From 8ebfa76d00989e466b7bf1e47ff0285ca9651716 Mon Sep 17 00:00:00 2001
From: guoyz <yizeguo1@126.com>
Date: Sat, 15 Mar 2025 18:47:48 +0800
Subject: [PATCH] vault backup: 2025-03-15 18:47:48

---
 补课/多体动力学/14_inertia.ipynb | 205 ++++++++++++++++++++++++++++++-
 1 file changed, 200 insertions(+), 5 deletions(-)

diff --git a/补课/多体动力学/14_inertia.ipynb b/补课/多体动力学/14_inertia.ipynb
index 14668ef..d969eaf 100644
--- a/补课/多体动力学/14_inertia.ipynb
+++ b/补课/多体动力学/14_inertia.ipynb
@@ -232,17 +232,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [],
    "source": [
     "B = me.ReferenceFrame('B')\n",
-    "H = me.dynamicsymbols('H')"
+    "H = me.ReferenceFrame('H')"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -258,7 +258,7 @@
        "⎣0   0   -1⎦"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -270,12 +270,207 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "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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",
+      "text/latex": [
+       "$\\displaystyle 6.32131102695751\\mathbf{\\hat{h}_x}\\otimes \\mathbf{\\hat{h}_x} + 6.32131102695751\\mathbf{\\hat{h}_y}\\otimes \\mathbf{\\hat{h}_y} + 6.32131102695751\\mathbf{\\hat{h}_z}\\otimes \\mathbf{\\hat{h}_z} - 0.00933723933080879\\mathbf{\\hat{b}_x}\\otimes \\mathbf{\\hat{b}_x} + 0.242768222601028\\mathbf{\\hat{b}_x}\\otimes \\mathbf{\\hat{b}_z} + 0.242768222601028\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_x} - 6.3119737876267\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_z}$"
+      ],
+      "text/plain": [
+       "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"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "r_Fo_Ho = r_O_Fo - r_O_Ho\n",
+    "U = me.outer(H.x, H.x) + me.outer(H.y, H.y) + me.outer(H.z, H.z)\n",
+    "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": [
+    {
+     "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": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/latex": [
+       "$\\displaystyle 0.411437699680511\\mathbf{\\hat{b}_x}\\otimes \\mathbf{\\hat{b}_x} + 2.20261980830671\\mathbf{\\hat{b}_x}\\otimes \\mathbf{\\hat{b}_z} + 1.3\\mathbf{\\hat{b}_y}\\otimes \\mathbf{\\hat{b}_y} + 2.20261980830671\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_x} - 59.0681150159744\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_z} + 71.2566773162939\\mathbf{\\hat{h}_x}\\otimes \\mathbf{\\hat{h}_x} + 70.9566773162939\\mathbf{\\hat{h}_y}\\otimes \\mathbf{\\hat{h}_y} + 62.2566773162939\\mathbf{\\hat{h}_z}\\otimes \\mathbf{\\hat{h}_z} - 1.7\\mathbf{\\hat{h}_y}\\otimes \\mathbf{\\hat{h}_z} - 1.7\\mathbf{\\hat{h}_z}\\otimes \\mathbf{\\hat{h}_y}$"
+      ],
+      "text/plain": [
+       "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"
+      ]
+     },
+     "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": {