{
  "id": "1210.4976",
  "version": "v2",
  "published": "2012-10-14T22:59:05.000Z",
  "updated": "2017-03-16T13:42:30.000Z",
  "title": "The role of integrability in a large class of physical systems",
  "authors": [
    "David Delphenich"
  ],
  "comment": "56 pages, 3 tables, minor correction to numbering of references",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A large class of physical systems involves the vanishing of a 1-form on a manifold as a constraint on the acceptable states. This means that one is always dealing with the Pfaff problem in those cases. In particular, knowing the degree of integrability of the 1-form is often essential, or, what amounts to the same thing, its canonical (i.e., normal) form. This paper consists of two parts: In the first part, the Pfaff problem is presented and discussed in a largely mathematical way, and in the second part, the mathematical generalities thus introduced are applied to various physical models in which the normal form of a 1-form has already been implicitly introduced, such as non-conservative forces, linear non-holonomic constraints, the theory of vortices and equilibrium thermodynamics. The role of integrability in the conservation of energy is a recurring theme.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-14T22:59:05.000Z",
      "comment": "56 pages, 3 tables",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2017-03-16T13:42:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large class",
      "physical systems",
      "integrability",
      "pfaff problem",
      "linear non-holonomic constraints"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1191803,
      "adsabs": "2012arXiv1210.4976D"
    }
  }
}