Definition:Curvature/Polar Form
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Definition
Let $C$ be a curve defined by a real function which is twice differentiable.
Let $C$ be embedded in a polar plane.
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The curvature $\kappa$ of $C$ at a point:
- $P = \polar {r, \theta}$
is given by:
- $\kappa = \dfrac {\paren {\map \arctan {\dfrac {r \theta'} {r'} } }' + \theta'} {\paren {r'^2 + \paren {r \theta'}^2}^{1/2} }$
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Also see
- Results about curvature can be found here.
Sources
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