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arXiv · 1311.2247

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

James Montaldi
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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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James Montaldi. 2013-11-10. Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry. https://doi.org/10.3934/jgm.2014.6.237

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