349 lines
11 KiB
Plaintext
349 lines
11 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"import sympy as sm"
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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": 8,
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"metadata": {},
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"outputs": [],
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"source": [
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"sm.init_printing()"
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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": 9,
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"metadata": {},
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"outputs": [],
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"source": [
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"theta, alpha = sm.symbols(\"theta, alpha\")"
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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": 10,
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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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"$\\displaystyle \\left[\\begin{matrix}\\cos{\\left(\\theta \\right)} & \\sin{\\left(\\theta \\right)} & 0\\\\- \\sin{\\left(\\theta \\right)} & \\cos{\\left(\\theta \\right)} & 0\\\\0 & 0 & 1\\end{matrix}\\right]$"
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],
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"text/plain": [
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"⎡cos(θ) sin(θ) 0⎤\n",
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"⎢ ⎥\n",
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"⎢-sin(θ) cos(θ) 0⎥\n",
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"⎢ ⎥\n",
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"⎣ 0 0 1⎦"
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]
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},
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"execution_count": 10,
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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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"B_C_A = sm.Matrix([[sm.cos(theta), sm.sin(theta), 0],\n",
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" [-sm.sin(theta), sm.cos(theta), 0],\n",
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" [0, 0, 1]])\n",
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"B_C_A"
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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": 11,
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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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"$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0\\\\0 & \\cos{\\left(\\alpha \\right)} & \\sin{\\left(\\alpha \\right)}\\\\0 & - \\sin{\\left(\\alpha \\right)} & \\cos{\\left(\\alpha \\right)}\\end{matrix}\\right]$"
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],
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"text/plain": [
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"⎡1 0 0 ⎤\n",
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"⎢ ⎥\n",
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"⎢0 cos(α) sin(α)⎥\n",
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"⎢ ⎥\n",
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"⎣0 -sin(α) cos(α)⎦"
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]
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},
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"execution_count": 11,
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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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"C_C_B = sm.Matrix([[1, 0, 0],\n",
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" [0, sm.cos(alpha), sm.sin(alpha)],\n",
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" [0, -sm.sin(alpha), sm.cos(alpha)]])\n",
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"C_C_B"
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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": 12,
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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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"$\\displaystyle \\left[\\begin{matrix}\\cos{\\left(\\theta \\right)} & \\sin{\\left(\\theta \\right)} & 0\\\\- \\sin{\\left(\\theta \\right)} \\cos{\\left(\\alpha \\right)} & \\cos{\\left(\\alpha \\right)} \\cos{\\left(\\theta \\right)} & \\sin{\\left(\\alpha \\right)}\\\\\\sin{\\left(\\alpha \\right)} \\sin{\\left(\\theta \\right)} & - \\sin{\\left(\\alpha \\right)} \\cos{\\left(\\theta \\right)} & \\cos{\\left(\\alpha \\right)}\\end{matrix}\\right]$"
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],
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"text/plain": [
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"⎡ cos(θ) sin(θ) 0 ⎤\n",
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"⎢ ⎥\n",
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"⎢-sin(θ)⋅cos(α) cos(α)⋅cos(θ) sin(α)⎥\n",
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"⎢ ⎥\n",
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"⎣sin(α)⋅sin(θ) -sin(α)⋅cos(θ) cos(α)⎦"
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]
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},
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"execution_count": 12,
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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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"C_C_A = C_C_B * B_C_A\n",
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"C_C_A"
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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": 13,
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"metadata": {},
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"outputs": [],
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"source": [
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"import sympy.physics.mechanics as me"
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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": 14,
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"metadata": {},
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"outputs": [],
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"source": [
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"A = me.ReferenceFrame('A')\n",
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"B = me.ReferenceFrame('B')\n",
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"C = me.ReferenceFrame('C')"
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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": 15,
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"metadata": {},
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"outputs": [],
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"source": [
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"B.orient_axis(A, theta, A.z)"
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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": 18,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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",
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"text/latex": [
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"$\\displaystyle \\mathbf{\\hat{a}_x}$"
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],
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"text/plain": [
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"a_x"
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]
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},
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"execution_count": 18,
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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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"A.x"
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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": 19,
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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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"$\\displaystyle \\left[\\begin{matrix}\\cos{\\left(\\theta \\right)} & \\sin{\\left(\\theta \\right)} & 0\\\\- \\sin{\\left(\\theta \\right)} & \\cos{\\left(\\theta \\right)} & 0\\\\0 & 0 & 1\\end{matrix}\\right]$"
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],
