{
  "id": "1109.3210",
  "version": "v2",
  "published": "2011-09-14T21:00:20.000Z",
  "updated": "2012-10-09T17:37:51.000Z",
  "title": "Nonholonomic LL systems on central extensions and the hydrodynamic Chaplygin sleigh with circulation",
  "authors": [
    "Luis C. García-Naranjo",
    "Joris Vankerschaver"
  ],
  "comment": "22 pages; 4 figures",
  "journal": "J. Geom. Phys. 73 (Nov 2013), pp 56-69",
  "doi": "10.1016/j.geomphys.2013.05.002",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider nonholonomic systems whose configuration space is the central extension of a Lie group and have left invariant kinetic energy and constraints. We study the structure of the associated Euler-Poincare-Suslov equations and show that there is a one-to-one correspondence between invariant measures on the original group and on the extended group. Our results are applied to the hydrodynamic Chaplygin sleigh, that is, a planar rigid body that moves in a potential flow subject to a nonholonomic constraint modeling a fin or keel attached to the body, in the case where there is circulation around the body.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-09T17:37:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hydrodynamic chaplygin sleigh",
      "nonholonomic ll systems",
      "central extension",
      "circulation",
      "left invariant kinetic energy"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.3210G"
    }
  }
}