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{ | |
"metadata": { | |
"name": "" | |
}, | |
"nbformat": 3, | |
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"worksheets": [ | |
{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"from sympy.abc import a\n", | |
"from sympy.physics.vector import dynamicsymbols, ReferenceFrame" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 1 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"a" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 2, | |
"text": [ | |
"a" | |
] | |
} | |
], | |
"prompt_number": 2 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega = dynamicsymbols('omega1')\n", | |
"omega" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 3, | |
"text": [ | |
"omega1(t)" | |
] | |
} | |
], | |
"prompt_number": 3 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega.diff()" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 4, | |
"text": [ | |
"Derivative(omega1(t), t)" | |
] | |
} | |
], | |
"prompt_number": 4 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"A = ReferenceFrame('A')" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 5 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"v = a * A.x + omega * A.y + omega.diff() * A.z\n", | |
"v" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 6, | |
"text": [ | |
"a*A.x + omega1*A.y + omega1'*A.z" | |
] | |
} | |
], | |
"prompt_number": 6 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"from sympy import init_printing\n", | |
"init_printing()" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 7 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"a" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"latex": [ | |
"$$a$$" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAAJBAMAAAAWSsseAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIquJdjLdEETvu2aZ\nVM0GsGrEAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAR0lEQVQIHWNgYFR2TWdgYOgU4PrAwMA+m4Fn\nAQMDz3cGNgcGBs4FDPUBDAz1Bgz3GQoY6i8wrOMVYOBz4E5iBqpUMRXyYAAAgLMMA5qDwz8AAAAA\nSUVORK5CYII=\n", | |
"prompt_number": 8, | |
"text": [ | |
"a" | |
] | |
} | |
], | |
"prompt_number": 8 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"latex": [ | |
"$$\\omega_{1}{\\left (t \\right )}$$" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"png": "iVBORw0KGgoAAAANSUhEUgAAACsAAAAVBAMAAAAtAwouAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAuyLvRGYQdpmJVN0y\nzauXc2k5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABC0lEQVQYGY2RsUvDQBjFf9YmbdIoUhA3jXTR\nXRCcOrgVpDh3qDg4GnByu39AEDrYSQKODgY3XYybm8HB2c3BJYOr4rseCsnkwXvv+358d5cj8I8V\nDe3QqD65PgOLeY2/gn8LRRW3ziEs4bSK52Noa/SwigdqO9qxkMKS6l5fBlPYW1tNCAyeJccJj4pl\n6UbyCtoKgvTpQ3EvnUlhxi5keDHXarekOykqSYgMAb/Y/3TY0ErZdFiHNEvGNDO6PBteHNaVQRHm\n9srJdOd7om+1Z1/qNW9HMsPBV36yLWTxABoriZ7TV+OWxZ3Y1T0X1q8kz9gKLlzINx7e5d1Z7xd/\n2BXuN8zFNdwYWrAPP5hHNrCIy2tAAAAAAElFTkSuQmCC\n", | |
"prompt_number": 9, | |
"text": [ | |
"\u03c9\u2081(t)" | |
] | |
} | |
], | |
"prompt_number": 9 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega.diff()" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"latex": [ | |
