{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sm\n",
    "import sympy.physics.mechanics as me\n",
    "me.init_vprinting()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N, A, B = sm.symbols(\"N, A, B\", cls=me.ReferenceFrame)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha, beta = me.dynamicsymbols(\"alpha, beta\")\n",
    "d, w, c, l = sm.symbols(\"d, w, c, l\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "A.orient_axis(N, alpha, N.z)\n",
    "B.orient_axis(A, beta, A.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle -  d \\dot{\\alpha}\\mathbf{\\hat{a}_y}$"
      ],
      "text/plain": [
       "-d⋅α̇ a_y"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N_v_s = -d * alpha.diff() * A.y\n",
    "N_v_s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\dot{\\alpha}\\mathbf{\\hat{n}_z} + \\dot{\\beta}\\mathbf{\\hat{a}_x}$"
      ],
      "text/plain": [
       "α̇ n_z + β̇ a_x"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.ang_vel_in(N) + B.ang_vel_in(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\dot{\\beta}\\mathbf{\\hat{a}_x} + \\dot{\\alpha}\\mathbf{\\hat{n}_z}$"
      ],
      "text/plain": [
       "β̇ a_x + α̇ n_z"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.ang_vel_in(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle -  w\\mathbf{\\hat{b}_x} + (- c - \\frac{l}{2})\\mathbf{\\hat{b}_z}$"
      ],
      "text/plain": [
       "         ⎛     l⎞    \n",
       "-w b_x + ⎜-c - ─⎟ b_z\n",
       "         ⎝     2⎠    "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_S_Q = -w * B.x - (c + l/2) * B.z\n",
    "r_S_Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle -  d \\dot{\\alpha}\\mathbf{\\hat{a}_y} + \\left(- c - \\frac{l}{2}\\right) \\sin{\\left(\\beta \\right)} \\dot{\\alpha}\\mathbf{\\hat{b}_x} + (- w \\cos{\\left(\\beta \\right)} \\dot{\\alpha} - \\left(- c - \\frac{l}{2}\\right) \\dot{\\beta})\\mathbf{\\hat{b}_y} + w \\sin{\\left(\\beta \\right)} \\dot{\\alpha}\\mathbf{\\hat{b}_z}$"
      ],
      "text/plain": [
       "           ⎛     l⎞                ⎛              ⎛     l⎞  ⎞                  ↪\n",
       "-d⋅α̇ a_y + ⎜-c - ─⎟⋅sin(β)⋅α̇ b_x + ⎜-w⋅cos(β)⋅α̇ - ⎜-c - ─⎟⋅β̇⎟ b_y + w⋅sin(β)⋅α̇ ↪\n",
       "           ⎝     2⎠                ⎝              ⎝     2⎠  ⎠                  ↪\n",
       "\n",
       "↪     \n",
       "↪  b_z\n",
       "↪     "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N_v_Q = N_v_s + B.ang_vel_in(N).cross(r_S_Q)\n",
    "N_v_Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left(- c - \\frac{l}{2}\\right) \\sin{\\left(\\beta \\right)} \\dot{\\alpha}\\mathbf{\\hat{b}_x} + (- d \\cos{\\left(\\beta \\right)} \\dot{\\alpha} - w \\cos{\\left(\\beta \\right)} \\dot{\\alpha} - \\left(- c - \\frac{l}{2}\\right) \\dot{\\beta})\\mathbf{\\hat{b}_y} + (d \\sin{\\left(\\beta \\right)} \\dot{\\alpha} + w \\sin{\\left(\\beta \\right)} \\dot{\\alpha})\\mathbf{\\hat{b}_z}$"
      ],
      "text/plain": [
       "⎛     l⎞                ⎛                           ⎛     l⎞  ⎞                ↪\n",
       "⎜-c - ─⎟⋅sin(β)⋅α̇ b_x + ⎜-d⋅cos(β)⋅α̇ - w⋅cos(β)⋅α̇ - ⎜-c - ─⎟⋅β̇⎟ b_y + (d⋅sin(β ↪\n",
       "⎝     2⎠                ⎝                           ⎝     2⎠  ⎠                ↪\n",
       "\n",
       "↪                      \n",
       "↪ )⋅α̇ + w⋅sin(β)⋅α̇) b_z\n",
       "↪                      "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N_v_Q.express(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "手动创建点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "S, Q = sm.symbols(\"S, Q\", cls=me.Point)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q.set_pos(S, r_S_Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle -  w\\mathbf{\\hat{b}_x} + (- c - \\frac{l}{2})\\mathbf{\\hat{b}_z}$"
      ],
      "text/plain": [
       "         ⎛     l⎞    \n",
       "-w b_x + ⎜-c - ─⎟ b_z\n",
       "         ⎝     2⎠    "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q.pos_from(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "S.set_vel(N, N_v_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle -  d \\dot{\\alpha}\\mathbf{\\hat{a}_y}$"
      ],
      "text/plain": [
