The inhomogeneous Suslov problem

Abstract

We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints. We show that if the direction along which the Suslov constraint is enforced is perpendicular to a principal axis of inertia of the body, then the reduced equations are integrable and, in the generic case, possess a smooth invariant measure. Interestingly, in this generic case, the first integral that permits integration is transcendental and the density of the invariant measure depends on the angular velocities. We also study the Painlevé property of the solutions.

10 pages, 5 figures

References in corpus (1)

• Unimodularity and preservation of volumes in nonholonomic mechanics

Cited by in corpus (4)

• Unimodularity and preservation of volumes in nonholonomic mechanics
• Moving energies as first integrals of nonholonomic systems with affine constraints
• On inhomogeneous nonholonomic Bilimovich system
• The geometric discretisation of the Suslov problem: a case study of consistency for nonholonomic integrators