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Commit fc467af

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Tidy up math notation
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‎symbolic/angvelxform_dot.ipynb

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+23-3Lines changed: 23 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -13,7 +13,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
@@ -41,14 +41,14 @@
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"\n",
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"\n",
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"$\n",
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"\\mathbf{A} = I_{3 \\times 3} - \\frac{1}{2} [v]_\\times + [v]^2_\\times \\frac{1}{\\theta^2} \\left( 1 - \\frac{\\theta}{2} \\frac{\\sin \\theta}{1 - \\cos \\theta} \\right)\n",
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"\\mathbf{A} = \\mathbf{1}_{3 \\times 3} - \\frac{1}{2} [v]_\\times + [v]^2_\\times \\frac{1}{\\theta^2} \\left( 1 - \\frac{\\theta}{2} \\frac{\\sin \\theta}{1 - \\cos \\theta} \\right)\n",
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"$\n",
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"where $\\theta = \\| \\varphi \\|$ and $v = \\hat{\\varphi}$\n",
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"\n",
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"We simplify the equation as\n",
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"\n",
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"$\n",
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"\\mathbf{A} = I_{3 \\times 3} - \\frac{1}{2} [v]_\\times + [v]^2_\\times \\Theta\n",
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"\\mathbf{A} = \\mathbf{1}_{3 \\times 3} - \\frac{1}{2} [v]_\\times + [v]^2_\\times \\Theta\n",
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"$\n",
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"\n",
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"where\n",
@@ -308,6 +308,26 @@
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"source": [
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"which is simply the dot product over the norm."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"exp(A(t))*Derivative(A(t), t)\n"
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]
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}
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],
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"source": [
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"A, t = symbols('A t', real=True)\n",
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"A_t = Function(A)(t)\n",
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"d = diff(exp(A_t), t)\n",
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"print(d)"
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]
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}
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],
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"metadata": {

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