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Non-existence of an invariant measure for a homogeneous ellipsoid rolling on the plane |
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| Authors: | Luis C. García-Naranjo Juan C. Marrero |
| Affiliation: | 1. Departamento de Matemáticas y Mecánica, IIMAS-UNAM, Apdo Postal 20-726, Mexico City, 01000, Mexico 2. ULL-CSIC Geometría Diferencial y Mecánica Geométrica Departamento de Matemática Fundamental, Facultad de Matemáticas, Universidad de La Laguna, La Laguna, Tenerife, Canary Islands, Spain |
| Abstract: | It is known that the reduced equations for an axially symmetric homogeneous ellipsoid that rolls without slipping on the plane possess a smooth invariant measure. We show that such an invariant measure does not exist in the case when all of the semi-axes of the ellipsoid have different length. |
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