Non-existence of an invariant measure for a homogeneous ellipsoid rolling on the plane

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.

Article: 
Non-existence of an invariant measure for a homogeneous ellipsoid rolling on the plane
Authors: 
Luis C. García-Naranjo, Juan C. Marrero
Journal: 
Preprint
Year: 
2013
URL: 
http://arxiv.org/abs/1306.4237