498 lines
72 KiB
Plaintext
498 lines
72 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()\n",
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"\n",
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"A = me.ReferenceFrame('A')\n",
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"B = me.ReferenceFrame('B')\n",
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"\n",
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"theta = me.dynamicsymbols('theta')\n",
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"\n",
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"B.orient_axis(A, theta, A.y)\n",
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"\n",
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"Q = 3*me.outer(B.x, A.z) + 4*me.outer(A.x, A.x) + 6*me.outer(A.z, B.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": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"M1, M2, M3 = me.dynamicsymbols('M1, M2, M3')\n",
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"A = me.ReferenceFrame('A')\n",
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"A = me.ReferenceFrame('A')\n",
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"\n",
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"w1, w2, w3 = me.dynamicsymbols('omega1, omega2, omega3')"
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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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{
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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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"$\\displaystyle \\omega_{1}\\mathbf{\\hat{b}_x} + \\omega_{2}\\mathbf{\\hat{b}_y} + \\omega_{3}\\mathbf{\\hat{b}_z}$"
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],
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"text/plain": [
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"ω₁ b_x + ω₂ b_y + ω₃ b_z"
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]
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},
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"execution_count": 4,
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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_w_B = w1*B.x + w2*B.y + w3*B.z\n",
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"A_w_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": 5,
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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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"$\\displaystyle M_{1}\\mathbf{\\hat{b}_x} + M_{2}\\mathbf{\\hat{b}_y} + M_{3}\\mathbf{\\hat{b}_z}$"
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],
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"text/plain": [
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"M₁ b_x + M₂ b_y + M₃ b_z"
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]
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},
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"execution_count": 5,
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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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"M = M1*B.x + M2*B.y + M3*B.z\n",
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"M"
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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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"source": [
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"I11, I22, I33 = sm.symbols('I_(11), I_(22), I_(33)')"
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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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"$\\displaystyle I_{(11)}\\mathbf{\\hat{b}_x}\\otimes \\mathbf{\\hat{b}_x} + I_{(22)}\\mathbf{\\hat{b}_y}\\otimes \\mathbf{\\hat{b}_y} + I_{(33)}\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_z}$"
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],
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"text/plain": [