"$$\\frac{d}{d t} \\omega_{1}{\\left (t \\right )}$$" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"png": "iVBORw0KGgoAAAANSUhEUgAAAEAAAAArBAMAAAA6dJN0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMARLvvmVQQid3NIqt2\nMmaorGxOAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAB40lEQVQ4EYWSP0gjURDGv43Jrgma809jl4CV\nNieijcixhY1YuGAjwuGijXJFAqZQUEh3cBan4DVyRTgFC0HERosIKxZpPBCxsjAWFtqpkBxicc68\nyaJx1+fA7sx889vs2/kCcLT1qaS5VTQzHhnVDwAr/wEQt7XA9mLZ0QHGAD67OmD6CsO6OUZdfNcC\nvTDvdYD5D7E7U0OYFURWJjQAfuNmN6sDvpUuii0B4JKV5GlA94VEWlWHfh/IcReYKSAeGPhCiYpJ\noOndww0QQPs1e/wn3mQjTwLv99frQZqaDfkey4ax91AEcq+AJM8yHs4oRa5A+6Xili4/olxYzvkB\npUYHiK5QMc5iLVqBPJIFpTXQrzVmaVDGfz/uPDTbsOQhBjJ0EfASNpocbAnAr0iBPO54maMbZRvr\nAvAhF/C1/pBzuf6nOXovn8vaBUZMDxiixo+px9PjQWoY4EX9OaFila63ob7sh6iJHs5Gpy2t3Mc4\nXUtteSp/ctjaWmz+pA0jIv2siCmXra2L2h+mW8R5ZW0dgB1uaa8q1sRaaQL3xP7filgbGInQXohU\nxdpwwPzCviprw4FolX1V1oYDDWn2VVkbDmSytANXWfsO4KArVlDWhgNxL7lsibXhgFlc2j4Sa0OB\nZ+3tbKXbALmpAAAAAElFTkSuQmCC\n", | |
"prompt_number": 10, | |
"text": [ | |
"d \n", | |
"\u2500\u2500(\u03c9\u2081(t))\n", | |
"dt " | |
] | |
} | |
], | |
"prompt_number": 10 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"v" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"latex": [ | |
"$$a\\mathbf{\\hat{a}_x} + \\omega_{1}\\mathbf{\\hat{a}_y} + \\dot{\\omega}_{1}\\mathbf{\\hat{a}_z}$$" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"png": "iVBORw0KGgoAAAANSUhEUgAAAKwAAAAWBAMAAACvTmr4AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nwlvu8dAwTP49D/YXk5rQ/WldzUcAAAAASUVORK5CYII=\n", | |
"prompt_number": 11, | |
"text": [ | |
"a*\u001b[94m\u001b[1ma_x\u001b[0;0m\u001b[0;0m + \u03c9\u2081*\u001b[94m\u001b[1ma_y\u001b[0;0m\u001b[0;0m + \u03c9\u2081\u0307*\u001b[94m\u001b[1ma_z\u001b[0;0m\u001b[0;0m" | |
] | |
} | |
], | |
"prompt_number": 11 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"init_printing(use_latex=False)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 12 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"a" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 13, | |
"text": [ | |
"a" | |
] | |
} | |
], | |
"prompt_number": 13 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 14, | |
"text": [ | |
"\u03c9\u2081(t)" | |
] | |
} | |
], | |
"prompt_number": 14 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega.diff()" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 15, | |
"text": [ | |
"d \n", | |
"\u2500\u2500(\u03c9\u2081(t))\n", | |
"dt " | |
] | |
} | |
], | |
"prompt_number": 15 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"v" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 16, | |
"text": [ | |
"a*\u001b[94m\u001b[1ma_x\u001b[0;0m\u001b[0;0m + \u03c9\u2081*\u001b[94m\u001b[1ma_y\u001b[0;0m\u001b[0;0m + \u03c9\u2081\u0307*\u001b[94m\u001b[1ma_z\u001b[0;0m\u001b[0;0m" | |
] | |
} | |
], | |
"prompt_number": 16 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"init_printing(use_latex=True)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 17 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"a" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"latex": [ | |
"$$a$$" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAAJBAMAAAAWSsseAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIquJdjLdEETvu2aZ\nVM0GsGrEAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAR0lEQVQIHWNgYFR2TWdgYOgU4PrAwMA+m4Fn\nAQMDz3cGNgcGBs4FDPUBDAz1Bgz3GQoY6i8wrOMVYOBz4E5iBqpUMRXyYAAAgLMMA5qDwz8AAAAA\nSUVORK5CYII=\n", | |
"prompt_number": 18, | |
"text": [ | |
"a" | |
] | |
} | |
], | |
"prompt_number": 18 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"latex": [ | |
