Montaldi, James
(2014)
*Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry.*
J. Geometric Mechanics, 6.
pp. 237-260.

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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.

Item Type: | Article |
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Uncontrolled Keywords: | momentum map, symplectic reduction, bifurcations, SO(3) symmetry, relative equilibria |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory |

Depositing User: | Dr James Montaldi |

Date Deposited: | 09 Apr 2014 |

Last Modified: | 20 Oct 2017 14:13 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/2115 |

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