata": {},
144 |      "source": [
145 |       "Una vez orientados los sistemas de referencia se puede obtener la matriz de cosenos directores que cambia de uno a otro, pero ni siquiera la vamos a necesitar.\n",
146 |       "\n",
147 |       "Se define el punto $A$. Los puntos no se definen ligados a sistemas de referencia, pero s\u00ed sus velocidades. Esto resulta un poco extra\u00f1o..."
148 |      ]
149 |     },
150 |     {
151 |      "cell_type": "code",
152 |      "collapsed": false,
153 |      "input": [
154 |       "A = Point('A')\n",
155 |       "\n",
156 |       "V = symbols('V')\n",
157 |       "A.set_vel(Tierra, V*Tierra.x)\n",
158 |       "A.set_vel(Arbol, 0)\n",
159 |       "\n",
160 |       "#la velocidad del punto A respecto a los ejes tierra es:\n",
161 |       "A.vel(Tierra)"
162 |      ],
163 |      "language": "python",
164 |      "metadata": {},
165 |      "outputs": [
166 |       {
167 |        "latex": [
168 |         "$$V\\mathbf{i}_{0}$$"
169 |        ],
170 |        "metadata": {},
171 |        "output_type": "pyout",
172 |        "png": "iVBORw0KGgoAAAANSUhEUgAAAB8AAAASBAMAAABRHhjUAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdt3NVDLvmRCrIolE\nZrtDPvbtAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwElEQVQYGWNggIFnDhCW0H8TBoagbwUs/w0g\nAhyfgTTLBAau/xMgAgxpQJoTiEOgfAZ7IEMUxgHR8xcwcG1gYOCHa9l/gIEdKM5lDzPjvgDDVZDK\n+gkMjBuBShnOF4B0gAVuM3gCGf0PQHaABVQZ+BuApincgQpw/GJgc2BgYPpVABVg/cHAdIGBge8f\nUBkQ1E8ACQgwMLD/AfNBAkAtQAHeCWAB/v//Ob4y8B+AyEJJHbAtSELiYHcgCXBXVzAAAGynMDTr\nYy0NAAAAAElFTkSuQmCC\n",
173 |        "prompt_number": 8,
174 |        "text": [
175 |         "V \u001b[94m\u001b[1m0_x\u001b[0;0m\u001b[0;0m"
176 |        ]
177 |       }
178 |      ],
179 |      "prompt_number": 8
180 |     },
181 |     {
182 |      "cell_type": "code",
183 |      "collapsed": false,
184 |      "input": [
185 |       "# y si la expresamos en ejes arbol:\n",
186 |       "A.vel(Tierra).express(Arbol)"
187 |      ],
188 |      "language": "python",
189 |      "metadata": {},
190 |      "outputs": [
191 |       {
192 |        "latex": [
193 |         "$$-  V\\mathbf{i}_{A}$$"
194 |        ],
195 |        "metadata": {},
196 |        "output_type": "pyout",
197 |        "png": "iVBORw0KGgoAAAANSUhEUgAAADMAAAASBAMAAAAEf/uKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEM3dMnZU75mrIolE\nZrsdjuuDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVQYGWNgQAfPE9BFgv+rMTA4f29g+6+A\nLsX4CSjCNoGB6/8EdCmGcqAIJxC7Ycgw6AOFQjCFQSLzFzBwbWBg4Mdi4P4DDBxAFVz6mHbdD2C4\nAtLdD5biWwBiQ8H5BpB5MKn7BxgYhIxBQIWBQf4ByH1QKcb+C2AOhOA3uANmgA3kFm5AkmL+BeGB\npVz5HiBJ8f0TAPPAUhM4DJCkOP5AOCAp3gTWD0hSvEAhIOD//5+BQbij7yOSFDKzi4HlCzIfwWa7\nwMDwF8FFZr1/wLDu8wUA3DA2zCgOhDMAAAAASUVORK5CYII=\n",
198 |        "prompt_number": 9,
199 |        "text": [
200 |         "- V \u001b[94m\u001b[1ma_x\u001b[0;0m\u001b[0;0m"
201 |        ]
202 |       }
203 |      ],
204 |      "prompt_number": 9
205 |     },
206 |     {
207 |      "cell_type": "markdown",
208 |      "metadata": {},
209 |      "source": [
210 |       "Se define ahora un punto $P$ a distancia $r$ sobre la pala:"
211 |      ]
212 |     },
213 |     {
214 |      "cell_type": "code",
215 |      "collapsed": false,
216 |      "input": [
217 |       "r = symbols('r')\n",