"$$\\omega_{1}{\\left (t \\right )}$$" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"png": "iVBORw0KGgoAAAANSUhEUgAAACsAAAAVBAMAAAAtAwouAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAuyLvRGYQdpmJVN0y\nzauXc2k5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABC0lEQVQYGY2RsUvDQBjFf9YmbdIoUhA3jXTR\nXRCcOrgVpDh3qDg4GnByu39AEDrYSQKODgY3XYybm8HB2c3BJYOr4rseCsnkwXvv+358d5cj8I8V\nDe3QqD65PgOLeY2/gn8LRRW3ziEs4bSK52Noa/SwigdqO9qxkMKS6l5fBlPYW1tNCAyeJccJj4pl\n6UbyCtoKgvTpQ3EvnUlhxi5keDHXarekOykqSYgMAb/Y/3TY0ErZdFiHNEvGNDO6PBteHNaVQRHm\n9srJdOd7om+1Z1/qNW9HMsPBV36yLWTxABoriZ7TV+OWxZ3Y1T0X1q8kz9gKLlzINx7e5d1Z7xd/\n2BXuN8zFNdwYWrAPP5hHNrCIy2tAAAAAAElFTkSuQmCC\n", | |
"prompt_number": 19, | |
"text": [ | |
"\u03c9\u2081(t)" | |
] | |
} | |
], | |
"prompt_number": 19 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega.diff()" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"latex": [ | |
"$$\\frac{d}{d t} \\omega_{1}{\\left (t \\right )}$$" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"png": "iVBORw0KGgoAAAANSUhEUgAAAEAAAAArBAMAAAA6dJN0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nZ+3tbKXbALmpAAAAAElFTkSuQmCC\n", | |
"prompt_number": 20, | |
"text": [ | |
"d \n", | |
"\u2500\u2500(\u03c9\u2081(t))\n", | |
"dt " | |
] | |
} | |
], | |
"prompt_number": 20 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"v" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"latex": [ | |
"$$a\\mathbf{\\hat{a}_x} + \\omega_{1}\\mathbf{\\hat{a}_y} + \\dot{\\omega}_{1}\\mathbf{\\hat{a}_z}$$" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"png": "iVBORw0KGgoAAAANSUhEUgAAAKwAAAAWBAMAAACvTmr4AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nwlvu8dAwTP49D/YXk5rQ/WldzUcAAAAASUVORK5CYII=\n", | |
"prompt_number": 21, | |
"text": [ | |
"a*\u001b[94m\u001b[1ma_x\u001b[0;0m\u001b[0;0m + \u03c9\u2081*\u001b[94m\u001b[1ma_y\u001b[0;0m\u001b[0;0m + \u03c9\u2081\u0307*\u001b[94m\u001b[1ma_z\u001b[0;0m\u001b[0;0m" | |
] | |
} | |
], | |
"prompt_number": 21 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"from sympy.physics.vector import init_printing\n", | |
"init_printing(pretty_print=False)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 22 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"a" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 23, | |
"text": [ | |
"a" | |
] | |
} | |
], | |
"prompt_number": 23 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 24, | |
"text": [ | |
"omega1" | |
] | |
} | |
], | |
"prompt_number": 24 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega.diff()" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 25, | |
"text": [ | |
"omega1'" | |
] | |
} | |
], | |
"prompt_number": 25 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"v" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 26, | |
"text": [ | |
"a*A.x + omega1*A.y + omega1'*A.z" | |
] | |
} | |
], | |
"prompt_number": 26 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"from sympy.physics.vector import init_printing\n", | |
"init_printing(use_latex=False, use_unicode=False)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 27 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"a" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 28, | |
"text": [ | |
"a" | |
] | |
} | |
], | |
