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Excalidraw/Drawing 2025-03-27 15.49.37.excalidraw.md
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---
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excalidraw-plugin: parsed
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tags: [excalidraw]
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---
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==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
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# Excalidraw Data
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## Text Elements
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%%
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## Drawing
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```compressed-json
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||||
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|
||||
|
||||
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||||
|
||||
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||||
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||||
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||||
|
||||
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|
||||
|
||||
36/Ov2m2/5mAkug9rUsg3q44O3YkswrMU56ru09nzQ+/uJF254ZEoqNAmmK/utkHWYXdiNAP6x0H2oZj7cs5+1yUE4XP3Z37Syv0tWikn9Eq5S3wO793oO4y3jc6D3385D34rd2T4e6aHnbwQovLg9t4RpUGcC6NX/igIuU05zbjS84nqC+mRDi8c73HPuJw9OgH9fS3rBA+DHg27/XPFrE3jUr2tOoLk3sZsEp8BfJ9XUuZ36B/nX1SqTFEB7vH
|
||||
|
||||
NPYvXmpfHRjO9F3OoPL3W24s352WaNbnvObhJseZTm6lTqa/iC2kXLtHZRMMjcFbUBJ0BzmAAOmq4Ebg+wHWp7cecA++fe3bhnclQ/prXyMdBFIFL48Gs6EroPfS3ba7lXZf2y32S9XYinYSN21GCz27fiueSNY3W4d2cCha0XkHOvyhqCb7TTpdXAnNP6vW+ajvEyDn8+zV38B8qlvPvbJPyqQLpZNLbQ9OE5xAiPVGe5W39A+KbOFUIcd66rro
|
||||
|
||||
R/a3Ia7EVYKrjXbVN3u+wd3ugzp9dW29Fzz5mSPIG9uHYG9XnXxOsr41M1jM7uLI/Uk5XFwHZNpBIoAhY4+AXdg5sgPUFL2+7w6Vsc0n6gJqZjQvkWyXYzWby8nbHy8RHHY/fn6S8y3qh6yXXa+46eg8f3iAIr5mcq9Fj/Yr7fkUVyL6k1pRh9SLCdex37Yn9H1veRXtvdeCPDdCnIkXzrVm4PHdM18n/LPwXqZrQrbnXWnbnqDXRjUfFNA4kMr7
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||||
|
||||
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|
||||
|
||||
