{
  "id": "1202.4739",
  "version": "v1",
  "published": "2012-02-21T19:59:42.000Z",
  "updated": "2012-02-21T19:59:42.000Z",
  "title": "The non-existence of centre-of-mass and linear-momentum integrals in the curved N-body problem",
  "authors": [
    "Florin Diacu"
  ],
  "comment": "12 pages",
  "journal": "Libertas Math (new series) 32, 1 (2012), 25-37",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We provide a class of orbits in the curved N-body problem for which no point that could play the role of the centre of mass is fixed or moves uniformly along a geodesic. This proves that the equations of motion lack centre-of-mass and linear-momentum integrals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-21T19:59:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F15"
    ],
    "keywords": [
      "curved n-body problem",
      "linear-momentum integrals",
      "non-existence",
      "motion lack centre-of-mass"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.4739D"
    }
  }
}