Rolling balls over spheres in R^n

Abstract

We study the rolling of the Chaplygin ball in ${\mathbb{R}}^n$ over a fixed $(n-1)$--dimensional sphere without slipping and without slipping and twisting. The problems can be naturally considered within a framework of appropriate modifications of the L+R and LR systems -- well known systems on Lie groups groups with an invariant measure. In the case of the rolling without slipping and twisting, we describe the $SO(n)$-Chaplygin reduction to $S^{n-1}$ and prove the Hamiltonization of the reduced system for a special inertia operator.

22 pages, figure is added, subsection 3.3 is rewritten, to appear in Nonlinearity

References in corpus (7)

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• The Rolling Motion of a Ball on a Surface. New Integrals and Hierarchy of Dynamics
• Chaplygin ball over a fixed sphere: explicit integration
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Cited by in corpus (5)

• Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere
• Gyroscopic Chaplygin systems and integrable magnetic flows on spheres
• 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