kd54d5jRnukIDI+F3ZBlODCksMTWp5E31ZNP6au/jDVds2D52dhbMy6MTtM7vF/ydLb6XJR+wQs73wWt3ur2zL1uGh9dr2x9dIkvX53jPCDHM2f9XTuoEE9J9d+oLfXvvPKjyR7KLjB+7tok8AyDOor3WiczX6ACcgsXVCgiZ30AgJOBJ7UM2AXQCxORh1WlOQ8Vn69p6zJ7ovzv27VnOxFsmPu66PFo5xtPy+tHnJ8h33J9cht075PkV1ll8Det
|
||||
|
||||
ng67KrqZf30A68IpUp/jrMp8YRbG9Hw6e5ZH7S+A70J8WXX45GN2PJwXxweTDLFqBlWzJQPY5frQDI5z1rpzePaC/C15AqePajxePmhb4nL8Zej9GKdP4BIXPg7JT1O5/89EU6OF04XKjpudCnQ1zbLyHoJsaxPfPdumI54tZxh1Ah/PUZ9A3U5apX2R/3hv56WmRvX68V6GwAMezgAFwBRMPS383+nNKF7EHIntR5eqII04XcVdrXSysczcg6S3
|
||||
|
||||
79OtDLJ+EX/u6v3Yi8bPwe77HgK6CdMlbxAHSR2hmq6gSVtwpzESjj3/pXfA5qkHP8To0rKe4eOuPdWPfGfWPdPGTqlrBQXm52yd9OvRsth6IZKKdKdN68IWCZ4lrxqr53OJvYbux5XPqVIp9+eUw7envYrtPqI74l48G+svx3eM6m9U58Fmz8hNcV56UThCzXP3eZa7Gw8l32VOutW2/2MZaRxS+u/kzgU/C1EtSqxBNl8vWyWTSIl57diHZNBB
|
||||
|
||||
nVoP4zwElWJodY0V8IXE+5AvupMdnLgk83EAHZNPsUNGYrrVoElqgawwDCgD6Cud6F77b7Hk0n2blQn9mag+sh9dx8h8V7La9Ivyh76Pg8P+XGI4K7TXvy3rpVGGPFE9ShNUcD7wF6vjE/aaxh9wBI5+xFiK4EvBi6Ev73LfTSp9is0l9Z7Xg59dzedCn9GMMTJaSG3A9fKjYnPC1NDI2vx57PX4CYdP6ha2vzOr8nyYbEv8vFG3im7wPaw7Iq7h
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||||
|
||||
/X5axMp7Fl9eCyR9NWz1+XnSJ6yPupJyPMQ83nbdiMARuI8gZUU1GQgCDpFAEBzSjivNb5NWlV9KLP+o7d3Abb96KNoodp+/zdQi9qvl+/qvHJ6y3Ax7R1OS/3zbZ4lQw2iTZk08HXanbboqYxiUIRoHPjrkGv7JOx3fat/7Q3es7dM3Ujli7xdd1pOPNLqE33VMO3rN5Ex2pYCPkBKZ9Pp7j9lp63Ppr3X5wCaaN7F31lvp9CDyB4DPBHMLbhwe
|
||||
|
||||
U337YMv0BVE3+suF3LN5acJ26iHZp9IW2t4xPRvX6WmAHwAqlouqyao+AFAFaAmAG9E+HmCgoh/znOWWto52Chm/Q0icm12+9WTb4KL6hCN8izWrhGernKN9S330/Rv7J/IvWN65P6h50Hbrfxv6pVng2h+JvJRizL712Oh20M4v1N4WPw56WP/bk5rCWZmnAB61LE6r9VLnbrTlK513JC/v4P19zgs3xeAzyG3zpy6ZSrQmcAYgFIAq4DUOJEvJ
|
||||
|
||||
PYstKnDy4FXW1xHbmCqqDVvuczyN6IvqN+6Plo8jbTqb1n6I7qHnU7YTURdVX08g1XPRNCzm3T6GAFH3TVN+DMNN7QZph5Gvl0fYn10aa7V6Y+TBzNVlOM5ORbnpXBtx/l4JnZZ3tquTH9O+4bwtu0TYTMnRoJ6+vat/XPNl8qTEnx0v4fJOZze9VvGkbQqb4Zez0Z4r9Lm4aTfM7rbeyHAAdEFIQ1hY1AaiG4A5YGgAiIAyAswDdoiwAYALzjVH
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||||
|
||||
mjNZA8d2If27LxLIgFfgjVnSAGoEIvRijIfGkA2glD5LwCh5zEdD4ofm4D7KhBpKAcofofWQEYf1D79RrD4Yf7D/4f87aXIgj94f7D7OQ6rXEfXJXYfCCup2Mj8Yf1hiyAXdlYg+AFMmuD+4fbD/SAyj/5dhACyZAnU0f5D6Ef6QAgNmABjgRAEVDswF68UdEUfwj+jgnWFawxdDsf6QFfWxAEcfMeETwccB5ALj+dzf6EGAnQjvgPj+YA+JcZA1
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||||
|
||||