218 |       "P = A.locatenew('P', r*A1.x)"
219 |      ],
220 |      "language": "python",
221 |      "metadata": {},
222 |      "outputs": [],
223 |      "prompt_number": 10
224 |     },
225 |     {
226 |      "cell_type": "markdown",
227 |      "metadata": {},
228 |      "source": [
229 |       "Conocida la velocidad de $A$ y la posici\u00f3n de $P$ con respecto a $A$, sabiendo que est\u00e1n en el mismo sistema de referencia ($A1$) se puede obtener la velocidad de $P$:"
230 |      ]
231 |     },
232 |     {
233 |      "cell_type": "code",
234 |      "collapsed": false,
235 |      "input": [
236 |       "#velocidad del punto P en ejes tierra\n",
237 |       "vel_P_0 = P.v2pt_theory(A, Tierra, A1)\n",
238 |       "vel_P_0"
239 |      ],
240 |      "language": "python",
241 |      "metadata": {},
242 |      "outputs": [
243 |       {
244 |        "latex": [
245 |         "$$V\\mathbf{i}_{0} + r \\dot{\\psi}\\mathbf{j}_{A1}$$"
246 |        ],
247 |        "metadata": {},
248 |        "output_type": "pyout",
249 |        "png": "iVBORw0KGgoAAAANSUhEUgAAAGsAAAAYBAMAAAAPJx5QAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
250 |        "prompt_number": 11,
251 |        "text": [
252 |         "V \u001b[94m\u001b[1m0_x\u001b[0;0m\u001b[0;0m + r\u22c5\\ps\u0307i \u001b[94m\u001b[1ma1_y\u001b[0;0m\u001b[0;0m"
253 |        ]
254 |       }
255 |      ],
256 |      "prompt_number": 11
257 |     },
258 |     {
259 |      "cell_type": "code",
260 |      "collapsed": false,
261 |      "input": [
262 |       "#se puede expresar en otros ejes\n",
263 |       "vel_P_0.express(A1)"
264 |      ],
265 |      "language": "python",
266 |      "metadata": {},
267 |      "outputs": [
268 |       {
269 |        "latex": [
270 |         "$$-  V \\operatorname{cos}\\left(\\psi\\right)\\mathbf{i}_{A1} + (V \\operatorname{sin}\\left(\\psi\\right) + r \\dot{\\psi})\\mathbf{j}_{A1}$$"
271 |        ],
272 |        "metadata": {},
273 |        "output_type": "pyout",
274 |        "png": "iVBORw0KGgoAAAANSUhEUgAAAUUAAAAZBAMAAABUYSFWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
275 |        "prompt_number": 12,
276 |        "text": [
277 |         "- V\u22c5cos(\\psi) \u001b[94m\u001b[1ma1_x\u001b[0;0m\u001b[0;0m + (V\u22c5sin(\\psi) + r\u22c5\\ps\u0307i) \u001b[94m\u001b[1ma1_y\u001b[0;0m\u001b[0;0m"
278 |        ]
279 |       }
280 |      ],
281 |      "prompt_number": 12
282 |     },
283 |     {
284 |      "cell_type": "code",
285 |      "collapsed": false,
286 |      "input": [
287 |       "omega = symbols('\\Omega')\n",
288 |       "vel_P_0 = vel_P_0.express(A1).subs(diff(psi), omega)\n",
289 |       "vel_P_0"
290 |      ],
291 |      "language": "python",
292 |      "metadata": {},
293 |      "outputs": [
294 |       {
295 |        "latex": [
296 |         "$$-  V \\operatorname{cos}\\left(\\psi\\right)\\mathbf{i}_{A1} + (V \\operatorname{sin}\\left(\\psi\\right) + \\Omega r)\\mathbf{j}_{A1}$$"
297 |        ],
298 |        "metadata": {},
299 |        "output_type": "pyout",
300 |        "png": "iVBORw0KGgoAAAANSUhEUgAAAUYAAAAVBAMAAADIlFouAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
301 |        "prompt_number": 14,
302 |        "text": [
303 |         "- V\u22c5cos(\\psi) \u001b[94m\u001b[1ma1_x\u001b[0;0m\u001b[0;0m + (V\u22c5sin(\\psi) + \\Omega\u22c5r) \u001b[94m\u001b[1ma1_y\u001b[0;0m\u001b[0;0m"