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"I₍₁₁₎ b_x⊗b_x + I₍₂₂₎ b_y⊗b_y + I₍₃₃₎ b_z⊗b_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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"I = I11 * me.outer(B.x, B.x) + I22 * me.outer(B.y, B.y) + I33 * me.outer(B.z, B.z)\n",
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"I"
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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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",
|
|
"text/latex": [
|
|
"$\\displaystyle I_{(11)} \\omega_{1}\\mathbf{\\hat{b}_x} + I_{(22)} \\omega_{2}\\mathbf{\\hat{b}_y} + I_{(33)} \\omega_{3}\\mathbf{\\hat{b}_z}$"
|
|
],
|
|
"text/plain": [
|
|
"I₍₁₁₎⋅ω₁ b_x + I₍₂₂₎⋅ω₂ b_y + I₍₃₃₎⋅ω₃ b_z"
|
|
]
|
|
},
|
|
"execution_count": 8,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"H = me.dot(I, A_w_B)\n",
|
|
"H"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
|
"text/latex": [
|
|
"$\\displaystyle (I_{(11)} \\dot{\\omega}_{1} - I_{(22)} \\omega_{2} \\omega_{3} + I_{(33)} \\omega_{2} \\omega_{3})\\mathbf{\\hat{b}_x} + (I_{(11)} \\omega_{1} \\omega_{3} + I_{(22)} \\dot{\\omega}_{2} - I_{(33)} \\omega_{1} \\omega_{3})\\mathbf{\\hat{b}_y} + (- I_{(11)} \\omega_{1} \\omega_{2} + I_{(22)} \\omega_{1} \\omega_{2} + I_{(33)} \\dot{\\omega}_{3})\\mathbf{\\hat{b}_z}$"
|
|
],
|
|
"text/plain": [
|
|
"(I₍₁₁₎⋅ω₁̇ - I₍₂₂₎⋅ω₂⋅ω₃ + I₍₃₃₎⋅ω₂⋅ω₃) b_x + (I₍₁₁₎⋅ω₁⋅ω₃ + I₍₂₂₎⋅ω₂̇ - I₍₃₃₎⋅ω ↪\n",
|
|
"\n",
|
|
"↪ ₁⋅ω₃) b_y + (-I₍₁₁₎⋅ω₁⋅ω₂ + I₍₂₂₎⋅ω₁⋅ω₂ + I₍₃₃₎⋅ω₃̇) b_z"
|
|
]
|
|
},
|
|
"execution_count": 9,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"t = me.dynamicsymbols._t\n",
|
|
"Hdot = H.diff(t, B) + me.cross(A_w_B, H)\n",
|
|
"Hdot"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
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"text/latex": [
|
|
"$\\displaystyle (- I_{(11)} \\dot{\\omega}_{1} + I_{(22)} \\omega_{2} \\omega_{3} - I_{(33)} \\omega_{2} \\omega_{3} + M_{1})\\mathbf{\\hat{b}_x} + (- I_{(11)} \\omega_{1} \\omega_{3} - I_{(22)} \\dot{\\omega}_{2} + I_{(33)} \\omega_{1} \\omega_{3} + M_{2})\\mathbf{\\hat{b}_y} + (I_{(11)} \\omega_{1} \\omega_{2} - I_{(22)} \\omega_{1} \\omega_{2} - I_{(33)} \\dot{\\omega}_{3} + M_{3})\\mathbf{\\hat{b}_z}$"
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],
|
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"text/plain": [
|
|
"(-I₍₁₁₎⋅ω₁̇ + I₍₂₂₎⋅ω₂⋅ω₃ - I₍₃₃₎⋅ω₂⋅ω₃ + M₁) b_x + (-I₍₁₁₎⋅ω₁⋅ω₃ - I₍₂₂₎⋅ω₂̇ + ↪\n",
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"\n",
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"↪ I₍₃₃₎⋅ω₁⋅ω₃ + M₂) b_y + (I₍₁₁₎⋅ω₁⋅ω₂ - I₍₂₂₎⋅ω₁⋅ω₂ - I₍₃₃₎⋅ω₃̇ + M₃) b_z"
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|
]
|
|
},
|
|
"execution_count": 10,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
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"source": [
|
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"M - Hdot"
|
|
]
|
|
},
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{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
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|
"metadata": {},
|
|
"outputs": [
|
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{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\displaystyle \\left[\\begin{matrix}M_{1}\\\\M_{2}\\\\M_{3}\\end{matrix}\\right] = \\left[\\begin{matrix}I_{(11)} \\dot{\\omega}_{1} - I_{(22)} \\omega_{2} \\omega_{3} + I_{(33)} \\omega_{2} \\omega_{3}\\\\I_{(11)} \\omega_{1} \\omega_{3} + I_{(22)} \\dot{\\omega}_{2} - I_{(33)} \\omega_{1} \\omega_{3}\\\\- I_{(11)} \\omega_{1} \\omega_{2} + I_{(22)} \\omega_{1} \\omega_{2} + I_{(33)} \\dot{\\omega}_{3}\\end{matrix}\\right]$"
|
|
],
|
|
"text/plain": [
|
|
"⎡M₁⎤ ⎡I₍₁₁₎⋅ω₁̇ - I₍₂₂₎⋅ω₂⋅ω₃ + I₍₃₃₎⋅ω₂⋅ω₃ ⎤\n",
|
|
"⎢ ⎥ ⎢ ⎥\n",
|
|
"⎢M₂⎥ = ⎢I₍₁₁₎⋅ω₁⋅ω₃ + I₍₂₂₎⋅ω₂̇ - I₍₃₃₎⋅ω₁⋅ω₃ ⎥\n",
|
|
"⎢ ⎥ ⎢ ⎥\n",
|
|
"⎣M₃⎦ ⎣-I₍₁₁₎⋅ω₁⋅ω₂ + I₍₂₂₎⋅ω₁⋅ω₂ + I₍₃₃₎⋅ω₃̇⎦"
|
|
]
|
|
},
|
|
"execution_count": 11,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"sm.Eq(M.to_matrix(B), Hdot.to_matrix(B))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Bicycle example"
|
|
]
|
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},
|