RS8oLbX1AoT7VA7yBIavjb1Xj1FwfxQIMAaD6JgBAAWQ5oAzwvj6kfmOvKAQT9wfQoBIAIwH0f1YFRt/JiKfm4HRME1AKf78P68bACvIr6wcLwQBHE5T/oy2cB/2+AFzgpADLwuAAAAFNNlqAGnwPwEM/Bn9xgAAJR6gCeLKACZCkobp98gfp+T8LfRegJZ+jP4BATPrJ9aPjaAiPhAAIKqADjgNbSfNCeK5gd+FB4DTC1YIRRuvLGC7OA+mEAKp
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||||
|
||||
+XrIRRYPnXrCAfqQ5gYLhZPuwAW4xBo8+IRRiu+p8IARp+XPlp/8gPZ+MAev2aBBGC9tuUMUgAwABPvogNLsPQlBEF/PrT8ngvpVDmQcADowdsxeZYAC1gEAC1gIAA==
|
||||
```
|
||||
%%
|
218
多体+耦合求解器/WindTurbine_Kane推导.ipynb
Normal file
218
多体+耦合求解器/WindTurbine_Kane推导.ipynb
Normal file
@ -0,0 +1,218 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import sympy as sm\n",
|
||||
"import sympy.physics.mechanics as me\n",
|
||||
"me.init_vprinting(use_latex='mathjax')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# 建立坐标系"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def smll_rot_trans(theta1, theta2, theta3):\n",
|
||||
" theta11 = theta1 * theta1\n",
|
||||
" theta22 = theta2 * theta2\n",
|
||||
" theta33 = theta3 * theta3\n",
|
||||
" sqrd_sum = theta11 + theta22 + theta33\n",
|
||||
" sqrt1_sqrd_sum = (1.0 + sqrd_sum)**0.5\n",
|
||||
" com_denom = sqrd_sum * sqrt1_sqrd_sum\n",
|
||||
" theta12s = theta1 * theta2 * (sqrt1_sqrd_sum - 1.0)\n",
|
||||
" theta13s = theta1 * theta3 * (sqrt1_sqrd_sum - 1.0)\n",
|
||||
" theta23s = theta2 * theta3 * (sqrt1_sqrd_sum - 1.0)\n",
|
||||
" \n",
|
||||
" if com_denom == 0.0:\n",
|
||||
" trans_mat = sm.Matrix([[1.0, 0.0, 0.0],\n",
|
||||
" [0.0, 1.0, 0.0],\n",
|
||||
" [0.0, 0.0, 1.0]])\n",
|
||||
" \n",
|
||||
" else:\n",
|
||||
" trans_mat = sm.Matrix([[(theta11 * sqrt1_sqrd_sum + theta22 + theta33) / com_denom, (theta3 * sqrd_sum + theta12s) / com_denom, (-theta2 * sqrd_sum + theta13s) / com_denom],\n",
|
||||
" [(-theta3 * sqrd_sum + theta12s) / com_denom, (theta11 + theta22 * sqrt1_sqrd_sum + theta33) / com_denom, (theta1 * sqrd_sum + theta23s) / com_denom],\n",
|
||||
" [(theta2 * sqrd_sum + theta13s) / com_denom, (-theta1 * sqrd_sum + theta23s) / com_denom, (theta11 + theta22 + theta33 * sqrt1_sqrd_sum) / com_denom]])\n",
|
||||
" return trans_mat"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 31,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/latex": [
|
||||