304 |        ]
305 |       }
306 |      ],
307 |      "prompt_number": 14
308 |     },
309 |     {
310 |      "cell_type": "code",
311 |      "collapsed": false,
312 |      "input": [
313 |       "#velocidad del punto P en ejes Arbol\n",
314 |       "vel_P_A = P.v2pt_theory(A, Arbol, A1)\n",
315 |       "vel_P_A"
316 |      ],
317 |      "language": "python",
318 |      "metadata": {},
319 |      "outputs": [
320 |       {
321 |        "latex": [
322 |         "$$r \\dot{\\psi}\\mathbf{j}_{A1}$$"
323 |        ],
324 |        "metadata": {},
325 |        "output_type": "pyout",
326 |        "png": "iVBORw0KGgoAAAANSUhEUgAAADIAAAAYBAMAAABKJrPSAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMARImrEHa7zVTvMt2Z\nImbh7FZmAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABK0lEQVQoFWNggAFuAxgLnfYvQBehDZ8LaOzK\nLdjMZgIK2n/FJRP/EZvMPaAghwA2mbfYBMFiCgwMjP8/IUkzKjuqBrDoBDAosG5guI0sw8RWwTaB\nieMDbwPrFwY2sAzbBQaGZQwMK7gNGBfc4NnA58AwASrzXoBhjTUDg4M/0D0OnApA7xyAyLCcf8DA\n0A20sB9kqfwFJgaWAIgMk/cBiMxxkIw2ww0GJgeIzFK2BIjMJKAEwzGGJwyNDBAZA54NYBlecIBI\nMgTwAe0DuY2vgfUDWIYRqAAYLCfyYoEUSMb7zLEvENNAEgwMXA0MDCwLQDJnGbh+IcuwOjAw8P/i\n/MHA8YCB4R8DQydQNQSAYof/4/oNDPkJDNd+P7iz3xQmwwpkMFbvcYDxGRgAJKJKfF0yAikAAAAA\nSUVORK5CYII=\n",
327 |        "prompt_number": 15,
328 |        "text": [
329 |         "r\u22c5\\ps\u0307i \u001b[94m\u001b[1ma1_y\u001b[0;0m\u001b[0;0m"
330 |        ]
331 |       }
332 |      ],
333 |      "prompt_number": 15
334 |     },
335 |     {
336 |      "cell_type": "code",
337 |      "collapsed": false,
338 |      "input": [
339 |       "vel_P_A.express(Arbol)"
340 |      ],
341 |      "language": "python",
342 |      "metadata": {},
343 |      "outputs": [
344 |       {
345 |        "latex": [
346 |         "$$-  r \\operatorname{sin}\\left(\\psi\\right) \\dot{\\psi}\\mathbf{i}_{A} + r \\operatorname{cos}\\left(\\psi\\right) \\dot{\\psi}\\mathbf{j}_{A}$$"
347 |        ],
348 |        "metadata": {},
349 |        "output_type": "pyout",
350 |        "png": "iVBORw0KGgoAAAANSUhEUgAAAQcAAAAZBAMAAADOLvbLAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\niAAAAABJRU5ErkJggg==\n",
351 |        "prompt_number": 16,
352 |        "text": [
353 |         "- r\u22c5sin(\\psi)\u22c5\\ps\u0307i \u001b[94m\u001b[1ma_x\u001b[0;0m\u001b[0;0m + r\u22c5cos(\\psi)\u22c5\\ps\u0307i \u001b[94m\u001b[1ma_y\u001b[0;0m\u001b[0;0m"
354 |        ]
355 |       }
356 |      ],
357 |      "prompt_number": 16
358 |     },
359 |     {
360 |      "cell_type": "markdown",
361 |      "metadata": {},
362 |      "source": [
363 |       "La componente tangencial de la velocidad es:"
364 |      ]
365 |     },
366 |     {
367 |      "cell_type": "code",
368 |      "collapsed": false,
369 |      "input": [
370 |       "V_T  = vel_P_0.dot(A1.y)\n",
371 |       "V_T"
372 |      ],
373 |      "language": "python",
374 |      "metadata": {},
375 |      "outputs": [
376 |       {
377 |        "latex": [
378 |         "$$V \\sin{\\left (\\psi{\\left (t \\right )} \\right )} + \\Omega r$$"
379 |        ],
380 |        "metadata": {},
381 |        "output_type": "pyout",
382 |        "png": "iVBORw0KGgoAAAANSUhEUgAAAJkAAAAVBAMAAACnAFEqAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nQmCC\n",
