{
  "id": "1508.04913",
  "version": "v1",
  "published": "2015-08-20T08:17:32.000Z",
  "updated": "2015-08-20T08:17:32.000Z",
  "title": "Invariant measures of modified LR and L+R systems",
  "authors": [
    "Bozidar Jovanovic"
  ],
  "comment": "13 pages, to appear in Regular and Chaotic Dynamics",
  "categories": [
    "math-ph",
    "math.DS",
    "math.MP"
  ],
  "abstract": "We introduce a class of dynamical systems having an invariant measure, the modifications of well known systems on Lie groups: LR and L+R systems. As an example, we study modified Veselova nonholonomic rigid body problem, considered as a dynamical system on the product of the Lie algebra $so(n)$ with the Stiefel variety $V_{n,r}$, as well as the associated $\\epsilon$L+R system on $so(n)\\times V_{n,r}$. In the 3--dimensional case, these systems model the nonholonomic problems of a motion of a ball and a rubber ball over a fixed sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-20T08:17:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J60",
      "70F25",
      "70H45"
    ],
    "keywords": [
      "invariant measure",
      "modified lr",
      "veselova nonholonomic rigid body problem",
      "modified veselova nonholonomic rigid body",
      "study modified veselova nonholonomic rigid"
    ],
    "publication": {
      "doi": "10.1134/S1560354715050032",
      "journal": "Regular and Chaotic Dynamics",
      "year": 2015,
      "month": "Sep",
      "volume": 20,
      "number": 5,
      "pages": 542
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015RCD....20..542J"
    }
  }
}