"$\\displaystyle \\left[\\begin{matrix}\\frac{\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5} \\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}}{\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5}} & \\frac{\\left(\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5} - 1.0\\right) \\theta_{1} \\theta_{2} + \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\theta_{3}}{\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5}} & \\frac{\\left(\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5} - 1.0\\right) \\theta_{1} \\theta_{3} - \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\theta_{2}}{\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5}}\\\\\\frac{\\left(\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5} - 1.0\\right) \\theta_{1} \\theta_{2} - \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\theta_{3}}{\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5}} & \\frac{\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5} \\theta_{2}^{2} + \\theta_{1}^{2} + \\theta_{3}^{2}}{\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5}} & \\frac{\\left(\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5} - 1.0\\right) \\theta_{2} \\theta_{3} + \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\theta_{1}}{\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5}}\\\\\\frac{\\left(\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5} - 1.0\\right) \\theta_{1} \\theta_{3} + \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\theta_{2}}{\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5}} & \\frac{\\left(\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5} - 1.0\\right) \\theta_{2} \\theta_{3} - \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\theta_{1}}{\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5}} & \\frac{\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5} \\theta_{3}^{2} + \\theta_{1}^{2} + \\theta_{2}^{2}}{\\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2}\\right) \\left(\\theta_{1}^{2} + \\theta_{2}^{2} + \\theta_{3}^{2} + 1.0\\right)^{0.5}}\\end{matrix}\\right]$"
|
||||
],
|
||||
"text/plain": [
|
||||
"⎡ ⎛ 0.5 ⎞ ↪\n",
|
||||
"⎢ ⎜⎛ 2 2 2 ⎞ 2 2 2⎟ ⎛ 2 2 2 ↪\n",
|
||||
"⎢ ⎝⎝θ₁ + θ₂ + θ₃ + 1.0⎠ ⋅θ₁ + θ₂ + θ₃ ⎠⋅⎝θ₁ + θ₂ + θ₃ + 1.0 ↪\n",
