{
  "id": "1310.8528",
  "version": "v3",
  "published": "2013-10-31T14:38:52.000Z",
  "updated": "2018-09-24T19:08:03.000Z",
  "title": "A comparison of vakonomic and nonholonomic dynamics with applications to non-invariant Chaplygin systems",
  "authors": [
    "Michał Jóźwikowski",
    "Witold Respondek"
  ],
  "comment": "42 pages, 4 figures, minor revision, submitted version",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study relations between vakonomically and nonholonomically constrained Lagrangian dynamics for the same set of linear constraints. The basic idea is to compare both situations at the level of variational principles, not equations of motion as has been done so far. The method seems to be quite powerful and effective. In particular, it allows to derive, interpret and generalize many known results on non-Abelian Chaplygin systems. We apply it also to a class of systems on Lie groups with a left-invariant constraints distribution. Concrete examples of the unicycle in a potential field, the two-wheeled carriage and the generalized Heisenberg system are discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-15T15:39:21.000Z",
      "abstract": "We study relations between vakonomically and nonholonomically constrained Lagrangian dynamics for the same set of linear constraints. The new idea is to compare both situations at the level of variational principles, not equations of motion as has been done so far. The method seems to be quite powerful and effective. In particular, it allows to derive and significantly generalize many known results on nonabelian Chaplygin systems. We apply it also to a class of systems on Lie groups with a left-invariant constraint distribution. Concrete examples of the unicycle in a potential field, the two-wheeled carriage and the generalized Heisenberg system are discussed.",
      "comment": "43 pages, 2 figures, after mayor revision, new results",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2018-09-24T19:08:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49S05",
      "70H45",
      "70H30",
      "70G45"
    ],
    "keywords": [
      "non-invariant chaplygin systems",
      "nonholonomic dynamics",
      "comparison",
      "applications",
      "left-invariant constraint distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.8528J"
    }
  }
}