The involute of an ellipse specified parametrically by
(1)
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(2)
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is given by the parametric equations
(3)
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(4)
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where is an elliptic integral of the second kind, and
(5)
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is the eccentricity.
The curvature and tangential angle are given by
(6)
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(7)
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where is an elliptic integral of the second kind.