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JOURNALS // Russian Journal of Nonlinear Dynamics // Archive

Nelin. Dinam., 2011 Volume 7, Number 3, Pages 559–568 (Mi nd277)

This article is cited in 6 papers

Two non-holonomic integrable systems of coupled rigid bodies

A. V. Borisovab, I. S. Mamaevba

a Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia
b Institute of Computer Science, Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: The paper considers two new integrable systems due to Chaplygin, which describe the rolling of a spherical shell on a plane, with a ball or Lagranges gyroscope inside. All necessary first integrals and an invariant measure are found. The reduction to quadratures is given.

Keywords: non-holonomic constraint; integrability; invariant measure; gyroscope; quadrature; coupled rigid bodies.

UDC: 532.5

MSC: 37J60

Received: 26.08.2011
Revised: 14.09.2011



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