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arXiv · 1804.03697

Rolling balls over spheres in R^n

Bozidar Jovanovic
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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.

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Bozidar Jovanovic. 2018-04-10. Rolling balls over spheres in R^n. https://doi.org/10.1088/1361-6544%2Faac75c

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