Geodesic
Geometry of the rolling ellipsoid
Kybernetika, Tome 52 (2016) no. 2, pp. 209-223.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{10_14736_kyb_2016_2_0209,
     author = {Krakowski, Krzysztof Andrzej and Silva Leite, F\'atima},
     title = {Geometry of the rolling ellipsoid},
     journal = {Kybernetika},
     pages = {209--223},
     publisher = {mathdoc},
     volume = {52},
     number = {2},
     year = {2016},
     doi = {10.14736/kyb-2016-2-0209},
     mrnumber = {3501158},
     zbl = {1374.53033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-2-0209/}
}
TY  - JOUR
AU  - Krakowski, Krzysztof Andrzej
AU  - Silva Leite, Fátima
TI  - Geometry of the rolling ellipsoid
JO  - Kybernetika
PY  - 2016
SP  - 209
EP  - 223
VL  - 52
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-2-0209/
DO  - 10.14736/kyb-2016-2-0209
LA  - en
ID  - 10_14736_kyb_2016_2_0209
ER  - 
%0 Journal Article
%A Krakowski, Krzysztof Andrzej
%A Silva Leite, Fátima
%T Geometry of the rolling ellipsoid
%J Kybernetika
%D 2016
%P 209-223
%V 52
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-2-0209/
%R 10.14736/kyb-2016-2-0209
%G en
%F 10_14736_kyb_2016_2_0209
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. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-2-0209/

Cité par Sources :