Rune Harlyk
100 lines
3.4 KiB
Plaintext
100 lines
3.4 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"import sympy as sp\n",
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"import numpy as np"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\left[\\begin{matrix}\\cos{\\left(\\phi \\right)} \\cos{\\left(\\psi \\right)} & - \\sin{\\left(\\psi \\right)} \\cos{\\left(\\phi \\right)} & \\sin{\\left(\\phi \\right)} & x\\\\\\sin{\\left(\\omega \\right)} \\sin{\\left(\\phi \\right)} \\cos{\\left(\\psi \\right)} + \\sin{\\left(\\psi \\right)} \\cos{\\left(\\omega \\right)} & - \\sin{\\left(\\omega \\right)} \\sin{\\left(\\phi \\right)} \\sin{\\left(\\psi \\right)} + \\cos{\\left(\\omega \\right)} \\cos{\\left(\\psi \\right)} & - \\sin{\\left(\\omega \\right)} \\cos{\\left(\\phi \\right)} & y\\\\\\sin{\\left(\\omega \\right)} \\sin{\\left(\\psi \\right)} - \\sin{\\left(\\phi \\right)} \\cos{\\left(\\omega \\right)} \\cos{\\left(\\psi \\right)} & \\sin{\\left(\\omega \\right)} \\cos{\\left(\\psi \\right)} + \\sin{\\left(\\phi \\right)} \\sin{\\left(\\psi \\right)} \\cos{\\left(\\omega \\right)} & \\cos{\\left(\\omega \\right)} \\cos{\\left(\\phi \\right)} & z\\\\0 & 0 & 0 & 1\\end{matrix}\\right]$"
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],
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"text/plain": [
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"Matrix([\n",
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"[ cos(phi)*cos(psi), -sin(psi)*cos(phi), sin(phi), x],\n",
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"[sin(omega)*sin(phi)*cos(psi) + sin(psi)*cos(omega), -sin(omega)*sin(phi)*sin(psi) + cos(omega)*cos(psi), -sin(omega)*cos(phi), y],\n",
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"[sin(omega)*sin(psi) - sin(phi)*cos(omega)*cos(psi), sin(omega)*cos(psi) + sin(phi)*sin(psi)*cos(omega), cos(omega)*cos(phi), z],\n",
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"[ 0, 0, 0, 1]])"
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]
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},
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"execution_count": 17,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"omega = sp.symbols('omega')\n",
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"psi = sp.symbols('psi')\n",
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"phi = sp.symbols('phi')\n",
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"x = sp.symbols('x')\n",
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"y = sp.symbols('y')\n",
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"z = sp.symbols('z')\n",
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"\n",
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"\n",
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"rx = sp.Matrix([\n",
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" [1, 0, 0, 0],\n",
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" [0, sp.cos(omega), -sp.sin(omega), 0],\n",
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" [0, sp.sin(omega), sp.cos(omega), 0],\n",
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" [0, 0, 0, 1],\n",
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"])\n",
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"\n",
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"ry = sp.Matrix([\n",
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" [sp.cos(phi), 0, sp.sin(phi), 0, ],\n",
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" [0, 1, 0, 0],\n",
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" [-sp.sin(phi), 0, sp.cos(phi), 0],\n",
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" [0, 0, 0, 1],\n",
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"])\n",
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"\n",
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"rz = sp.Matrix([\n",
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" [sp.cos(psi), -sp.sin(psi), 0, 0],\n",
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" [sp.sin(psi), sp.cos(psi), 0, 0],\n",
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" [0, 0, 1, 0],\n",
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" [0, 0, 0, 1],\n",
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"])\n",
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"\n",
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"t = sp.Matrix([\n",
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" [0, 0, 0, x],\n",
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" [0, 0, 0, y],\n",
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" [0, 0, 0, z],\n",
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" [0, 0, 0, 0],\n",
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"])\n",
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"\n",
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"tm = t + rx * ry * rz\n",
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"tm"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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