|
||||
"⎢ ─────────────────────────────────────────────────────────────────── ↪\n",
|
||||
"⎢ 2 2 2 ↪\n",
|
||||
"⎢ θ₁ + θ₂ + θ₃ ↪\n",
|
||||
"⎢ ↪\n",
|
||||
"⎢⎛⎛ 0.5 ⎞ ⎞ ↪\n",
|
||||
"⎢⎜⎜⎛ 2 2 2 ⎞ ⎟ ⎛ 2 2 2⎞ ⎟ ⎛ 2 2 ↪\n",
|
||||
"⎢⎝⎝⎝θ₁ + θ₂ + θ₃ + 1.0⎠ - 1.0⎠⋅θ₁⋅θ₂ - ⎝θ₁ + θ₂ + θ₃ ⎠⋅θ₃⎠⋅⎝θ₁ + θ₂ ↪\n",
|
||||
"⎢───────────────────────────────────────────────────────────────────────────── ↪\n",
|
||||
"⎢ 2 2 2 ↪\n",
|
||||
"⎢ θ₁ + θ₂ + θ₃ ↪\n",
|
||||
"⎢ ↪\n",
|
||||
"⎢⎛⎛ 0.5 ⎞ ⎞ ↪\n",
|
||||
"⎢⎜⎜⎛ 2 2 2 ⎞ ⎟ ⎛ 2 2 2⎞ ⎟ ⎛ 2 2 ↪\n",
|
||||
"⎢⎝⎝⎝θ₁ + θ₂ + θ₃ + 1.0⎠ - 1.0⎠⋅θ₁⋅θ₃ + ⎝θ₁ + θ₂ + θ₃ ⎠⋅θ₂⎠⋅⎝θ₁ + θ₂ ↪\n",
|
||||
"⎢───────────────────────────────────────────────────────────────────────────── ↪\n",
|
||||
"⎢ 2 2 2 ↪\n",
|
||||
"⎣ θ₁ + θ₂ + θ₃ ↪\n",
|
||||
"\n",
|
||||
"↪ -0.5 ⎛⎛ 0.5 ⎞ ↪\n",
|
||||
"↪ ⎞ ⎜⎜⎛ 2 2 2 ⎞ ⎟ ⎛ 2 2 ↪\n",
|
||||
"↪ ⎠ ⎝⎝⎝θ₁ + θ₂ + θ₃ + 1.0⎠ - 1.0⎠⋅θ₁⋅θ₂ + ⎝θ₁ + θ₂ + θ ↪\n",
|
||||
"↪ ───── ────────────────────────────────────────────────────────── ↪\n",
|
||||
"↪ 2 2 2 ↪\n",
|
||||
"↪ θ₁ + θ₂ + θ₃ ↪\n",
|
||||
"↪ ↪\n",
|
||||
"↪ -0.5 ⎛ 0.5 ⎞ ↪\n",
|
||||
"↪ 2 ⎞ ⎜⎛ 2 2 2 ⎞ 2 2 2⎟ ⎛ ↪\n",
|
||||
"↪ + θ₃ + 1.0⎠ ⎝⎝θ₁ + θ₂ + θ₃ + 1.0⎠ ⋅θ₂ + θ₁ + θ₃ ⎠⋅⎝θ₁ ↪\n",
|
||||
"↪ ──────────────── ──────────────────────────────────────────────── ↪\n",
|
||||
"↪ 2 2 2 ↪\n",
|
||||
"↪ θ₁ + θ₂ + θ₃ ↪\n",
|
||||
"↪ ↪\n",
|
||||
"↪ -0.5 ⎛⎛ 0.5 ⎞ ↪\n",
|
||||
"↪ 2 ⎞ ⎜⎜⎛ 2 2 2 ⎞ ⎟ ⎛ 2 2 ↪\n",
|
||||
"↪ + θ₃ + 1.0⎠ ⎝⎝⎝θ₁ + θ₂ + θ₃ + 1.0⎠ - 1.0⎠⋅θ₂⋅θ₃ - ⎝θ₁ + θ₂ + θ ↪\n",
|
||||
"↪ ──────────────── ────────────────────────────────────────────────────────── ↪\n",
|
||||
"↪ 2 2 2 ↪\n",
|
||||
"↪ θ₁ + θ₂ + θ₃ ↪\n",
|
||||
"\n",
|
||||
"↪ ⎞ -0.5 ⎛⎛ 0.5 ⎞ ↪\n",
|
||||
"↪ 2⎞ ⎟ ⎛ 2 2 2 ⎞ ⎜⎜⎛ 2 2 2 ⎞ ⎟ ↪\n",
|
||||
"↪ ₃ ⎠⋅θ₃⎠⋅⎝θ₁ + θ₂ + θ₃ + 1.0⎠ ⎝⎝⎝θ₁ + θ₂ + θ₃ + 1.0⎠ - 1.0⎠⋅θ₁⋅ ↪\n",
|
||||
"↪ ─────────────────────────────────── ─────────────────────────────────────── ↪\n",
|
||||
"↪ ↪\n",
|
||||
"↪ ↪\n",
|
||||
"↪ ↪\n",
|
||||
"↪ -0.5 ⎛⎛ 0.5 ⎞ ↪\n",
|
||||
"↪ 2 2 2 ⎞ ⎜⎜⎛ 2 2 2 ⎞ ⎟ ↪\n",
|
||||
"↪ + θ₂ + θ₃ + 1.0⎠ ⎝⎝⎝θ₁ + θ₂ + θ₃ + 1.0⎠ - 1.0⎠⋅θ₂⋅ ↪\n",
|
||||
"↪ ──────────────────────── ─────────────────────────────────────── ↪\n",
|
||||
"↪ ↪\n",
|
||||
"↪ ↪\n",
|
||||
"↪ ↪\n",
|
||||
"↪ ⎞ -0.5 ⎛ 0.5 ↪\n",
|
||||
