LR and L+R Systems

Abstract

We consider coupled nonholonomic LR systems on the product of Lie groups. As examples, we study $n$-dimensional variants of the spherical support system and the rubber Chaplygin sphere. For a special choice of the inertia operator, it is proved that the rubber Chaplygin sphere, after reduction and a time reparametrization becomes an integrable Hamiltonian system on the $(n-1)$--dimensional sphere. Also, we showed that an arbitrary L+R system introduced by Fedorov can be seen as a reduced system of an appropriate coupled LR system.

18 pages, 1 figure

References in corpus (5)

• Nonholonomic LR systems as Generalized Chaplygin systems with an Invariant Measure and Geodesic Flows on Homogeneous Spaces
• Rubber rolling over a sphere
• Quasi-Chaplygin Systems and Nonholonimic Rigid Body Dynamics
• Some multidimensional integrable cases of nonholonomic rigid body dynamics
• Geometry and integrability of Euler-Poincare-Suslov equations

Cited by in corpus (8)

• Hamiltonization and Integrability of the Chaplygin Sphere in R^n
• Rolling balls over spheres in R^n
• Generalisation of Chaplygin's Reducing Multiplier Theorem with an application to multi-dimensional nonholonomic dynamics
• Integrability and dynamics of the n-dimensional symmetric Veselova top
• Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere
• Stochastic Chaplygin systems
• Spherical and planar ball bearings -- nonholonomic systems with invariant measures
• Spherical and Planar Ball Bearings -- a Study of Integrable Cases