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

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.

v2: Minor changes after journal review. This text uses the theory developed in arXiv:1304.1788 for the specific example of a homogeneous ellipsoid rolling on the plane

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