vault backup: 2025-03-21 14:31:32

补课/多体动力学/16_generalized_forces.ipynb

@@ -0,0 +1,95 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle l \\dot{q}_{1}\\mathbf{\\hat{a}_x} + l \\dot{q}_{2}\\mathbf{\\hat{b}_x}$"
+      ],
+      "text/plain": [
+       "l⋅q₁̇ a_x + l⋅q₂̇ b_x"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import sympy as sm\n",
+    "import sympy.physics.mechanics as me\n",
+    "me.init_vprinting(use_latex='mathjax')\n",
+    "\n",
+    "l = sm.symbols('l')\n",
+    "q1, q2, u1, u2 = me.dynamicsymbols('q1, q2, u1, u2')\n",
+    "\n",
+    "N = me.ReferenceFrame('N')\n",
+    "A = me.ReferenceFrame('A')\n",
+    "B = me.ReferenceFrame('B')\n",
+    "\n",
+    "A.orient_axis(N, q1, N.z)\n",
+    "B.orient_axis(N, q2, N.z)\n",
+    "\n",
+    "O = me.Point('O')\n",
+    "P1 = me.Point('P1')\n",
+    "P2 = me.Point('P2')\n",
+    "\n",
+    "O.set_vel(N, 0)\n",
+    "\n",
+    "P1.set_pos(O, -l*A.y)\n",
+    "P2.set_pos(P1, -l*B.y)\n",
+    "\n",
+    "P1.v2pt_theory(O, N, A)\n",
+    "P2.v2pt_theory(P1, N, B)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle l \\cos{\\left(q_{1} \\right)} \\dot{q}_{1}\\mathbf{\\hat{n}_x} + l \\sin{\\left(q_{1} \\right)} \\dot{q}_{1}\\mathbf{\\hat{n}_y}$"
+      ],
+      "text/plain": [
+       "l⋅cos(q₁)⋅q₁̇ n_x + l⋅sin(q₁)⋅q₁̇ n_y"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "P1.vel(N).express(N)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "TagUIFocus5",
+   "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": "3.12.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

补课/多体动力学/16_generalized_forces.py

@@ -0,0 +1,27 @@
+import sympy as sm
+import sympy.physics.mechanics as me
+me.init_vprinting(use_latex='mathjax')
+
+l = sm.symbols('l')
+q1, q2, u1, u2 = me.dynamicsymbols('q1, q2, u1, u2')
+
+N = me.ReferenceFrame('N')
+A = me.ReferenceFrame('A')
+B = me.ReferenceFrame('B')
+
+A.orient_axis(N, q1, N.z)
+B.orient_axis(N, q2, N.z)
+
+O = me.Point('O')
+P1 = me.Point('P1')
+P2 = me.Point('P2')
+
+O.set_vel(N, 0)
+
+P1.set_pos(O, -l*A.y)
+P2.set_pos(P1, -l*B.y)
+
+P1.v2pt_theory(O, N, A)
+P2.v2pt_theory(P1, N, B)
+
+print(P1.vel(N).express(N))