Luis C. García-Naranjo, Juan C. Marrero, “Non-Existence of an Invariant Measure for a Homogeneous Ellipsoid Rolling on the Plane”, Regul. Chaotic Dyn., 2013, Volume 18, Issue 4,Pages <nobr>372

This article is cited in 9 papers

Non-Existence of an Invariant Measure for a Homogeneous Ellipsoid Rolling on the Plane

Luis C. García-Naranjo^a, Juan C. Marrero^b

^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

Language: English

DOI: 10.1134/S1560354713040047