{
  "id": "1311.2247",
  "version": "v2",
  "published": "2013-11-10T07:38:18.000Z",
  "updated": "2014-04-09T15:45:58.000Z",
  "title": "Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry",
  "authors": [
    "James Montaldi"
  ],
  "comment": "24 pp; to appear in J. Geometric Mechanics",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-09T15:45:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70H33",
      "58F14",
      "37J20"
    ],
    "keywords": [
      "hamiltonian systems",
      "spherical symmetry",
      "bifurcations",
      "marked difference",
      "non-zero momentum values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.2247M"
    }
  }
}