Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry
| Autor: | Montaldi, James |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | J. Geom. Mech. Vol 6 (2014), 237 - 260 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3934/jgm.2014.6.237 |
| Popis: | 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. Comment: 24 pp; to appear in J. Geometric Mechanics |
| Databáze: | arXiv |
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