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Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems

Patrick, GW, Roberts, M and Wulff, C (2008) Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems NONLINEARITY, 21 (2). 325 - 352. ISSN 0951-7715

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Abstract

In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of Hamiltonian systems with Euclidean symmetry, we investigate different mechanisms of stability: stability by energy–momentum confinement, KAM, and Nekhoroshev stability, and we explain the transitions between them. We apply our results to the Kirchhoff model for the motion of an axisymmetric underwater vehicle, and we numerically study dissipation induced instability of KAM stable relative equilibria for this system.

Item Type: Article
Additional Information: Copyright 2008 Institute of Physics. This is the author's accepted manuscript.
Uncontrolled Keywords: Science & Technology, Physical Sciences, Mathematics, Applied, Physics, Mathematical, Mathematics, Physics, UNDERWATER VEHICLE, DISSIPATION
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Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 28 Jun 2012 09:08
Last Modified: 23 Sep 2013 19:10
URI: http://epubs.surrey.ac.uk/id/eprint/202014

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