obsidian_backup/补课/多体动力学/05_vectors.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sm\n",
    "import sympy.physics.mechanics as me\n",
    "sm.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "q1, q2, q3, q4 = sm.symbols('q1:5')\n",
    "l1, l2, l3, l4 = sm.symbols('l1:5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "N, A, B, C = sm.symbols(\"N, A, B, C\", cls=me.ReferenceFrame)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\cos{\\left(q_{1} \\right)} & \\sin{\\left(q_{1} \\right)} & 0\\\\- \\sin{\\left(q_{1} \\right)} \\cos{\\left(q_{2} \\right)} & \\cos{\\left(q_{1} \\right)} \\cos{\\left(q_{2} \\right)} & \\sin{\\left(q_{2} \\right)}\\\\\\sin{\\left(q_{1} \\right)} \\sin{\\left(q_{2} \\right)} & - \\sin{\\left(q_{2} \\right)} \\cos{\\left(q_{1} \\right)} & \\cos{\\left(q_{2} \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡    cos(q₁)           sin(q₁)          0   ⎤\n",
       "⎢                                           ⎥\n",
       "⎢-sin(q₁)⋅cos(q₂)  cos(q₁)⋅cos(q₂)   sin(q₂)⎥\n",
       "⎢                                           ⎥\n",
       "⎣sin(q₁)⋅sin(q₂)   -sin(q₂)⋅cos(q₁)  cos(q₂)⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.orient_body_fixed(N, (q1, q2, 0),'ZXZ')\n",
    "A.dcm(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "B.orient_axis(A, q3, A.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "C.orient_body_fixed(B, (q3, q4, 0), 'XZX')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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