Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry

James Montaldi

doi:10.3934/jgm.2014.6.237

Article Contents

2014, Volume 6, Issue 2: 237-260. Doi: 10.3934/jgm.2014.6.237

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Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry

James Montaldi^1,

1.
School of Mathematics, University of Manchester, Manchester, M13 9PL

Received: October 31, 2013

Revised: March 31, 2014

Published: May 2014

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Abstract

For Hamiltonian systems with spherical symmetry there is a marked difference between zero and non-zero momentum values, and amongst all relative equilibria with zero momentum there is a marked difference between those of zero and those of non-zero angular velocity. We use techniques from singularity theory to study the family of relative equilibria that arise as a symmetric Hamiltonian which has a group orbit of equilibria with zero momentum is perturbed so that the zero-momentum relative equilibrium are no longer equilibria. We also analyze the stability of these perturbed relative equilibria, and consider an application to satellites controlled by means of rotors.

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Mathematics Subject Classification: 70H33, 58F14, 37J20.

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