383 |        "prompt_number": 17,
384 |        "text": [
385 |         "V\u22c5sin(\\psi(t)) + \\Omega\u22c5r"
386 |        ]
387 |       }
388 |      ],
389 |      "prompt_number": 17
390 |     },
391 |     {
392 |      "cell_type": "code",
393 |      "collapsed": false,
394 |      "input": [
395 |       "solucion_r = solve(V_T, r)\n",
396 |       "solucion_r"
397 |      ],
398 |      "language": "python",
399 |      "metadata": {},
400 |      "outputs": [
401 |       {
402 |        "latex": [
403 |         "$$\\begin{bmatrix}- \\frac{V}{\\Omega} \\sin{\\left (\\psi{\\left (t \\right )} \\right )}\\end{bmatrix}$$"
404 |        ],
405 |        "metadata": {},
406 |        "output_type": "pyout",
407 |        "png": "iVBORw0KGgoAAAANSUhEUgAAAIIAAAAaBAMAAACJGJngAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
408 |        "prompt_number": 18,
409 |        "text": [
410 |         "\u23a1-V\u22c5sin(\\psi(t)) \u23a4\n",
411 |         "\u23a2\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
412 |         "\u23a3     \\Omega     \u23a6"
413 |        ]
414 |       }
415 |      ],
416 |      "prompt_number": 18
417 |     },
418 |     {
419 |      "cell_type": "markdown",
420 |      "metadata": {},
421 |      "source": [
422 |       "Esta expresi\u00f3n se puede particulariza utilizando `.subs()` o transformarla con `simpify` para obtener un mejor rendimiento"
423 |      ]
424 |     },
425 |     {
426 |      "cell_type": "code",
427 |      "collapsed": false,
428 |      "input": [
429 |       "for ii in range(1,6):\n",
430 |       "    radio = solucion_r[0].subs([(V,100), (omega, 12), (psi,ii*(2*pi/5))])\n",
431 |       "    print(radio)"
432 |      ],
433 |      "language": "python",
434 |      "metadata": {},
435 |      "outputs": [
436 |       {
437 |        "output_type": "stream",
438 |        "stream": "stdout",
439 |        "text": [
440 |         "-25*sqrt(sqrt(5)/8 + 5/8)/3\n",
441 |         "-25*sqrt(-sqrt(5)/8 + 5/8)/3\n",
442 |         "25*sqrt(-sqrt(5)/8 + 5/8)/3\n",
443 |         "25*sqrt(sqrt(5)/8 + 5/8)/3\n",
444 |         "0\n"
445 |        ]
446 |       }
447 |      ],
448 |      "prompt_number": 19
449 |     },
450 |     {
451 |      "cell_type": "markdown",
452 |      "metadata": {},
453 |      "source": [
454 |       "Para representar el c\u00edrculo de inversi\u00f3n:"
455 |      ]
456 |     },
457 |     {
458 |      "cell_type": "code",
459 |      "collapsed": false,
460 |      "input": [
461 |       "sol_particular = solucion_r[0].subs([(V,100), (omega, 12)])\n",
462 |       "\n",
463 |       "#la funci\u00f3n plot no acepta pintar en funci\u00f3n de psi porque\n",
464 |       "#es una funci\u00f3n de t. Hay que transformarlo en un s\u00edmbolo primero\n",
465 |       "\n",
466 |       "x = symbols('x')\n",
467 |       "sol_particular = sol_particular.subs(psi, x)\n",
468 |       "\n",
469 |       "%matplotlib inline\n",
470 |       "\n",
471 |       "plot(sol_particular, (x, 0, 2*pi))"
472 |      ],
473 |      "language": "python",
474 |      "metadata": {},
475 |      "outputs": [
476 |       {
477 |        "metadata": {},
478 |        "output_type": "display_data",
479 |        "png": 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PuahfX/7jCBEqYdnBl/L7oVOnWAYMcNGzpyck7yECt3evif79Y9mzJ4+4OK3T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\n",
