Geometry of the rolling ellipsoid

Krakowski, Krzysztof Andrzej   ; Silva Leite, Fátima

Kybernetika, Tome 52 (2016) no. 2, pp. 209-223

Abstract (VO)

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.

Détail

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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