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"text/plain": [
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"⎡cos(θ) sin(θ) 0⎤\n",
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"⎢ ⎥\n",
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"⎢-sin(θ) cos(θ) 0⎥\n",
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"⎢ ⎥\n",
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"⎣ 0 0 1⎦"
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]
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},
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"execution_count": 19,
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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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"B.dcm(A)"
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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": 20,
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"metadata": {},
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"outputs": [],
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"source": [
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"C.orient_axis(B, alpha, B.x)"
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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": 21,
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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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"$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0\\\\0 & \\cos{\\left(\\alpha \\right)} & \\sin{\\left(\\alpha \\right)}\\\\0 & - \\sin{\\left(\\alpha \\right)} & \\cos{\\left(\\alpha \\right)}\\end{matrix}\\right]$"
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],
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"text/plain": [
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"⎡1 0 0 ⎤\n",
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"⎢ ⎥\n",
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"⎢0 cos(α) sin(α)⎥\n",
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"⎢ ⎥\n",
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"⎣0 -sin(α) cos(α)⎦"
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]
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},
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"execution_count": 21,
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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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"C.dcm(B)"
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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": 22,
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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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"$\\displaystyle \\left[\\begin{matrix}\\cos{\\left(\\theta \\right)} & \\sin{\\left(\\theta \\right)} & 0\\\\- \\sin{\\left(\\theta \\right)} \\cos{\\left(\\alpha \\right)} & \\cos{\\left(\\alpha \\right)} \\cos{\\left(\\theta \\right)} & \\sin{\\left(\\alpha \\right)}\\\\\\sin{\\left(\\alpha \\right)} \\sin{\\left(\\theta \\right)} & - \\sin{\\left(\\alpha \\right)} \\cos{\\left(\\theta \\right)} & \\cos{\\left(\\alpha \\right)}\\end{matrix}\\right]$"
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],
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"text/plain": [
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"⎡ cos(θ) sin(θ) 0 ⎤\n",
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"⎢ ⎥\n",
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"⎢-sin(θ)⋅cos(α) cos(α)⋅cos(θ) sin(α)⎥\n",
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"⎢ ⎥\n",
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"⎣sin(α)⋅sin(θ) -sin(α)⋅cos(θ) cos(α)⎦"
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]
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},
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"execution_count": 22,
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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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"C.dcm(A)"
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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": 23,
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"metadata": {},
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"outputs": [],
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"source": [
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"A = me.ReferenceFrame(\"A\")\n",
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"C = me.ReferenceFrame(\"C\")"
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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": 24,
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"metadata": {},
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"outputs": [],
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"source": [
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"psi, theta, phi = sm.symbols('psi, theta, varphi')"
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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": 25,
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"metadata": {},
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"outputs": [],
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"source": [
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"C.orient_body_fixed(A, (phi, theta, phi), 'ZXZ')"
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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": 26,
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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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"$\\displaystyle \\left[\\begin{matrix}- \\sin^{2}{\\left(\\varphi \\right)} \\cos{\\left(\\theta \\right)} + \\cos^{2}{\\left(\\varphi \\right)} & \\sin{\\left(\\varphi \\right)} \\cos{\\left(\\theta \\right)} \\cos{\\left(\\varphi \\right)} + \\sin{\\left(\\varphi \\right)} \\cos{\\left(\\varphi \\right)} & \\sin{\\left(\\theta \\right)} \\sin{\\left(\\varphi \\right)}\\\\- \\sin{\\left(\\varphi \\right)} \\cos{\\left(\\theta \\right)} \\cos{\\left(\\varphi \\right)} - \\sin{\\left(\\varphi \\right)} \\cos{\\left(\\varphi \\right)} & - \\sin^{2}{\\left(\\varphi \\right)} + \\cos{\\left(\\theta \\right)} \\cos^{2}{\\left(\\varphi \\right)} & \\sin{\\left(\\theta \\right)} \\cos{\\left(\\varphi \\right)}\\\\\\sin{\\left(\\theta \\right)} \\sin{\\left(\\varphi \\right)} & - \\sin{\\left(\\theta \\right)} \\cos{\\left(\\varphi \\right)} & \\cos{\\left(\\theta \\right)}\\end{matrix}\\right]$"
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],
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"text/plain": [
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"⎡ 2 2 ↪\n",
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"⎢ - sin (varphi)⋅cos(θ) + cos (varphi) sin(varphi)⋅cos(θ) ↪\n",
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"⎢ ↪\n",
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"⎢ 2 ↪\n",
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"⎢-sin(varphi)⋅cos(θ)⋅cos(varphi) - sin(varphi)⋅cos(varphi) - sin (v ↪\n",
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"⎢ ↪\n",
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"⎣ sin(θ)⋅sin(varphi) ↪\n",
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"\n",
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"↪ ⎤\n",
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"↪ ⋅cos(varphi) + sin(varphi)⋅cos(varphi) sin(θ)⋅sin(varphi)⎥\n",
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"↪ ⎥\n",
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"↪ 2 ⎥\n",
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"↪ arphi) + cos(θ)⋅cos (varphi) sin(θ)⋅cos(varphi)⎥\n",
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"↪ ⎥\n",
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"↪ -sin(θ)⋅cos(varphi) cos(θ) ⎦"
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]
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},
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"execution_count": 26,
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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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"C.dcm(A)"
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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": "Turtle",
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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": "3.11.8"
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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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}
|