In this paper, we investigate the dynamics of systems describing the rolling without slipping and spinning (rubber rolling) of an ellipsoid on a plane and a sphere. We research these problems using Poincare maps, which investigation helps to discover a new integrable case.
Keywords:
nonholonomic constraint, invariant measure, first integral, Poincare map, integrability and chaos
Citation:
Bizyaev I. A., Kazakov A. O., Integrability and stochastic behavior in some nonholonomic dynamics problems, Rus. J. Nonlin. Dyn.,
2013, Vol. 9, No. 2,
pp. 257-265
DOI:10.20537/nd1302005