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
Citation:
García-Naranjo L. C., Marrero J. C., Non-Existence of an Invariant Measure for a Homogeneous Ellipsoid Rolling on the Plane, Regular and Chaotic Dynamics,
2013, Volume 18, Number 4,
pp. 372-379