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{
|
|
"cell_type": "code",
|
|
"execution_count": 17,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"B = me.ReferenceFrame('B')\n",
|
|
"H = me.ReferenceFrame('H')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 18,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\displaystyle \\left[\\begin{matrix}0 & -1 & 0\\\\-1 & 0 & 0\\\\0 & 0 & -1\\end{matrix}\\right]$"
|
|
],
|
|
"text/plain": [
|
|
"⎡0 -1 0 ⎤\n",
|
|
"⎢ ⎥\n",
|
|
"⎢-1 0 0 ⎥\n",
|
|
"⎢ ⎥\n",
|
|
"⎣0 0 -1⎦"
|
|
]
|
|
},
|
|
"execution_count": 18,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"B_C_H = sm.Matrix([[0, -1, 0], [-1, 0, 0], [0, 0, -1]])\n",
|
|
"B_C_H"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 19,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"B.orient_explicit(H, B_C_H.transpose())"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 20,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"mH = 84\n",
|
|
"mB = 9.9"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 21,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"r_O_Ho = 0.4 * B.x - 1.1 * B.z\n",
|
|
"r_O_Bo = 0.3 * B.x + 1.5 * B.z"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 22,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
|
"text/latex": [
|
|
"$\\displaystyle 0.389456869009585\\mathbf{\\hat{b}_x} - 0.825878594249201\\mathbf{\\hat{b}_z}$"
|
|
],
|
|
"text/plain": [
|
|
"0.389456869009585 b_x + -0.825878594249201 b_z"
|
|
]
|
|
},
|
|
"execution_count": 22,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"r_O_Fo = (mB * r_O_Bo + mH * r_O_Ho) / (mB + mH)\n",
|
|
"r_O_Fo"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 23,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"I_H_Ho = me.inertia(H, 11.3, 11.0, 2.3, iyz=-1.7)\n",
|
|
"I_B_Bo = me.inertia(B, 0.5, 1.3, 0.8, izx=-0.1)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 24,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
|
"text/latex": [
|
|
"$\\displaystyle 11.3\\mathbf{\\hat{h}_x}\\otimes \\mathbf{\\hat{h}_x} + 11.0\\mathbf{\\hat{h}_y}\\otimes \\mathbf{\\hat{h}_y} - 1.7\\mathbf{\\hat{h}_y}\\otimes \\mathbf{\\hat{h}_z} - 1.7\\mathbf{\\hat{h}_z}\\otimes \\mathbf{\\hat{h}_y} + 2.3\\mathbf{\\hat{h}_z}\\otimes \\mathbf{\\hat{h}_z}$"
|
|
],
|
|
"text/plain": [
|
|
"11.3000000000000 h_x⊗h_x + 11.0000000000000 h_y⊗h_y - 1.70000000000000 h_y⊗h_z - 1.70000000000000 h_z⊗h_y + 2.30000000000000 h_z⊗h_z"
|
|
]
|
|
},
|
|
"execution_count": 24,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"I_H_Ho"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 25,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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",
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"text/latex": [
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|
"$\\displaystyle 6.32131102695751\\mathbf{\\hat{h}_x}\\otimes \\mathbf{\\hat{h}_x} + 6.32131102695751\\mathbf{\\hat{h}_y}\\otimes \\mathbf{\\hat{h}_y} + 6.32131102695751\\mathbf{\\hat{h}_z}\\otimes \\mathbf{\\hat{h}_z} - 0.00933723933080879\\mathbf{\\hat{b}_x}\\otimes \\mathbf{\\hat{b}_x} + 0.242768222601028\\mathbf{\\hat{b}_x}\\otimes \\mathbf{\\hat{b}_z} + 0.242768222601028\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_x} - 6.3119737876267\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_z}$"
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],
|
|
"text/plain": [
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"6.32131102695751 h_x⊗h_x + 6.32131102695751 h_y⊗h_y + 6.32131102695751 h_z⊗h_z - 0.00933723933080879 b_x⊗b_x + 0.242768222601028 b_x⊗b_z + 0.242768222601028 b_z⊗b_x - 6.31197378762670 b_z⊗b_z"
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]
|
|
},
|
|
"execution_count": 25,
|
|
"metadata": {},
|
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"output_type": "execute_result"
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|
}
|
|
],
|
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"source": [
|
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"r_Fo_Ho = r_O_Fo - r_O_Ho\n",
|
