279 lines
32 KiB
Plaintext
279 lines
32 KiB
Plaintext
{
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"cells": [
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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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"import sympy as sm\n",
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"import sympy.physics.mechanics as me\n",
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"me.init_vprinting()"
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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": 16,
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"metadata": {},
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"outputs": [],
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"source": [
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"theta, beta, alpha, l = me.dynamicsymbols('theta, beta, alpha, l')\n",
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"A, B, C, D = sm.symbols('A, B, C, D', cls=me.ReferenceFrame)"
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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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"$\\displaystyle \\left[\\begin{matrix}- \\sin{\\left(\\alpha \\right)} \\sin{\\left(\\theta \\right)} \\cos{\\left(\\beta \\right)} + \\cos{\\left(\\alpha \\right)} \\cos{\\left(\\theta \\right)} & \\sin{\\left(\\alpha \\right)} \\cos{\\left(\\beta \\right)} \\cos{\\left(\\theta \\right)} + \\sin{\\left(\\theta \\right)} \\cos{\\left(\\alpha \\right)} & - \\sin{\\left(\\alpha \\right)} \\sin{\\left(\\beta \\right)}\\\\- \\sin{\\left(\\alpha \\right)} \\cos{\\left(\\theta \\right)} - \\sin{\\left(\\theta \\right)} \\cos{\\left(\\alpha \\right)} \\cos{\\left(\\beta \\right)} & - \\sin{\\left(\\alpha \\right)} \\sin{\\left(\\theta \\right)} + \\cos{\\left(\\alpha \\right)} \\cos{\\left(\\beta \\right)} \\cos{\\left(\\theta \\right)} & - \\sin{\\left(\\beta \\right)} \\cos{\\left(\\alpha \\right)}\\\\- \\sin{\\left(\\beta \\right)} \\sin{\\left(\\theta \\right)} & \\sin{\\left(\\beta \\right)} \\cos{\\left(\\theta \\right)} & \\cos{\\left(\\beta \\right)}\\end{matrix}\\right]$"
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],
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"text/plain": [
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"⎡-sin(α)⋅sin(θ)⋅cos(β) + cos(α)⋅cos(θ) sin(α)⋅cos(β)⋅cos(θ) + sin(θ)⋅cos(α) ↪\n",
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"⎢ ↪\n",
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"⎢-sin(α)⋅cos(θ) - sin(θ)⋅cos(α)⋅cos(β) -sin(α)⋅sin(θ) + cos(α)⋅cos(β)⋅cos(θ) ↪\n",
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"⎢ ↪\n",
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"⎣ -sin(β)⋅sin(θ) sin(β)⋅cos(θ) ↪\n",
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"\n",
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"↪ -sin(α)⋅sin(β)⎤\n",
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"↪ ⎥\n",
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"↪ -sin(β)⋅cos(α)⎥\n",
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"↪ ⎥\n",
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"↪ cos(β) ⎦"
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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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"B.orient_axis(A, theta, A.z)\n",
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"C.orient_axis(B, beta, -B.x)\n",
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"D.orient_axis(C, alpha, C.z)\n",
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"D.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": 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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"$\\displaystyle l\\mathbf{\\hat{d}_x}$"
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],
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"text/plain": [
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"l d_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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"r = l *D.x\n",
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"r"
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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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"image/png": "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",
