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This article is cited in 9 scientific papers (total in 9 papers)
Non-Existence of an Invariant Measure for a Homogeneous Ellipsoid Rolling on the Plane
Luis C. García-Naranjoa, Juan C. Marrerob a Departamento de Matemáticas y Mecánica, IIMAS-UNAM
Apdo Postal 20-726, Mexico City, 01000, Mexico
b 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.
Keywords:
nonholonomic mechanical systems, invariant volume forms, symmetries, reduction.
Received: 19.06.2013 Accepted: 30.06.2013
Citation:
Luis C. García-Naranjo, Juan C. Marrero, “Non-Existence of an Invariant Measure for a Homogeneous Ellipsoid Rolling on the Plane”, Regul. Chaotic Dyn., 18:4 (2013), 372–379
Linking options:
https://www.mathnet.ru/eng/rcd118 https://www.mathnet.ru/eng/rcd/v18/i4/p372
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Abstract page: | 194 | References: | 40 |
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