vault backup: 2025-03-28 09:27:26

This commit is contained in:
yz 2025-03-28 09:27:28 +08:00
parent 1f0dc8fce3
commit b7ca127094
10 changed files with 4903 additions and 774 deletions

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---
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
%%
## Drawing
```compressed-json
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```
%%

View 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
}

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---
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
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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}
],

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```
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{"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},
{"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},
{"id":"4fb6c3b08416426b","x":-537,"y":300,"width":429,"height":220,"type":"text","text":"对于holonomic系统中的刚体BB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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