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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