{
  "id": "1104.3221",
  "version": "v1",
  "published": "2011-04-16T09:28:15.000Z",
  "updated": "2011-04-16T09:28:15.000Z",
  "title": "On the geometry of higher-order variational problems on Lie groups",
  "authors": [
    "Leonardo Colombo",
    "David Martin de Diego"
  ],
  "comment": "20 pages, 4 figures",
  "categories": [
    "math-ph",
    "cs.SY",
    "math.DG",
    "math.MP",
    "math.OC"
  ],
  "abstract": "In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we deduce an intrinsic framework for this type of dynamical systems. Interesting applications as, for instance, a geometric derivation of the higher-order Euler-Poincar\\'e equations, optimal control of underactuated control systems whose configuration space is a Lie group are shown, among others, along the paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-16T09:28:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B66",
      "22A22",
      "70G45",
      "70Hxx"
    ],
    "keywords": [
      "lie group",
      "higher-order variational problems",
      "higher-order lagrangian problems",
      "higher-order tangent bundle",
      "higher-order euler-poincare equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.3221C"
    }
  }
}