305 lines
25 KiB
Plaintext
305 lines
25 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 2,
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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": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"N, A, B = sm.symbols(\"N, A, B\", 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": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"alpha, beta, d = me.dynamicsymbols('alpha, beta, d')"
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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": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"A.orient_axis(N, alpha, N.z)\n",
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"B.orient_axis(A, beta, 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": 6,
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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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"$\\displaystyle \\dot{\\alpha}\\mathbf{\\hat{n}_z}$"
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],
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"text/plain": [
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"α̇ n_z"
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]
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},
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"execution_count": 6,
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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.ang_vel_in(N)"
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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": 7,
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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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"$\\displaystyle \\dot{\\alpha}\\mathbf{\\hat{a}_z}$"
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],
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"text/plain": [
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"α̇ a_z"
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]
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},
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"execution_count": 7,
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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.ang_vel_in(N).express(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": 8,
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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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"$\\displaystyle \\dot{\\beta}\\mathbf{\\hat{a}_x}$"
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],
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"text/plain": [
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"β̇ a_x"
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]
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},
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"execution_count": 8,
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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.ang_vel_in(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": 9,
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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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"$\\displaystyle \\dot{\\alpha}\\mathbf{\\hat{n}_z} + \\dot{\\beta}\\mathbf{\\hat{a}_x}$"
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],
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"text/plain": [
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"α̇ n_z + β̇ a_x"
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]
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},
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"execution_count": 9,
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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.ang_vel_in(N) + B.ang_vel_in(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": 10,
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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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"$\\displaystyle \\dot{\\beta}\\mathbf{\\hat{a}_x} + \\dot{\\alpha}\\mathbf{\\hat{n}_z}$"
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],
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"text/plain": [
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"β̇ a_x + α̇ n_z"
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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.ang_vel_in(N)"
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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": {},
|
|
"outputs": [
|
|
{
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|
"data": {
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAACQAAAAVCAYAAAAuJkyQAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAABJ0AAASdAHeZh94AAACeElEQVR4nM3WS2hdVRQG4C+hUjMQ0gp1JrUKOlI6iDiRiFTRQasDRUWEjnwg2AwsnfXvUhARJaFSqiDYmY8qUhxYpAVBVBwJCkJBsVDwResDtTVUjYOzL9ykucmNROMPh7PX8/zss9bae2Rubs5iqKopjGOmqabwU5KZRQPmx27FHU18Pcnny8X0MLqEbQpppMbbemoIMpfgDextMYeramxYQusGGZJsXqAaGTLnAWzBLozhaTyLR4cJHhn0y/4JqupevIJ9SarpnsFu7Ejy9n9KaDWwVA2tCf53hC4o6qq6SFeAO3E1zuAw9jT/r3Asyf1VtRMv94VfiVvxcIv9De/i8SRfD0No3g5V1UZ8gGmcwn78rGv3x9qHNuraeTEcwkFch4txKe7D8apav2JCeA0T2JVke5I9mMQsbtd1y6EkXwzIdyOO40l81qe/BneuiFBVbcM2vI/ne/okp3ESN2MDnlgi31u4Jcle3IQ/+2zXr4gQHmjvmSQLZ8Hv7f1iklNL5DvYi03yA0732TaslNAkzuPoAN+zeGqZfCcXyLMDvjUQ66CdNZfjyyRn+x2qaouuBj5M8t0y+c4vkC+YulW1Wdepi6F6bT+mO6v+WsRpGuvxxzJkhsUsPu6TN+GKtj7XI/QjfsVVVXVtkk+hqh7BjuYzvhpsknyDG1r+y3RjBj7C/tHmNKebIaM4VlUHqupN3cl9BO9hoqpeqKqJ1SDWrinv6IbpCWxPcq6/0HbjOd2WPqibKdO4WzelT+Ahq7BTbUgewVZ8i9uSnGENTvuqGtUN4LvwCyaTfNKzrwWhe/BqE783v+NeGnhj/BfRf53d1J4ejv4Np/zFW7gveVYAAAAASUVORK5CYII=",
|
|
"text/latex": [
|
|
"$\\displaystyle \\ddot{\\alpha}\\mathbf{\\hat{n}_z}$"
|
|
],
|
|
"text/plain": [
|
|
"α̈ n_z"
|
|
]
|
|
},
|
|
"execution_count": 11,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"A.ang_acc_in(N)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
|
"text/latex": [
|
|
"$\\displaystyle \\ddot{\\beta}\\mathbf{\\hat{a}_x}$"
|
|
],
|
|
"text/plain": [
|
|
"β̈ a_x"
|
|
]
|
|
},
|
|
"execution_count": 12,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"B.ang_acc_in(A)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 13,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
|
"text/latex": [
|
|
"$\\displaystyle \\ddot{\\beta}\\mathbf{\\hat{a}_x} + \\dot{\\alpha} \\dot{\\beta}\\mathbf{\\hat{a}_y} + \\ddot{\\alpha}\\mathbf{\\hat{n}_z}$"
|
|
],
|
|
"text/plain": [
|
|
"β̈ a_x + α̇⋅β̇ a_y + α̈ n_z"
|
|
]
|
|
},
|
|
"execution_count": 13,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"B.ang_acc_in(N)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 14,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
|
"text/latex": [
|
|
"$\\displaystyle \\ddot{\\alpha}\\mathbf{\\hat{n}_z} + \\ddot{\\beta}\\mathbf{\\hat{a}_x}$"
|
|
],
|
|
"text/plain": [
|
|
"α̈ n_z + β̈ a_x"
|
|
]
|
|
},
|
|
"execution_count": 14,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"A.ang_acc_in(N) + B.ang_acc_in(A)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 15,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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",
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"text/latex": [
|
|
"$\\displaystyle \\ddot{\\beta}\\mathbf{\\hat{b}_x} + (\\sin{\\left(\\beta \\right)} \\ddot{\\alpha} + \\cos{\\left(\\beta \\right)} \\dot{\\alpha} \\dot{\\beta})\\mathbf{\\hat{b}_y} + (- \\sin{\\left(\\beta \\right)} \\dot{\\alpha} \\dot{\\beta} + \\cos{\\left(\\beta \\right)} \\ddot{\\alpha})\\mathbf{\\hat{b}_z}$"
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],
|
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"text/plain": [
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"β̈ b_x + (sin(β)⋅α̈ + cos(β)⋅α̇⋅β̇) b_y + (-sin(β)⋅α̇⋅β̇ + cos(β)⋅α̈) b_z"
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]
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},
|
|
"execution_count": 15,
|
|
"metadata": {},
|
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"output_type": "execute_result"
|
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}
|
|
],
|
|
"source": [
|
|
"B.ang_acc_in(N).express(B)"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Turtle",
|
|
"language": "python",
|
|
"name": "python3"
|
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},
|
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"language_info": {
|
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"codemirror_mode": {
|
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"name": "ipython",
|
|
"version": 3
|
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},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.11.8"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
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}
|