{
  "id": "2001.06771",
  "version": "v1",
  "published": "2020-01-19T04:34:29.000Z",
  "updated": "2020-01-19T04:34:29.000Z",
  "title": "The inverse problem in the calculus of variations: new developments",
  "authors": [
    "Thoan Do",
    "Geoff Prince"
  ],
  "categories": [
    "math.DG",
    "math-ph",
    "math.DS",
    "math.MP",
    "math.OC"
  ],
  "abstract": "We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of $n$ second order ordinary differential equations. A number of recent theorems are presented, using exterior differential systems theory (EDS). In particular, we indicate how to generalise Jesse Douglas's famous solution for $n=2$. We then examine a new class of solutions in arbitrary dimension $n$ and give some non-trivial examples in dimension 3",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-19T04:34:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J05",
      "70H03",
      "58A15",
      "49N45"
    ],
    "keywords": [
      "inverse problem",
      "second order ordinary differential equations",
      "variations",
      "developments",
      "exterior differential systems theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}