arXiv:1311.2247 [math.DS]AbstractReferencesReviewsResources
Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry
Published 2013-11-10, updated 2014-04-09Version 2
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.
Comments: 24 pp; to appear in J. Geometric Mechanics
Related articles: Most relevant | Search more
Bifurcations for Hamiltonian systems
Spectral flow, crossing forms and homoclinics of Hamiltonian systems
arXiv:1506.00057 [math.DS] (Published 2015-05-30)
Domains of analyticity of Lindstedt expansions of KAM tori in dissipative perturbations of Hamiltonian systems