UNSPECIFIED (1997) Bifurcations from relative equilibria of Hamiltonian systems. NONLINEARITY, 10 (6). pp. 1719-1738. ISSN 0951-7715

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Abstract

A symplectic version of the slice theorem for compact group actions is used to give a general description of the dynamics of a symmetric Hamiltonian system near a relative equilibrium as an interaction between rotational and vibrational motion. This is then used to prove a bifurcation theorem for relative equilibria. The bifurcation theorem is applied to two examples, the classical dynamics of an XY2 molecule near a symmetric linear equilibrium, and the dynamics of a system of two coupled identical axisymmetric rigid bodies near an equilibrium for which the two bodies are aligned on top of each other. Slice reduction of these systems is also used to describe other aspects of their dynamics. The results suggest that this will be a useful general technique for describing the dynamics of systems near relative equilibria which are singular points of the associated momentum maps.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	NONLINEARITY
Publisher:	IOP PUBLISHING LTD
ISSN:	0951-7715
Date:	November 1997
Volume:	10
Number:	6
Number of Pages:	20
Page Range:	pp. 1719-1738
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/16233

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