Geometry of the rolling ellipsoid

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Geometry of the rolling ellipsoid

We study rolling maps of the Euclidean ellipsoid, rolling upon its affine tangent space at a point. Driven by the geometry of rolling maps, we find a simple formula for the angular velocity of the rolling ellipsoid along any piecewise smooth curve in terms of the Gauss map. This result is then generalised to rolling any smooth hyper-surface. On the way, we derive a formula for the Gaussian curv...

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ژورنال

عنوان ژورنال: Kybernetika

سال: 2016

ISSN: 0023-5954,1805-949X

DOI: 10.14736/kyb-2016-2-0209