Geodesic
Geometry of the rolling ellipsoid
Kybernetika, Tome 52 (2016) no. 2, pp. 209-223 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 curvature of an ellipsoid which has an elementary proof and has been previously known only for dimension two.
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 curvature of an ellipsoid which has an elementary proof and has been previously known only for dimension two.
DOI : 10.14736/kyb-2016-2-0209
Classification : 35B06, 53A05, 53B21, 58E10, 70B10
Keywords: ellipsoid; rolling maps; Gaussian curvature; geodesics; hypersurface 
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Krakowski, Krzysztof Andrzej; Silva Leite, Fátima. Geometry of the rolling ellipsoid. Kybernetika, Tome 52 (2016) no. 2, pp. 209-223. doi: 10.14736/kyb-2016-2-0209

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