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"text/latex": [
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"$\\displaystyle l \\cos{\\left(\\alpha \\right)}\\mathbf{\\hat{c}_x} + l \\sin{\\left(\\alpha \\right)}\\mathbf{\\hat{c}_y}$"
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],
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"text/plain": [
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"l⋅cos(α) c_x + l⋅sin(α) c_y"
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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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"r.express(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": 20,
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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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",
|
||
"text/latex": [
|
||
"$\\displaystyle l \\cos{\\left(\\alpha \\right)}\\mathbf{\\hat{b}_x} + l \\sin{\\left(\\alpha \\right)} \\cos{\\left(\\beta \\right)}\\mathbf{\\hat{b}_y} - l \\sin{\\left(\\alpha \\right)} \\sin{\\left(\\beta \\right)}\\mathbf{\\hat{b}_z}$"
|
||
],
|
||
"text/plain": [
|
||
"l⋅cos(α) b_x + l⋅sin(α)⋅cos(β) b_y + -l⋅sin(α)⋅sin(β) b_z"
|
||
]
|
||
},
|
||
"execution_count": 20,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"r.express(B)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": "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",
|
||
"text/latex": [
|
||
"$\\displaystyle \\left(- \\sin{\\left(\\alpha \\right)} \\sin{\\left(\\theta \\right)} \\cos{\\left(\\beta \\right)} + \\cos{\\left(\\alpha \\right)} \\cos{\\left(\\theta \\right)}\\right) l\\mathbf{\\hat{a}_x} + \\left(\\sin{\\left(\\alpha \\right)} \\cos{\\left(\\beta \\right)} \\cos{\\left(\\theta \\right)} + \\sin{\\left(\\theta \\right)} \\cos{\\left(\\alpha \\right)}\\right) l\\mathbf{\\hat{a}_y} - l \\sin{\\left(\\alpha \\right)} \\sin{\\left(\\beta \\right)}\\mathbf{\\hat{a}_z}$"
|
||
],
|
||
"text/plain": [
|
||
"(-sin(α)⋅sin(θ)⋅cos(β) + cos(α)⋅cos(θ))⋅l a_x + (sin(α)⋅cos(β)⋅cos(θ) + sin(θ) ↪\n",
|
||
"\n",
|
||
"↪ ⋅cos(α))⋅l a_y + -l⋅sin(α)⋅sin(β) a_z"
|
||
]
|
||
},
|
||
"execution_count": 21,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"r.express(A)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 22,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": "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",
|
||
"text/latex": [
|
||
"$\\displaystyle - l \\sin{\\left(\\alpha \\right)}$"
|
||
],
|
||
"text/plain": [
|
||
"-l⋅sin(α)"
|
||
]
|
||
},
|
||
"execution_count": 22,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"r.dot(C.x).diff(alpha)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 23,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": "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",
|
||
"text/latex": [
|
||
"$\\displaystyle l \\cos{\\left(\\alpha \\right)}$"
|
||
],
|
||
"text/plain": [
|
||
"l⋅cos(α)"
|
||
]
|
||
},
|
||
"execution_count": 23,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"r.dot(C.y).diff(alpha)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 25,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": "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",
|
||
"text/latex": [
|
||
"$\\displaystyle - l \\sin{\\left(\\alpha \\right)}\\mathbf{\\hat{c}_x} + l \\cos{\\left(\\alpha \\right)}\\mathbf{\\hat{c}_y}$"
|
||
],
|
||
"text/plain": [
|
||
"-l⋅sin(α) c_x + l⋅cos(α) c_y"
|
||
]
|
||
},
|
||
"execution_count": 25,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"r_alpha_C = r.dot(C.x).diff(alpha) * C.x + r.dot(C.y).diff(alpha) * C.y + r.dot(C.z).diff(alpha) * C.z\n",
|
||
"r_alpha_C"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 27,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": "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",
|
||
"text/latex": [
|
||
"$\\displaystyle - l \\sin{\\left(\\alpha \\right)}\\mathbf{\\hat{c}_x} + l \\cos{\\left(\\alpha \\right)}\\mathbf{\\hat{c}_y}$"
|
||
],
|
||
"text/plain": [
|
||
"-l⋅sin(α) c_x + l⋅cos(α) c_y"
|
||
]
|
||
},
|
||
"execution_count": 27,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"r.diff(alpha, C).express(C)"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Turtle",
|
||
"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": "3.11.8"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 4
|
||
}
|