From 5f275430bd7800cc60b73ff08e69d0435d1dbe33 Mon Sep 17 00:00:00 2001 From: gyz Date: Sat, 15 Mar 2025 10:11:40 +0800 Subject: [PATCH] vault backup: 2025-03-15 10:11:39 --- .../obsidian-excalidraw-plugin/data.json | 4 +- 补课/多体动力学/14_inertia.ipynb | 207 +++++++++++++++++- 2 files changed, 207 insertions(+), 4 deletions(-) diff --git a/.obsidian/plugins/obsidian-excalidraw-plugin/data.json b/.obsidian/plugins/obsidian-excalidraw-plugin/data.json index e369f1d..800fe2f 100644 --- a/.obsidian/plugins/obsidian-excalidraw-plugin/data.json +++ b/.obsidian/plugins/obsidian-excalidraw-plugin/data.json @@ -100,7 +100,7 @@ "library2": { "type": "excalidrawlib", "version": 2, - "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.7.5", + "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.9.2", "libraryItems": [] }, "imageElementNotice": true, @@ -116,6 +116,7 @@ "showReleaseNotes": true, "showNewVersionNotification": true, "latexBoilerplate": "\\color{blue}", + "latexPreambleLocation": "preamble.sty", "taskboneEnabled": false, "taskboneAPIkey": "", "pinnedScripts": [], @@ -786,7 +787,6 @@ } ], "showSplashscreen": true, - "latexPreambleLocation": "preamble.sty", "pdfSettings": { "pageSize": "A4", "pageOrientation": "portrait", 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 3f2684b..080d4a9 100644 --- a/补课/多体动力学/14_inertia.ipynb +++ b/补课/多体动力学/14_inertia.ipynb @@ -19,11 +19,214 @@ "\n", "Q = 3*me.outer(B.x, A.z) + 4*me.outer(A.x, A.x) + 6*me.outer(A.z, B.z)" ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "M1, M2, M3 = me.dynamicsymbols('M1, M2, M3')\n", + "A = me.ReferenceFrame('A')\n", + "A = me.ReferenceFrame('A')\n", + "\n", + "w1, w2, w3 = me.dynamicsymbols('omega1, omega2, omega3')" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/latex": [ + "$\\displaystyle \\omega_{1}\\mathbf{\\hat{b}_x} + \\omega_{2}\\mathbf{\\hat{b}_y} + \\omega_{3}\\mathbf{\\hat{b}_z}$" + ], + "text/plain": [ + "ω₁ b_x + ω₂ b_y + ω₃ b_z" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A_w_B = w1*B.x + w2*B.y + w3*B.z\n", + "A_w_B" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/latex": [ + "$\\displaystyle M_{1}\\mathbf{\\hat{b}_x} + M_{2}\\mathbf{\\hat{b}_y} + M_{3}\\mathbf{\\hat{b}_z}$" + ], + "text/plain": [ + "M₁ b_x + M₂ b_y + M₃ b_z" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "M = M1*B.x + M2*B.y + M3*B.z\n", + "M" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "I11, I22, I33 = sm.symbols('I_(11), I_(22), I_(33)')" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/latex": [ + "$\\displaystyle I_{(11)}\\mathbf{\\hat{b}_x}\\otimes \\mathbf{\\hat{b}_x} + I_{(22)}\\mathbf{\\hat{b}_y}\\otimes \\mathbf{\\hat{b}_y} + I_{(33)}\\mathbf{\\hat{b}_z}\\otimes \\mathbf{\\hat{b}_z}$" + ], + "text/plain": [ + "I₍₁₁₎ b_x⊗b_x + I₍₂₂₎ b_y⊗b_y + I₍₃₃₎ b_z⊗b_z" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "I = I11 * me.outer(B.x, B.x) + I22 * me.outer(B.y, B.y) + I33 * me.outer(B.z, B.z)\n", + "I" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/latex": [ + "$\\displaystyle I_{(11)} \\omega_{1}\\mathbf{\\hat{b}_x} + I_{(22)} \\omega_{2}\\mathbf{\\hat{b}_y} + I_{(33)} \\omega_{3}\\mathbf{\\hat{b}_z}$" + ], + "text/plain": [ + "I₍₁₁₎⋅ω₁ b_x + I₍₂₂₎⋅ω₂ b_y + I₍₃₃₎⋅ω₃ b_z" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "H = me.dot(I, A_w_B)\n", + "H" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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dhmEYRtWxyQTDMAzDMAzDMAzDMDLxfyjW1DWnlEzYAAAAAElFTkSuQmCC", + "text/latex": [ + "$\\displaystyle (I_{(11)} \\dot{\\omega}_{1} - I_{(22)} \\omega_{2} \\omega_{3} + I_{(33)} \\omega_{2} \\omega_{3})\\mathbf{\\hat{b}_x} + (I_{(11)} \\omega_{1} \\omega_{3} + I_{(22)} \\dot{\\omega}_{2} - I_{(33)} \\omega_{1} \\omega_{3})\\mathbf{\\hat{b}_y} + (- I_{(11)} \\omega_{1} \\omega_{2} + I_{(22)} \\omega_{1} \\omega_{2} + I_{(33)} \\dot{\\omega}_{3})\\mathbf{\\hat{b}_z}$" + ], + "text/plain": [ + "(I₍₁₁₎⋅ω₁̇ - I₍₂₂₎⋅ω₂⋅ω₃ + I₍₃₃₎⋅ω₂⋅ω₃) b_x + (I₍₁₁₎⋅ω₁⋅ω₃ + I₍₂₂₎⋅ω₂̇ - I₍₃₃₎⋅ω ↪\n", + "\n", + "↪ ₁⋅ω₃) b_y + (-I₍₁₁₎⋅ω₁⋅ω₂ + I₍₂₂₎⋅ω₁⋅ω₂ + I₍₃₃₎⋅ω₃̇) b_z" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t = me.dynamicsymbols._t\n", + "Hdot = H.diff(t, B) + me.cross(A_w_B, H)\n", + "Hdot" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/latex": [ + "$\\displaystyle (- I_{(11)} \\dot{\\omega}_{1} + I_{(22)} \\omega_{2} \\omega_{3} - I_{(33)} \\omega_{2} \\omega_{3} + M_{1})\\mathbf{\\hat{b}_x} + (- I_{(11)} \\omega_{1} \\omega_{3} - I_{(22)} \\dot{\\omega}_{2} + I_{(33)} \\omega_{1} \\omega_{3} + M_{2})\\mathbf{\\hat{b}_y} + (I_{(11)} \\omega_{1} \\omega_{2} - I_{(22)} \\omega_{1} \\omega_{2} - I_{(33)} \\dot{\\omega}_{3} + M_{3})\\mathbf{\\hat{b}_z}$" + ], + "text/plain": [ + "(-I₍₁₁₎⋅ω₁̇ + I₍₂₂₎⋅ω₂⋅ω₃ - I₍₃₃₎⋅ω₂⋅ω₃ + M₁) b_x + (-I₍₁₁₎⋅ω₁⋅ω₃ - I₍₂₂₎⋅ω₂̇ + ↪\n", + "\n", + "↪ I₍₃₃₎⋅ω₁⋅ω₃ + M₂) b_y + (I₍₁₁₎⋅ω₁⋅ω₂ - I₍₂₂₎⋅ω₁⋅ω₂ - I₍₃₃₎⋅ω₃̇ + M₃) b_z" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "M - Hdot" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}M_{1}\\\\M_{2}\\\\M_{3}\\end{matrix}\\right] = \\left[\\begin{matrix}I_{(11)} \\dot{\\omega}_{1} - I_{(22)} \\omega_{2} \\omega_{3} + I_{(33)} \\omega_{2} \\omega_{3}\\\\I_{(11)} \\omega_{1} \\omega_{3} + I_{(22)} \\dot{\\omega}_{2} - I_{(33)} \\omega_{1} \\omega_{3}\\\\- I_{(11)} \\omega_{1} \\omega_{2} + I_{(22)} \\omega_{1} \\omega_{2} + I_{(33)} \\dot{\\omega}_{3}\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡M₁⎤ ⎡I₍₁₁₎⋅ω₁̇ - I₍₂₂₎⋅ω₂⋅ω₃ + I₍₃₃₎⋅ω₂⋅ω₃ ⎤\n", + "⎢ ⎥ ⎢ ⎥\n", + "⎢M₂⎥ = ⎢I₍₁₁₎⋅ω₁⋅ω₃ + I₍₂₂₎⋅ω₂̇ - I₍₃₃₎⋅ω₁⋅ω₃ ⎥\n", + "⎢ ⎥ ⎢ ⎥\n", + "⎣M₃⎦ ⎣-I₍₁₁₎⋅ω₁⋅ω₂ + I₍₂₂₎⋅ω₁⋅ω₂ + I₍₃₃₎⋅ω₃̇⎦" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sm.Eq(M.to_matrix(B), Hdot.to_matrix(B))" + ] } ], "metadata": { "kernelspec": { - "display_name": "TagUIFocus5", + "display_name": "Turtle", "language": "python", "name": "python3" }, @@ -37,7 +240,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.4" + "version": "3.11.8" } }, "nbformat": 4,