"↪ 2⎞ ⎟ ⎛ 2 2 2 ⎞ ⎜⎛ 2 2 2 ⎞ ↪\n",
|
||||
"↪ ₃ ⎠⋅θ₁⎠⋅⎝θ₁ + θ₂ + θ₃ + 1.0⎠ ⎝⎝θ₁ + θ₂ + θ₃ + 1.0⎠ ⋅θ ↪\n",
|
||||
"↪ ─────────────────────────────────── ───────────────────────────── ↪\n",
|
||||
"↪ ↪\n",
|
||||
"↪ θ ↪\n",
|
||||
"\n",
|
||||
"↪ ⎞ -0.5⎤\n",
|
||||
"↪ ⎛ 2 2 2⎞ ⎟ ⎛ 2 2 2 ⎞ ⎥\n",
|
||||
"↪ θ₃ - ⎝θ₁ + θ₂ + θ₃ ⎠⋅θ₂⎠⋅⎝θ₁ + θ₂ + θ₃ + 1.0⎠ ⎥\n",
|
||||
"↪ ──────────────────────────────────────────────────────⎥\n",
|
||||
"↪ 2 2 2 ⎥\n",
|
||||
"↪ θ₁ + θ₂ + θ₃ ⎥\n",
|
||||
"↪ ⎥\n",
|
||||
"↪ ⎞ -0.5⎥\n",
|
||||
"↪ ⎛ 2 2 2⎞ ⎟ ⎛ 2 2 2 ⎞ ⎥\n",
|
||||
"↪ θ₃ + ⎝θ₁ + θ₂ + θ₃ ⎠⋅θ₁⎠⋅⎝θ₁ + θ₂ + θ₃ + 1.0⎠ ⎥\n",
|
||||
"↪ ──────────────────────────────────────────────────────⎥\n",
|
||||
"↪ 2 2 2 ⎥\n",
|
||||
"↪ θ₁ + θ₂ + θ₃ ⎥\n",
|
||||
"↪ ⎥\n",
|
||||
"↪ ⎞ -0.5 ⎥\n",
|
||||
"↪ 2 2 2⎟ ⎛ 2 2 2 ⎞ ⎥\n",
|
||||
"↪ ₃ + θ₁ + θ₂ ⎠⋅⎝θ₁ + θ₂ + θ₃ + 1.0⎠ ⎥\n",
|
||||
"↪ ─────────────────────────────────────────── ⎥\n",
|
||||
"↪ 2 2 2 ⎥\n",
|
||||
"↪ ₁ + θ₂ + θ₃ ⎦"
|
||||
]
|
||||
},
|
||||
"execution_count": 31,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"A = me.ReferenceFrame('A')\n",
|
||||
"B = me.ReferenceFrame('B')\n",
|
||||
"D = me.ReferenceFrame('D')\n",
|
||||
"C = me.ReferenceFrame('C')\n",
|
||||
"G = me.ReferenceFrame('G')\n",
|
||||
"G_prime1 = me.ReferenceFrame('G_prime1')\n",
|
||||
"G_prime2 = me.ReferenceFrame('G_prime2')\n",
|
||||
"G_prime3 = me.ReferenceFrame('G_prime3')\n",
|
||||
"# fast x-1, -y-3, z-2\n",
|
||||
"\n",
|
||||
"# 广义坐标\n",
|
||||
"q1, q2, q3, q4, q_yaw, q_drtr, q_geaz, q_1f1, q_1f2, q_1e1, q_2f1, q_2f2, q_2e1, q_3f1, q_3f2, q_3e1 = me.dynamicsymbols('q1, q2, q3, q4, q_yaw, q_drtr, q_geaz, q_1f1, q_1f2, q_1e1, q_2f1, q_2f2, q_2e1, q_3f1, q_3f2, q_3e1')\n",
|
||||
"# tower top\n",
|
||||
"theta1, theta2, theta3 = me.dynamicsymbols(\"theta1, theta2, theta3\")\n",
|
||||
"dcm = smll_rot_trans(theta1, theta2, theta3)\n",
|
||||
"B.orient_dcm(A, dcm)\n",
|
||||
"\n",
|
||||
"# nacelle\n",
|
||||
"D.orient_axis(B, q_yaw, B.y)\n",
|
||||
"\n",
|
||||
"# shaft C \n",
|
||||
"theta_tilt = sm.symbols(\"theta_tilt\")\n",
|
||||
"C.orient_axis(D, theta_tilt, D.z)\n",
|
||||
"\n",
|
||||
"# Hub G = Azimuth E\n",
|
||||
"Azimuth = q_drtr + q_geaz\n",
|
||||
"G.orient_axis(C, Azimuth, C.x)\n",
|
||||
