{
  "id": "1304.1788",
  "version": "v3",
  "published": "2013-04-05T19:19:14.000Z",
  "updated": "2014-11-28T18:52:39.000Z",
  "title": "Unimodularity and preservation of volumes in nonholonomic mechanics",
  "authors": [
    "Yuri N. Fedorov",
    "Luis C. García-Naranjo",
    "Juan C. Marrero"
  ],
  "comment": "37 pages, 3 figures; v3 includes several changes to v2 that were done in accordance to the referee suggestions",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The equations of motion of a mechanical system subjected to nonholonomic linear constraints can be formulated in terms of a linear almost Poisson structure in a vector bundle. We study the existence of invariant measures for the system in terms of the unimodularity of this structure. In the presence of symmetries, our approach allows us to give necessary and sufficient conditions for the existence of an invariant volume, that unify and improve results existing in the literature. We present an algorithm to study the existence of a smooth invariant volume for nonholonomic mechanical systems with symmetry and we apply it to several concrete mechanical examples.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-16T19:16:54.000Z",
      "comment": "42 pages, 3 figures. v2 includes minor changes from v1. The theory developed in this paper was used to treat a specific example in arXiv: 1306.4237",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-11-28T18:52:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C40",
      "37J60",
      "70F25",
      "70G45",
      "70G65"
    ],
    "keywords": [
      "nonholonomic mechanics",
      "unimodularity",
      "preservation",
      "smooth invariant volume",
      "nonholonomic linear constraints"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00332-014-9227-4",
      "journal": "Journal of NonLinear Science",
      "year": 2015,
      "month": "Feb",
      "volume": 25,
      "number": 1,
      "pages": 203
    },
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JNS....25..203F"
    }
  }
}