Rolling of a homogeneous ball over a dynamically asymmetric sphere

A. V. Borisov ; A. A. Kilin ; I. S. Mamaev

Russian journal of nonlinear dynamics, Tome 6 (2010) no. 4, pp. 869-889.

Résumé

We consider a novel mechanical system consisting of two spherical bodies rolling over each other, which is a natural extension of the famous Chaplygin problem of rolling motion of a ball on a plane. In contrast to the previously explored non-holonomic systems, this one has a higher dimension and is considerably more complicated. One remarkable property of our system is the existence of “clandestine” linear in momenta first integrals. For a more trivial integrable system, their counterparts were discovered by Chaplygin. We have also found a few cases of integrability.

Détail

Keywords: nonholonomic constraint, rolling motion, Chaplygin ball, integral, invariant measure.

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