diff --git a/补课/多体动力学/16_Generalized_Forces.excalidraw.md b/补课/多体动力学/16_Generalized_Forces.excalidraw.md index 4e25ebf..87569cb 100644 --- a/补课/多体动力学/16_Generalized_Forces.excalidraw.md +++ b/补课/多体动力学/16_Generalized_Forces.excalidraw.md @@ -20,4820 +20,6128 @@ N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyh AA4ANm0AdgBWJcgYVYBGDePtRuaNte34tbWeNeOefYLIChJ1bh4+N6kEQjKaTcS4HCDWZTBbgABjBzCgpDYAGsEABhNj4NikcoAYmOCHx+LGJU0IyRykRQg4xHRmOxEgR1mYcFwgSyxMg00I+HwvVgUIkgg8HIg8MRKIA6p9JDDtK9xqKEciEHyYAL0EKymDKUCOOEcmhjmC2CzsGojobobC/hThHAAJLEA2oXIAXTBs1wGUd3A4Qh5YMI1Kw5Vw -yW1wmpeuYzr9Ab+YXm3DWjQAzI1btD4vEwYwWOwuGgXrmmKxOAA5ThibjHRop+Kpja7JuB5gAETSUCTaGmBDCYM0keI7WCGSysf9+DBQjgxFwXeINe2zVTe3i0NTPHXYKIHCRvsnO7Y2BRi57fYQYLgbCD2TybzA+XGxWtz7A0If7ofT+fr+fzkabQNmA65tmhY5jm2Y4bl2T8DkfB8wGcc5U1Q1DdhuDZGiwlNUzWeCkI2ODv0Q5w4hAjYoL2Lc 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"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 +} diff --git a/补课/多体动力学/16_generalized_forces.py b/补课/多体动力学/16_generalized_forces.py new file mode 100644 index 0000000..0372075 --- /dev/null +++ b/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)) \ No newline at end of file