Authors: Jovanović, Božidar 
Title: Note on a ball rolling over a sphere: Integrable Chaplygin system with an invariant measure without Chaplygin hamiltonization
Journal: Theoretical and Applied Mechanics
Volume: 46
Issue: 1
First page: 97
Last page: 108
Issue Date: 1-Jan-2019
Rank: M24
ISSN: 1450-5584
DOI: 10.2298/TAM190322003J
Abstract: 
In this note we consider the nonholonomic problem of rolling without slipping and twisting of an n-dimensional balanced ball over a fixed sphere. This is a SO(n)-Chaplygin system with an invariant measure that reduces to the cotangent bundle T* Sn-1. For the rigid body inertia operator Iω = Iω + ωI, I = diag(I1, ..., In) with a symmetry I1 = I2 = ··· = Ir ≠ Ir+1 = Ir+2 = ··· = In, we prove that the reduced system is integrable, general trajectories are quasi-periodic, while for r ≠ 1, n - 1 the Chaplygin reducing multiplier method does not apply.
Keywords: Integrability | Invariant measure | Nonholonomic Chaplygin systems
Publisher: Serbian Society of Mechanics
Project: Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 

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