       "-d⋅α̇ a_y"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.vel(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle -  d \\dot{\\alpha}\\mathbf{\\hat{a}_y} + \\left(- c - \\frac{l}{2}\\right) \\sin{\\left(\\beta \\right)} \\dot{\\alpha}\\mathbf{\\hat{b}_x} + (- w \\cos{\\left(\\beta \\right)} \\dot{\\alpha} - \\left(- c - \\frac{l}{2}\\right) \\dot{\\beta})\\mathbf{\\hat{b}_y} + w \\sin{\\left(\\beta \\right)} \\dot{\\alpha}\\mathbf{\\hat{b}_z}$"
      ],
      "text/plain": [
       "           ⎛     l⎞                ⎛              ⎛     l⎞  ⎞                  ↪\n",
       "-d⋅α̇ a_y + ⎜-c - ─⎟⋅sin(β)⋅α̇ b_x + ⎜-w⋅cos(β)⋅α̇ - ⎜-c - ─⎟⋅β̇⎟ b_y + w⋅sin(β)⋅α̇ ↪\n",
       "           ⎝     2⎠                ⎝              ⎝     2⎠  ⎠                  ↪\n",
       "\n",
       "↪     \n",
       "↪  b_z\n",
       "↪     "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q.v2pt_theory(S, N, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = me.dynamicsymbols(\"s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle (- w + s)\\mathbf{\\hat{b}_x} + (- c + \\frac{l}{2})\\mathbf{\\hat{b}_z}$"
      ],
      "text/plain": [
       "               ⎛     l⎞    \n",
       "(-w + s) b_x + ⎜-c + ─⎟ b_z\n",
       "               ⎝     2⎠    "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_S_R = (s - w) * B.x + (l/2 -c) * B.z\n",
    "r_S_R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\dot{s}\\mathbf{\\hat{b}_x}$"
      ],
      "text/plain": [
       "ṡ b_x"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B_v_R = s.diff() * B.x\n",
    "B_v_R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\dot{\\beta}\\mathbf{\\hat{a}_x}$"
      ],
      "text/plain": [
       "β̇ a_x"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.ang_vel_in(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\dot{s}\\mathbf{\\hat{b}_x} -  \\left(- c + \\frac{l}{2}\\right) \\dot{\\beta}\\mathbf{\\hat{b}_y}$"
      ],
      "text/plain": [
       "         ⎛     l⎞      \n",
       "ṡ b_x + -⎜-c + ─⎟⋅β̇ b_y\n",
       "         ⎝     2⎠      "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_V_R = B_v_R + me.cross(B.ang_vel_in(A), r_S_R)\n",
    "A_V_R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle -  \\left(- c + \\frac{l}{2}\\right) \\ddot{\\beta}\\mathbf{\\hat{b}_y}$"
      ],
      "text/plain": [
       " ⎛     l⎞      \n",
       "-⎜-c + ─⎟⋅β̈ b_y\n",
       " ⎝     2⎠      "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "me.cross(B.ang_acc_in(A), r_S_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle -  \\left(- c + \\frac{l}{2}\\right) \\dot{\\beta}^{2}\\mathbf{\\hat{b}_z}$"
      ],
      "text/plain": [
       " ⎛     l⎞  2    \n",
       "-⎜-c + ─⎟⋅β̇  b_z\n",
       " ⎝     2⎠       "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "me.cross(B.ang_vel_in(A), me.cross(B.ang_vel_in(A), r_S_R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*B.ang_vel_in(A).cross(B_v_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = me.dynamicsymbols._t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\ddot{s}\\mathbf{\\hat{b}_x}$"
      ],
      "text/plain": [
       "s̈ b_x"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B_v_R.diff(t, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "R = me.Point(\"R\")\n",
    "\n",
    "R.set_pos(S, r_S_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "R.set_vel(B, B_v_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "S.set_vel(A, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\ddot{s}\\mathbf{\\hat{b}_x} -  \\left(- c + \\frac{l}{2}\\right) \\ddot{\\beta}\\mathbf{\\hat{b}_y} -  \\left(- c + \\frac{l}{2}\\right) \\dot{\\beta}^{2}\\mathbf{\\hat{b}_z}$"
      ],
      "text/plain": [
       "         ⎛     l⎞          ⎛     l⎞  2    \n",
       "s̈ b_x + -⎜-c + ─⎟⋅β̈ b_y + -⎜-c + ─⎟⋅β̇  b_z\n",
       "         ⎝     2⎠          ⎝     2⎠       "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R.a1pt_theory(S, A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "R.a1pt_theory(S, N, B)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Turtle",
   "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": "3.11.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}