Hamiltonian Systems near Relative Equilibria

Authors: Roberts M.¹; Wulff C.²; Lamb J.S.W.³

Source: Journal of Differential Equations, Volume 179, Number 2, March 2002 , pp. 562-604(43)

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Abstract:

We give explicit differential equations for the dynamics of Hamiltonian systems near relative equilibria. These split the dynamics into motion along the group orbit and motion inside a slice transversal to the group orbit. The form of the differential equations that is inherited from the symplectic structure and symmetry properties of the Hamiltonian system is analysed and the effects of time reversing symmetries are included. The results will be applicable to the stability and bifurcation theories of relative equilibria of Hamiltonian systems. © 2002 Elsevier Science (USA).

Language: English

Document Type: Research article

Affiliations: 1: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom 2: Institut für Mathematik I, Freie Universität Berlin, Berlin, 14195, Germany 3: Department of Mathematics, Imperial College, London, SW7 2BZ, United Kingdom

Publication date: 2002-03-01