"\n",
|
||||
"# 到每只叶片\n",
|
||||
"angle = 2*sm.pi/3\n",
|
||||
"G_prime1.orient_axis(G, angle * 0, G.x)\n",
|
||||
"G_prime2.orient_axis(G, angle * 1, G.x)\n",
|
||||
"G_prime3.orient_axis(G, angle * 2, G.x)\n",
|
||||
"\n",
|
||||
"B.dcm(A)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# 速度"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "MinerU",
|
||||
"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
|
||||
}
|
943
多体+耦合求解器/风机模型.excalidraw.md
Normal file
943
多体+耦合求解器/风机模型.excalidraw.md
Normal file
@ -0,0 +1,943 @@
|
||||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
## Embedded Files
|
||||
c0166535889251fc00499757c5d32377c8fd6767: [[Pasted Image 20250120103502_252.png]]
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
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||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
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||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
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|
||||
```
|
||||
%%
|
@ -1,7 +1,7 @@
|
||||
{
|
||||
"nodes":[
|
||||
{"id":"b698e88ca5fb9c51","type":"text","text":"状态指标:\n推进OKR的时候也要关注这些事情,它们是完成OKR的保障。\n\n\n效率状态 green","x":-96,"y":80,"width":456,"height":347},
|
||||
{"id":"58be7961ae7275a7","type":"text","text":"# 计划\n这周要做的3~5件重要的事情,这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\nP1 多体原理学习 YouTube课程 016\nP1 根据公共mesh模块调整代码 yes\nP1 气动模块联合调试,跑通 no\nP1 稳态工况多体动力学求解方法\n\n","x":-620,"y":-307,"width":450,"height":347},
|
||||
{"id":"58be7961ae7275a7","type":"text","text":"# 计划\n这周要做的3~5件重要的事情,这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\nP1 多体原理学习 YouTube课程 018\nP1 气动模块联合调试,跑通 no\nP1 稳态工况多体动力学求解方法\nP1 使用python搭建风电机组多体模型\n\n","x":-620,"y":-307,"width":450,"height":347},
|
||||
{"id":"2b068bfe5df15a72","type":"text","text":"# 目标:多体动力学模块完善\n### 每周盘点一下它们\n\n\n关键结果:建模原理、建模方法掌握 (6.8/10)\n\n关键结果:对标Bladed模块完成 (7.2/10)\n\n关键结果:风机多体动力学文献调研情况完成 (5/10)","x":-96,"y":-307,"width":456,"height":347},
|
||||
{"id":"01ee5c157d0deeae","type":"text","text":"# 推进计划\n未来四周计划推进的重要事情\n\n文献调研启动\n\n建模重新推导\n\n\n","x":-620,"y":80,"width":456,"height":347}
|
||||
],
|
||||
|
BIN
工作总结/周报/周报70-郭翼泽.docx
Normal file
BIN
工作总结/周报/周报70-郭翼泽.docx
Normal file
Binary file not shown.
