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Original file line number Diff line number Diff line change 13
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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" : [
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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 " ,
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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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