480 |        "text": [
481 |         "<matplotlib.figure.Figure at 0x7f7685bfdf28>"
482 |        ]
483 |       },
484 |       {
485 |        "metadata": {},
486 |        "output_type": "pyout",
487 |        "prompt_number": 20,
488 |        "text": [
489 |         "<sympy.plotting.plot.Plot at 0x7f7687f04cf8>"
490 |        ]
491 |       }
492 |      ],
493 |      "prompt_number": 20
494 |     },
495 |     {
496 |      "cell_type": "code",
497 |      "collapsed": false,
498 |      "input": [
499 |       "import matplotlib.pyplot as plt\n",
500 |       "import numpy as np"
501 |      ],
502 |      "language": "python",
503 |      "metadata": {},
504 |      "outputs": [],
505 |      "prompt_number": 21
506 |     },
507 |     {
508 |      "cell_type": "code",
509 |      "collapsed": false,
510 |      "input": [
511 |       "# sympy todav\u00eda no est\u00e1 bien preparado para pintar en polares\n",
512 |       "# se podr\u00eda hacer usando plot_parametrics\n",
513 |       "# pero se ha usado matplotlib\n",
514 |       "\n",
515 |       "xx = np.linspace(0,2*np.pi,100)\n",
516 |       "y = lambdify(x, sol_particular, 'numpy')\n",
517 |       "yy = y(xx)\n",
518 |       "\n",
519 |       "plt.polar(xx, yy, lw=2)"
520 |      ],
521 |      "language": "python",
522 |      "metadata": {},
523 |      "outputs": [
524 |       {
525 |        "metadata": {},
526 |        "output_type": "pyout",
527 |        "prompt_number": 22,
528 |        "text": [
529 |         "[<matplotlib.lines.Line2D at 0x7f767efc6048>]"
530 |        ]
531 |       },
532 |       {
533 |        "metadata": {},
534 |        "output_type": "display_data",
535 |        "png": 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Mw+Cdd94hOodUKmUNiUqlQllZGdH5BsJXeiZvvvkmKxTN5/O9bkh0Oh0qKyvZ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\nLxOuBZR6FtkAAAAASUVORK5CYII=\n",
536 |        "text": [
537 |         "<matplotlib.figure.Figure at 0x7f7687f04198>"
538 |        ]
539 |       }
540 |      ],
541 |      "prompt_number": 22
542 |     },
543 |     {
544 |      "cell_type": "markdown",
545 |      "metadata": {},
546 |      "source": [
547 |       "Si se quieren pintar varios casos de velocidad:"
548 |      ]
549 |     },
550 |     {
551 |      "cell_type": "code",
552 |      "collapsed": false,
553 |      "input": [
554 |       "velocidades = np.linspace(0.1,100,6)\n",
555 |       "solucion = solucion_r[0].subs([(omega, 12), (psi, x)])\n",
556 |       "plt.figure()\n",
557 |       "\n",
558 |       "for ii in velocidades:\n",
559 |       "    solucion_caso = solucion.subs(V,ii)\n",
560 |       "    solucion_caso_num = lambdify(x, solucion_caso, 'numpy')\n",
561 |       "    \n",
562 |       "    xx = np.linspace(0,2*np.pi,100)\n",
563 |       "    yy = solucion_caso_num(xx)\n",
564 |       "    \n",
565 |       "    plt.polar(xx, yy, lw=2, color='b', alpha=ii/100)"
566 |      ],
567 |      "language": "python",
568 |      "metadata": {},
569 |      "outputs": [
570 |       {
571 |        "metadata": {},
572 |        "output_type": "display_data",
573 |        "png": 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GiMViv/xRnIHjOLz77rtE51AoFIIg0Wg0KCwsJDpfT/iqnslbb70lFIoWiURe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\n4f8BITMIJJ/dtGYAAAAASUVORK5CYII=\n",
