{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8a403def",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sm\n",
    "import sympy.physics.mechanics as me\n",
    "me.init_vprinting()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e3ef9c68",
   "metadata": {},
   "outputs": [],
   "source": [
    "N, A, B = sm.symbols(\"N, A, B\", cls=me.ReferenceFrame)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cc2c3292",
   "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": null,
   "id": "adea1e25",
   "metadata": {},
   "outputs": [],
   "source": [
    "A.orient_axis(N, alpha, N.z)\n",
    "B.orient_axis(A, beta, A.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12110949",
   "metadata": {},
   "outputs": [],
   "source": [
    "N_v_S = -d*alpha.diff()*A.y\n",
    "N_v_S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a0934aac",
   "metadata": {},
   "outputs": [],
   "source": [
    "A.ang_vel_in(N) + B.ang_vel_in(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "342c2c2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "B.ang_vel_in(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fe502526",
   "metadata": {},
   "outputs": [],
   "source": [
    "r_S_Q = -w*B.x - (c + l/2)*B.z\n",
    "r_S_Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "52e9c74f",
   "metadata": {},
   "outputs": [],
   "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": null,
   "id": "a44dd22b",
   "metadata": {},
   "outputs": [],
   "source": [
    "N_v_Q.express(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e6e2a169",
   "metadata": {},
   "outputs": [],
   "source": [
    "S, Q = sm.symbols('S, Q', cls=me.Point)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f256f998",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q.set_pos(S, r_S_Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2d92dc1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q.pos_from(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b35ae5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "S.set_vel(N, N_v_S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0f36fa94",
   "metadata": {},
   "outputs": [],
   "source": [
    "S.vel(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c00e642f",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q.v2pt_theory(S, N, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "544de114",
   "metadata": {},
   "outputs": [],
   "source": [
    "s = me.dynamicsymbols('s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d2429e55",
   "metadata": {},
   "outputs": [],
   "source": [
    "r_S_R = (s-w)*B.x + (l/2-c)*B.z\n",
    "r_S_R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "347cb387",
   "metadata": {},
   "outputs": [],
   "source": [
    "B_v_R = s.diff()*B.x\n",
    "B_v_R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "82940f3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "B.ang_vel_in(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cf660c85",
   "metadata": {},
   "outputs": [],
   "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": null,
   "id": "826fccc0",
   "metadata": {},
   "outputs": [],
   "source": [
    "me.cross(B.ang_acc_in(A), r_S_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8c783cf5",
   "metadata": {},
   "outputs": [],
   "source": [
    "me.cross(B.ang_vel_in(A), me.cross(B.ang_vel_in(A), r_S_R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c72f8897",
   "metadata": {},
   "outputs": [],
   "source": [
    "2*me.cross(B.ang_vel_in(A), B_v_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "873535c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "B_v_R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "259f1443",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = me.dynamicsymbols._t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b2b74c2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "B_v_R.diff(t, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4a4e4b5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "R = me.Point('R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ced534bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "R.set_pos(S, r_S_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7a4a8720",
   "metadata": {},
   "outputs": [],
   "source": [
    "R.set_vel(B, B_v_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8dca98a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "S.set_vel(A, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "78098491",
   "metadata": {},
   "outputs": [],
   "source": [
    "R.a1pt_theory(S, A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0a5c34ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "R.a1pt_theory(S, N, B)"
   ]
  }
 ],
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