{
  "id": "1103.3267",
  "version": "v1",
  "published": "2011-03-09T23:02:18.000Z",
  "updated": "2011-03-09T23:02:18.000Z",
  "title": "Extensions of Noether's Second Theorem: from continuous to discrete systems",
  "authors": [
    "Peter E. Hydon",
    "Elizabeth L. Mansfield"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational problem whose symmetries depend upon a set of free or partly-constrained functions. Our approach extends further to deal with finite difference systems. The results are easy to apply; several well-known continuous and discrete systems are used as illustrations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-09T23:02:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "noethers second theorem",
      "discrete systems",
      "extensions",
      "simple local proof",
      "continuous"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1098/rspa.2011.0158",
      "journal": "Proceedings of the Royal Society of London Series A",
      "year": 2011,
      "month": "Nov",
      "volume": 467,
      "number": 2135,
      "pages": 3206
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011RSPSA.467.3206H"
    }
  }
}