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"U = me.outer(H.x, H.x) + me.outer(H.y, H.y) + me.outer(H.z, H.z)\n",
|
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"I_Ho_Fo = mH * (r_Fo_Ho.dot(r_Fo_Ho) * U - me.outer(r_Fo_Ho, r_Fo_Ho))\n",
|
|
"I_Ho_Fo"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 26,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
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"data": {
|
|
"image/png": "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",
|
|
"text/latex": [
|
|
"$\\displaystyle 53.6353662893364\\mathbf{\\hat{h}_x}\\otimes \\mathbf{\\hat{h}_x} + 53.6353662893364\\mathbf{\\hat{h}_y}\\otimes \\mathbf{\\hat{h}_y} + 53.6353662893364\\mathbf{\\hat{h}_z}\\otimes \\mathbf{\\hat{h}_z} - 0.0792250609886801\\mathbf{\\hat{b}_x}\\otimes \\mathbf{\\hat{b}_x} + 2.05985158570568\\mathbf{\\hat{b}_x}\\otimes \\mathbf{\\hat{b}_z} + 2.05985158570568\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_x} - 53.5561412283477\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_z}$"
|
|
],
|
|
"text/plain": [
|
|
"53.6353662893364 h_x⊗h_x + 53.6353662893364 h_y⊗h_y + 53.6353662893364 h_z⊗h_z - 0.0792250609886801 b_x⊗b_x + 2.05985158570568 b_x⊗b_z + 2.05985158570568 b_z⊗b_x - 53.5561412283477 b_z⊗b_z"
|
|
]
|
|
},
|
|
"execution_count": 26,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"r_Fo_Bo = r_O_Fo - r_O_Bo\n",
|
|
"U = me.outer(H.x, H.x) + me.outer(H.y, H.y) + me.outer(H.z, H.z)\n",
|
|
"I_Bo_Fo = mB * (r_Fo_Bo.dot(r_Fo_Bo) * U - me.outer(r_Fo_Bo, r_Fo_Bo))\n",
|
|
"I_Bo_Fo"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 27,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"I_B_Fo = I_B_Bo + I_Bo_Fo\n",
|
|
"I_H_Fo = I_H_Ho + I_Ho_Fo"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 28,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
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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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"$\\displaystyle 0.411437699680511\\mathbf{\\hat{b}_x}\\otimes \\mathbf{\\hat{b}_x} + 2.20261980830671\\mathbf{\\hat{b}_x}\\otimes \\mathbf{\\hat{b}_z} + 1.3\\mathbf{\\hat{b}_y}\\otimes \\mathbf{\\hat{b}_y} + 2.20261980830671\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_x} - 59.0681150159744\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_z} + 71.2566773162939\\mathbf{\\hat{h}_x}\\otimes \\mathbf{\\hat{h}_x} + 70.9566773162939\\mathbf{\\hat{h}_y}\\otimes \\mathbf{\\hat{h}_y} + 62.2566773162939\\mathbf{\\hat{h}_z}\\otimes \\mathbf{\\hat{h}_z} - 1.7\\mathbf{\\hat{h}_y}\\otimes \\mathbf{\\hat{h}_z} - 1.7\\mathbf{\\hat{h}_z}\\otimes \\mathbf{\\hat{h}_y}$"
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],
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"text/plain": [
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"0.411437699680511 b_x⊗b_x + 2.20261980830671 b_x⊗b_z + 1.30000000000000 b_y⊗b_y + 2.20261980830671 b_z⊗b_x - 59.0681150159744 b_z⊗b_z + 71.2566773162939 h_x⊗h_x + 70.9566773162939 h_y⊗h_y + 62.2566773162939 h_z⊗h_z - 1.70000000000000 h_y⊗h_z - 1.70000000000000 h_z⊗h_y"
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]
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},
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"execution_count": 28,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"I_F_Fo = I_B_Fo + I_H_Fo\n",
|
|
"I_F_Fo"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 29,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\displaystyle \\left[\\begin{matrix}71.3681150159744 & 0 & 0.50261980830671\\\\0 & 72.5566773162939 & 0\\\\0.50261980830671 & 0 & 3.18856230031949\\end{matrix}\\right]$"
|
|
],
|
|
"text/plain": [
|
|
"⎡71.3681150159744 0 0.50261980830671⎤\n",
|
|
"⎢ ⎥\n",
|
|
"⎢ 0 72.5566773162939 0 ⎥\n",
|
|
"⎢ ⎥\n",
|
|
"⎣0.50261980830671 0 3.18856230031949⎦"
|
|
]
|
|
},
|
|
"execution_count": 29,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"I_F_Fo.to_matrix(B)"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "turtle_trade",
|
|
"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": "3.10.16"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|