Authors: Jovanović, Božidar 
Title: Rolling balls over spheres in R<sup>n</sup>
Journal: Nonlinearity
Volume: 31
Issue: 9
First page: 4006
Last page: 4030
Issue Date: 25-Jul-2018
Rank: M21
ISSN: 0951-7715
DOI: 10.1088/1361-6544/aac75c
Abstract: 
We study the rolling of the Chaplygin ball inRn over a fxed (n - 1)-dimensional sphere without slipping and without slipping and twisting. The problems can be naturally considered within a framework of appropriate modifcations of the L + R and LR systems-well known systems on Lie groups with an invariant measure. In the case of the rolling without slipping and twisting, we describe the SO(n)-Chaplygin reduction to Sn-1 and prove the Hamiltonization of the reduced system for a special inertia operator.
Keywords: Chaplygin Hamiltonization | invariant measure | Nonholonomic systems
Publisher: London Mathematical Society
Project: Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 

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