A Generalization of Chaplygin's Reducibility Theorem

Abstract

In this paper we study Chaplygin's Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton-Poincare-d'Alembert equations in arbitrary degrees of freedom. As special cases we extract the extension of the Theorem to nonholonomic Chaplygin systems with nonabelian symmetry groups as well as Euler-Poincare-Suslov systems in arbitrary degrees of freedom. In the latter case, we also extend the Hamiltonization Theorem to nonholonomic systems which do not possess an invariant measure. Lastly, we extend previous work on conditionally variational systems using the results above. We illustrate the results through various examples of well-known nonholonomic systems.

27 pages, 3 figures, submitted to Reg. and Chaotic Dyn

References in corpus (2)

• Nonholonomic LR systems as Generalized Chaplygin systems with an Invariant Measure and Geodesic Flows on Homogeneous Spaces
• Poisson structures for reduced non-holonomic systems

Cited by in corpus (8)

• Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization
• Gauge Transformations, Twisted Poisson Brackets and Hamiltonization of Nonholonomic Systems
• The Jacobiator of nonholonomic systems and the geometry of reduced nonholonomic brackets
• Hamiltonization and separation of variables for Chaplygin ball on a rotating plane
• Hamiltonization of solids of revolution through reduction
• Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?
• Generalisation of Chaplygin's Reducing Multiplier Theorem with an application to multi-dimensional nonholonomic dynamics
• Geodesic extensions of mechanical systems with nonholonomic constraints