|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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