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@fjsanti
Created September 20, 2019 07:29
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Ejercicios 12.09.2019\n",
"\n",
"1. Convertir de coordenadas esféricas a cartesianas:\n",
" \n",
" $(4,\\frac{\\pi}{6},\\frac{\\pi}{4})$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"import sympy as sym\n",
"import numpy as np\n",
"\n",
"def spherical_to_cartesian(rr, theta, phi):\n",
" if 0 <= theta < 2*sym.pi and 0 <= phi < sym.pi:\n",
" xx = rr * sym.cos(theta)*sym.sin(phi)\n",
" yy = rr * sym.sin(theta)*sym.sin(phi)\n",
" zz = rr*sym.cos(phi)\n",
" return(xx, yy, zz)\n",
" else:\n",
" return('Ángulos fuera de rango')\n",
"\n",
"def cartesian_to_spherical(x, y, z): \n",
" rr = sym.sqrt(x**2 + y**2 + z**2)\n",
" theta = sym.atan2(y, x)\n",
" phi = sym.acos(z / rr )\n",
" return(rr, theta, phi )"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(2.44948974278318, 1.41421356237309, 2.82842712474619)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"spherical_to_cartesian(4,np.pi/6,np.pi/4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. Convertir de coordenadas cilíndricas a cartesianas:\n",
" \n",
" $(3,\\frac{\\pi}{2},5)$\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"import sympy as sym\n",
"import numpy as np\n",
"\n",
"def cylindrical_to_cartesian(rr, theta, zz):\n",
" if 0<= theta < 2*sym.pi:\n",
" xx = rr * sym.cos(theta)\n",
" yy = rr * sym.sin(theta)\n",
" #if theta == np.pi/2:\n",
" # xx = 0\n",
" # return(xx, yy, zz)\n",
" return(xx, yy, zz)\n",
" else:\n",
" return('Ángulos fuera de rango')\n",
"\n",
"def cartesian_to_cylindrical(x, y, z): \n",
" rr = sym.sqrt(x**2 + y**2 )\n",
" theta = sym.atan2(y, x)\n",
" return(rr, theta, z )\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1.83697019872103e-16, 3.00000000000000, 5)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cylindrical_to_cartesian(3, np.pi/2, 5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"El resutado anterior no me gusta, ya que, de hecho, el primer número debe ser \n",
"cero; así que modifiqué tu código para tomar en cuenta que pasa si el angúlo es $\\frac{\\pi}{2}$ o$\\frac{3\\pi}{2}$ en donde el coseno es cero y por tanto la coordenada $x$ también lo es."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"import sympy as sym\n",
"import numpy as np\n",
"\n",
"def cylindrical_to_cartesian(rr, theta, zz):\n",
" if 0<= theta < 2*sym.pi:\n",
" xx = rr * sym.cos(theta)\n",
" yy = rr * sym.sin(theta)\n",
" if theta == np.pi/2 or theta == 3*np.pi/2:\n",
" xx = 0\n",
" return(xx, yy, zz)\n",
" return(xx, yy, zz)\n",
" else:\n",
" return('Ángulos fuera de rango')\n",
"\n",
"def cartesian_to_cylindrical(x, y, z): \n",
" rr = sym.sqrt(x**2 + y**2 )\n",
" theta = sym.atan2(y, x)\n",
" return(rr, theta, z )"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0, 3.00000000000000, 5)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cylindrical_to_cartesian(3, np.pi/2, 5)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0, -3.00000000000000, 5)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cylindrical_to_cartesian(3, 3*np.pi/2, 5) # De hecho este caso \"voltea\" la coordenada y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Responde:\n",
"\n",
"3. ¿Qué lugar geométrico corresponde la ecuación $\\theta = constante$ en coordenadas cilíndricas?\n",
"\n",
"Un semiplano parecido a una lámina paralela al eje $z$ y que va de $0<\\rho$ y con $z\\in{\\mathbb{R}}$\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from matplotlib import animation\n",
"import matplotlib.pyplot as plt\n",
"import mpl_toolkits.mplot3d.axes3d as axes3d\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(1,1,1, projection='3d')\n",
"\n",
"RR = np.arange(0, 10, 0.1)\n",
"ZZ = np.arange(-10, 10, 0.1)\n",
"RR, ZZ = np.meshgrid(RR, ZZ)\n",
"\n",
"theta = np.pi/3\n",
"\n",
"X = RR * np.cos(theta)\n",
"Y = RR * np.sin(theta)\n",
"Z = ZZ\n",
"\n",
"plot = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=plt.get_cmap('jet') , linewidth=0 , antialiased=False , alpha=0.5)\n",
"\n",
"plt.title('Grafica con theta igual a pi tercios')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"4. ¿Qué lugar geométrico corresponde la ecuación $\\phi = constante$ en coordenadas esféricas?\n",
"\n",
"Serán anillos concentricos en $z=0$ que se hacen más y más anchos conforme $\\rho$ crece, además si $z\\in{\\mathbb{R}}$ será como dos conos que está uno debajo del otro, en mi gráfica puse a propósito un intervalo $(-15, 10)$ en $\\rho$ para ver como un cono es más grande que el otro c:"
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import mpl_toolkits.mplot3d.axes3d as axes3d\n",
"\n",
"theta, r = np.linspace(0, 2 * np.pi, 100), np.linspace(-15, 10, 60)\n",
"THETA, R = np.meshgrid(theta, r)\n",
"\n",
"PHI = np.pi/3\n",
"\n",
"X = R * np.sin(PHI) * np.cos(THETA)\n",
"Y = R * np.sin(PHI) * np.sin(THETA)\n",
"Z = R * np.cos(PHI)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(1,1,1, projection='3d')\n",
"plot = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=plt.get_cmap('jet'), linewidth=0, antialiased=False, alpha=0.5)\n",
"\n",
"\n",
"plt.show()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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