"prompt_number": 28 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 29, | |
"text": [ | |
"omega1" | |
] | |
} | |
], | |
"prompt_number": 29 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega.diff()" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 30, | |
"text": [ | |
"omeg\u0307a1" | |
] | |
} | |
], | |
"prompt_number": 30 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"v" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 31, | |
"text": [ | |
"a*\u001b[94m\u001b[1ma_x\u001b[0;0m\u001b[0;0m + omega1*\u001b[94m\u001b[1ma_y\u001b[0;0m\u001b[0;0m + omeg\u0307a1*\u001b[94m\u001b[1ma_z\u001b[0;0m\u001b[0;0m" | |
] | |
} | |
], | |
"prompt_number": 31 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"init_printing()" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 32 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"a" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"latex": [ | |
"$$a$$" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAAJBAMAAAAWSsseAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIquJdjLdEETvu2aZ\nVM0GsGrEAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAR0lEQVQIHWNgYFR2TWdgYOgU4PrAwMA+m4Fn\nAQMDz3cGNgcGBs4FDPUBDAz1Bgz3GQoY6i8wrOMVYOBz4E5iBqpUMRXyYAAAgLMMA5qDwz8AAAAA\nSUVORK5CYII=\n", | |
"prompt_number": 33, | |
"text": [ | |
"a" | |
] | |
} | |
], | |
"prompt_number": 33 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"latex": [ | |
"$$\\omega_{1}$$" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAAMBAMAAACQIoDIAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAuyLvRGYQdpmJVN0y\nzauXc2k5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAZElEQVQIHWNgEGBgYFB2ABIMrCAyv4DhIAMD\nB4jPueDEawYGFwaGDQysCgyrGRgKGHgaGDgZQMwGBvYFDJpgphDD+QaGS2Dm5BlW/yZPADMT/x4o\nNgcaAlQLA0jMxTAxBo39zwHrjRfKjm9/cgAAAABJRU5ErkJggg==\n", | |
"prompt_number": 35, | |
"text": [ | |
"\u03c9\u2081" | |
] | |
} | |
], | |
"prompt_number": 35 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"omega.diff()" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"latex": [ | |
"$$\\dot{\\omega}_{1}$$" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAARBAMAAAAvapGNAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA3asQzbsi70RmdpmJ\nVDIG68jPAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAb0lEQVQIHWNgYGAQAmIIYP4CYxGkA4Aq0htA\nyjhBpP0ChqcMDNwgPs+F14oMDB0MDAIMnAkMFxkYFjDwbWDgYQAxNzBwXWDIATPDGN5vYHADM4+f\nrv10/ACYafrlwfIqoCFAtTCAxLwOE2PIltcCAM6pHBFEQ9sqAAAAAElFTkSuQmCC\n", | |
"prompt_number": 36, | |
"text": [ | |
"\u03c9\u2081\u0307" | |
] | |
} | |
], | |
"prompt_number": 36 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"v" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"latex": [ | |
"$$a\\mathbf{\\hat{a}_x} + \\omega_{1}\\mathbf{\\hat{a}_y} + \\dot{\\omega}_{1}\\mathbf{\\hat{a}_z}$$" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"png": "iVBORw0KGgoAAAANSUhEUgAAAKwAAAAWBAMAAACvTmr4AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nwlvu8dAwTP49D/YXk5rQ/WldzUcAAAAASUVORK5CYII=\n", | |
"prompt_number": 37, | |
"text": [ | |
"a*\u001b[94m\u001b[1ma_x\u001b[0;0m\u001b[0;0m + \u03c9\u2081*\u001b[94m\u001b[1ma_y\u001b[0;0m\u001b[0;0m + \u03c9\u2081\u0307*\u001b[94m\u001b[1ma_z\u001b[0;0m\u001b[0;0m" | |
] | |
} | |
], | |
"prompt_number": 37 | |
} | |
], | |
"metadata": {} | |
} | |
] | |
} |
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