574 |        "text": [
575 |         "<matplotlib.figure.Figure at 0x7f767efbf080>"
576 |        ]
577 |       }
578 |      ],
579 |      "prompt_number": 23
580 |     },
581 |     {
582 |      "cell_type": "heading",
583 |      "level": 2,
584 |      "metadata": {},
585 |      "source": [
586 |       "Deslizadores"
587 |      ]
588 |     },
589 |     {
590 |      "cell_type": "code",
591 |      "collapsed": false,
592 |      "input": [
593 |       "def circulo_inversion(OMEGA, VEL):\n",
594 |       "    solucion = solucion_r[0].subs([(omega, OMEGA), (psi, x)])\n",
595 |       "    plt.figure()\n",
596 |       "\n",
597 |       "    solucion_caso = solucion.subs(V,VEL)\n",
598 |       "    solucion_caso_num = lambdify(x, solucion_caso, 'numpy')\n",
599 |       "\n",
600 |       "    xx = np.linspace(0,2*np.pi,150)\n",
601 |       "    yy = solucion_caso_num(xx)\n",
602 |       "\n",
603 |       "    fig, ax = plt.subplots(1,1, subplot_kw=dict(polar=True))\n",
604 |       "    \n",
605 |       "    fig.set_size_inches((6,6))\n",
606 |       "    ax.plot(xx, yy, lw=2, color='b', alpha=ii/100)\n",
607 |       "    ax.fill_between(xx, yy, alpha=0.5, color='gray')\n",
608 |       "    \n",
609 |       "    ax.set_rmax(15)"
610 |      ],
611 |      "language": "python",
612 |      "metadata": {},
613 |      "outputs": [],
614 |      "prompt_number": 24
615 |     },
616 |     {
617 |      "cell_type": "code",
618 |      "collapsed": false,
619 |      "input": [
620 |       "from IPython.html.widgets import interact\n",
621 |       "from IPython.display import clear_output, display"
622 |      ],
623 |      "language": "python",
624 |      "metadata": {},
625 |      "outputs": [],
626 |      "prompt_number": 25
627 |     },
628 |     {
629 |      "cell_type": "code",
630 |      "collapsed": false,
631 |      "input": [
632 |       "interactive = interact(circulo_inversion, OMEGA=(0.,20), VEL=(0.5,100))"
633 |      ],
634 |      "language": "python",
635 |      "metadata": {},
636 |      "outputs": [
637 |       {
638 |        "metadata": {},
639 |        "output_type": "display_data",
640 |        "text": [
641 |         "<matplotlib.figure.Figure at 0x7f767ef50ef0>"
642 |        ]
643 |       },
644 |       {
645 |        "metadata": {},
646 |        "output_type": "display_data",
647 |        "png": 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MK1ascPom7nm9Vqu1qytZa2sr64gX80Nh3rx5bq003LEfh0wmY5WGxWLB2rVr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8kEo9GImJgYTJ48Gbm5uYoQM0pkUdbdT1EcsbGxmDp1KpYtW4aioiIMDw/j1KlTQv9npaw7Fi9e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\nSUVORK5CYII=\n",
648 |        "text": [
649 |         "<matplotlib.figure.Figure at 0x7f767ef4df98>"
650 |        ]
651 |       }
652 |      ],
653 |      "prompt_number": 26
654 |     },
655 |     {
656 |      "cell_type": "code",
657 |      "collapsed": false,
658 |      "input": [],
659 |      "language": "python",
660 |      "metadata": {},
661 |      "outputs": [],
662 |      "prompt_number": 24
663 |     }
664 |    ],
665 |    "metadata": {}
666 |   }
667 |  ]
668 | }


--------------------------------------------------------------------------------