Integrability and dynamics of the n-dimensional symmetric Veselova top

Fasso, Francesco and García-Naranjo, Luis C. and Montaldi, James (2018) Integrability and dynamics of the n-dimensional symmetric Veselova top. J. Nonlinear Science. ISSN 1432-1467 (In Press)

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Abstract

We consider the the n-dimensional generalisation of the nonholonomic Veselova problem. We derive the reduced equations of motion in terms of the mass tensor of the body and determine some general properties of the dynamics. In particular we give a closed formula for the invariant measure, we indicate the existence of steady rotation solutions, and obtain some results on their stability. We then focus our attention on bodies whose mass tensor has a specific type of symmetry. We show that the phase space is foliated by invariant tori that carry quasi-periodic dynamics in the natural time variable. Our results enlarge the known cases of integrability of the multi-dimensional Veselova top. Moreover, they show that in some previously known instances of integrability, the flow is quasi-periodic without the need of a time reparametrisation.

Item Type: Article
Uncontrolled Keywords: Nonholonomic systems, systems with symmetry,
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems
Depositing User: Dr James Montaldi
Date Deposited: 28 Apr 2018 10:25
Last Modified: 14 Nov 2018 22:26
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2634

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