From 3b0257d780f29df5b1bbc5d56a122be4736901d1 Mon Sep 17 00:00:00 2001 From: gyz Date: Sun, 23 Mar 2025 12:18:58 +0800 Subject: [PATCH] vault backup: 2025-03-23 12:18:57 --- .../08_Translational Kinematics.ipynb | 37 +- 补课/多体动力学/14_inertia.ipynb | 4 +- .../16_Generalized_Forces.excalidraw.md | 1696 +++++++++-------- 补课/多体动力学/16_generalized_forces.ipynb | 11 +- .../17_Equations_of_Motions.excalidraw.md | 1344 +++++++++++++ 补课/多体动力学/17_Equations_of_Motions.ipynb | 16 + 补课/多体动力学/框架.canvas | 11 + 7 files changed, 2280 insertions(+), 839 deletions(-) create mode 100644 补课/多体动力学/17_Equations_of_Motions.excalidraw.md create mode 100644 补课/多体动力学/17_Equations_of_Motions.ipynb create mode 100644 补课/多体动力学/框架.canvas diff --git a/补课/多体动力学/08_Translational Kinematics.ipynb b/补课/多体动力学/08_Translational Kinematics.ipynb index e11c0af..ca25903 100644 --- a/补课/多体动力学/08_Translational Kinematics.ipynb +++ b/补课/多体动力学/08_Translational Kinematics.ipynb @@ -593,9 +593,42 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 33, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/latex": [ + "$\\displaystyle (\\left(- c + \\frac{l}{2}\\right) \\left(\\sin{\\left(\\beta \\right)} \\ddot{\\alpha} + \\cos{\\left(\\beta \\right)} \\dot{\\alpha} \\dot{\\beta}\\right) - \\left(- w + s\\right) \\sin^{2}{\\left(\\beta \\right)} \\dot{\\alpha}^{2} - \\left(- \\left(- c + \\frac{l}{2}\\right) \\dot{\\beta} + \\left(- w + s\\right) \\cos{\\left(\\beta \\right)} \\dot{\\alpha}\\right) \\cos{\\left(\\beta \\right)} \\dot{\\alpha} + \\ddot{s})\\mathbf{\\hat{b}_x} + (\\left(- c + \\frac{l}{2}\\right) \\sin{\\left(\\beta \\right)} \\cos{\\left(\\beta \\right)} \\dot{\\alpha}^{2} - \\left(- c + \\frac{l}{2}\\right) \\ddot{\\beta} + \\left(- w + s\\right) \\left(- \\sin{\\left(\\beta \\right)} \\dot{\\alpha} \\dot{\\beta} + \\cos{\\left(\\beta \\right)} \\ddot{\\alpha}\\right) + \\left(- w + s\\right) \\sin{\\left(\\beta \\right)} \\dot{\\alpha} \\dot{\\beta} + 2 \\cos{\\left(\\beta \\right)} \\dot{\\alpha} \\dot{s})\\mathbf{\\hat{b}_y} + (- \\left(- c + \\frac{l}{2}\\right) \\sin^{2}{\\left(\\beta \\right)} \\dot{\\alpha}^{2} - \\left(- w + s\\right) \\left(\\sin{\\left(\\beta \\right)} \\ddot{\\alpha} + \\cos{\\left(\\beta \\right)} \\dot{\\alpha} \\dot{\\beta}\\right) + \\left(- \\left(- c + \\frac{l}{2}\\right) \\dot{\\beta} + \\left(- w + s\\right) \\cos{\\left(\\beta \\right)} \\dot{\\alpha}\\right) \\dot{\\beta} - 2 \\sin{\\left(\\beta \\right)} \\dot{\\alpha} \\dot{s})\\mathbf{\\hat{b}_z} + d \\dot{\\alpha}^{2}\\mathbf{\\hat{a}_x} - d \\ddot{\\alpha}\\mathbf{\\hat{a}_y}$" + ], + "text/plain": [ + "⎛⎛ l⎞ 2 2 ⎛ ⎛ l⎞ ↪\n", + "⎜⎜-c + ─⎟⋅(sin(β)⋅α̈ + cos(β)⋅α̇⋅β̇) - (-w + s)⋅sin (β)⋅α̇ - ⎜- ⎜-c + ─⎟⋅β̇ + (-w ↪\n", + "⎝⎝ 2⎠ ⎝ ⎝ 2⎠ ↪\n", + "\n", + "↪ ⎞ ⎞ ⎛⎛ l⎞ 2 ⎛ l⎞ ↪\n", + "↪ + s)⋅cos(β)⋅α̇⎟⋅cos(β)⋅α̇ + s̈⎟ b_x + ⎜⎜-c + ─⎟⋅sin(β)⋅cos(β)⋅α̇ - ⎜-c + ─⎟⋅β̈ + ↪\n", + "↪ ⎠ ⎠ ⎝⎝ 2⎠ ⎝ 2⎠ ↪\n", + "\n", + "↪ ⎞ ↪\n", + "↪ (-w + s)⋅(-sin(β)⋅α̇⋅β̇ + cos(β)⋅α̈) + (-w + s)⋅sin(β)⋅α̇⋅β̇ + 2⋅cos(β)⋅α̇⋅ṡ⎟ b_y ↪\n", + "↪ ⎠ ↪\n", + "\n", + "↪ ⎛ ⎛ l⎞ 2 2 ⎛ ⎛ l⎞ ↪\n", + "↪ + ⎜- ⎜-c + ─⎟⋅sin (β)⋅α̇ - (-w + s)⋅(sin(β)⋅α̈ + cos(β)⋅α̇⋅β̇) + ⎜- ⎜-c + ─⎟⋅β̇ ↪\n", + "↪ ⎝ ⎝ 2⎠ ⎝ ⎝ 2⎠ ↪\n", + "\n", + "↪ ⎞ ⎞ 2 \n", + "↪ + (-w + s)⋅cos(β)⋅α̇⎟⋅β̇ - 2⋅sin(β)⋅α̇⋅ṡ⎟ b_z + d⋅α̇ a_x + -d⋅α̈ a_y\n", + "↪ ⎠ ⎠ " + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "R.a1pt_theory(S, N, B)" ] diff --git a/补课/多体动力学/14_inertia.ipynb b/补课/多体动力学/14_inertia.ipynb index 4c3b104..de3546c 100644 --- a/补课/多体动力学/14_inertia.ipynb +++ b/补课/多体动力学/14_inertia.ipynb @@ -475,7 +475,7 @@ ], "metadata": { "kernelspec": { - "display_name": "TagUIFocus5", + "display_name": "Turtle", "language": "python", "name": "python3" }, @@ -489,7 +489,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.4" + "version": "3.11.8" } }, "nbformat": 4, 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 9640585..201ba5a 100644 --- 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a/补课/多体动力学/16_generalized_forces.ipynb +++ b/补课/多体动力学/16_generalized_forces.ipynb @@ -69,11 +69,18 @@ "source": [ "P1.vel(N).express(N)" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 两杆连接" + ] } ], "metadata": { "kernelspec": { - "display_name": "TagUIFocus5", + "display_name": "Turtle", "language": "python", "name": "python3" }, @@ -87,7 +94,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.4" + "version": "3.11.8" } }, "nbformat": 4, diff --git a/补课/多体动力学/17_Equations_of_Motions.excalidraw.md b/补课/多体动力学/17_Equations_of_Motions.excalidraw.md new file mode 100644 index 0000000..d5b2a81 --- /dev/null +++ b/补课/多体动力学/17_Equations_of_Motions.excalidraw.md @@ -0,0 +1,1344 @@ +--- + +excalidraw-plugin: parsed +tags: [excalidraw] + +--- +==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving' + + +# Excalidraw Data + +## Text Elements +%% +## Drawing +```compressed-json +N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyhQ4zZAHoFAc0JRJQgEYA6bGwC2CgF7N6hbEcK4OCtptbErHALRY8RMpWdx8Q1TdIEfARcZgRmBShcZQUebQBObR4aOiCEfQQOKGZuAG1wMFAwYogSbggAaQBFAGYAfQBZADZsJoArAFUAFWUAYQAFOCEASQA1OBgAMRTiyFhEcoAzQIRP + +Kn4SzG5nAEYdgAZtfYAOGrOAVmOAdiaAFjvj243IGG2eGqbtA/iaq/PniAUEjqbg7RJnCGXG73W6PJ4FSCSBCEZTSbg1W7aJrYprnO7xW47W77Jo8f4IiDWZTBbj7AHMKCkNgAawQvTY+DYpHKAGIdgh+fyZiVNLhsMzlEyhBxiOzOdyJIzrMw4LhAllhZBFoR8PgAMqwGkSQQeTUQBlM1kAdWBklp2nJs3NjJZCANMCN6BNZQBUtRHHCOTQOwBb + +FV2DUr2D+zpFMlwjgw2IQdQuQAugDlrgMknuBwhLqAYQZVhyrgamapTKA8wU/nCxSwqtuLCdrjjvtfgDGCx2Fxg8du0xWJwAHKcMSgnjxHjveI7MlF5gAETSUGbaEWBDCAM0whlAFFghksnWC/gAUI4MRcOviKCrrceE0djUY/sboOKUQOMy8+eAU5cUN1QLd8B3Ck4DYYtsjyBEwHyWZiljJCwH2eCM3gxCkJQpDnEOHFcXxQliVJc4MOeBD4LA + 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