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||||
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|
||||
```
|
||||
%%
|
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1374
补课/多体动力学/18_Simulation_and_Visualization.ipynb
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1374
补课/多体动力学/18_Simulation_and_Visualization.ipynb
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@ -1,11 +1,17 @@
|
||||
{
|
||||
"nodes":[
|
||||
{"id":"330ceae2327436f1","type":"text","text":"牛顿-欧拉方程\n\n$$\n\\begin{split}\\bar{F} = & \\frac{{}^N d \\bar{p}}{dt} \\quad \\textrm{ where } \\bar{p} = m_B{}^N\\bar{v}^{B_o} \\\\\\bar{M} = & \\frac{{}^N d\\bar{H}}{dt} \\quad \\textrm{ where }\\bar{H} = \\breve{I}^{B/B_o} \\cdot {}^N\\bar{\\omega}^{B}\\end{split}|","x":-242,"y":-194,"width":542,"height":174},
|
||||
{"id":"04fa17192ff0596c","x":-242,"y":160,"width":250,"height":60,"type":"text","text":"GAF Generalized Active Force 左端项"},
|
||||
{"id":"c574d94bf9b233b4","x":50,"y":160,"width":250,"height":60,"type":"text","text":"GIF Generalized Inertia Force 右端项"}
|
||||
{"id":"04fa17192ff0596c","type":"text","text":"GAF Generalized Active Force 左端项","x":-448,"y":160,"width":250,"height":60},
|
||||
{"id":"3dd1bf823248bf74","type":"text","text":"完整约束(holonomic)\n**约束方程中不包含坐标对时间的导数(不包含运动约束)**,或者约束方程中的微分项可以积分为有限形式的约束(几何约束或可积分的运动约束)\n$f_s(x_k, y_k, z_k;;t)=0$\n$f_s(x_k, y_k, z_k;\\dot{x_k},\\dot{y_k},\\dot{z_k};t)=0$","x":960,"y":-214,"width":340,"height":214},
|
||||
{"id":"3f3febc750ff1af8","type":"text","text":"非完整约束(nonholonomic)\n**约束方程中包含坐标对时间的导数(包含运动约束,对广义速度u1...ur的约束)**,且不可能积分成有限形式的约束(包括积分的运动约束)\n$f_s(x_k, y_k, z_k;\\dot{x_k},\\dot{y_k},\\dot{z_k};t)=0$","x":960,"y":60,"width":340,"height":200},
|
||||
{"id":"c574d94bf9b233b4","type":"text","text":"GIF Generalized Inertia Force 右端项","x":231,"y":160,"width":250,"height":60},
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{"id":"027a3e957d393870","type":"text","text":"对于holonomic系统中的刚体B,质量$m_B$,质量中心$B_o$,中心inertia dyadic $\\breve{I}^{B/Bo}$。\n$(F_r^*)_B := {}^A\\bar{v}^{B_o}_r \\cdot \\bar{R}^* + {}^A\\bar{\\omega}^B_r \\cdot \\bar{T}^*$\n${}^A\\bar{v}^{B_o}_r$对广义速度$u_r$的偏速度\n${}^A\\bar{\\omega}^B_r$对广义速度$u_r$的偏角速度\n inertia force on the body:\n $\\bar{R}^* := -m_{B} {}^A\\bar{a}^{B_o}$\n ${}^A\\bar{a}^{B_o}$ $B_0$在A的线加速度\n _inertia torque_ on the body:\n $\\bar{T}^* := -\\left({}^A\\bar{\\alpha}^B \\cdot \\breve{I}^{B/Bo} +{}^A\\bar{\\omega}^B \\times\\breve{I}^{B/Bo} \\cdot {}^A\\bar{\\omega}^B\\right)$\n${}^A\\bar{\\alpha}^B$ $B$在A的角加速度\n \n ","x":126,"y":300,"width":460,"height":320},
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{"id":"4fb6c3b08416426b","x":-537,"y":300,"width":429,"height":220,"type":"text","text":"对于holonomic系统中的刚体B,B上的力表示为一个作用与B上Q点的合力与合力偶。\n$(F_r)_B := {}^A\\bar{v}^Q_r \\cdot \\bar{R} + {}^A\\bar{\\omega}^B_r \\cdot \\bar{T}$\n${}^A\\bar{v}^Q_r$对广义速度$u_r$的偏速度\n${}^A\\bar{\\omega}^B_r$对广义速度$u_r$的偏角速度\n$\\bar{R}$ 作用线通过B上Q点的合力,Q可以是质量中心$B_o$\n$\\bar{T}$ B上的扭矩"}
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],
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}
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