{
  "id": "0906.3357",
  "version": "v4",
  "published": "2009-06-18T06:09:44.000Z",
  "updated": "2009-12-18T21:05:18.000Z",
  "title": "Nonholonomic Hamilton-Jacobi equation and Integrability",
  "authors": [
    "Tomoki Ohsawa",
    "Anthony M. Bloch"
  ],
  "comment": "16 pages, 3 figures, submitted to Journal of Geometric Mechanics",
  "journal": "Journal of Geometric Mechanics, 1 (2009), pp. 461-481",
  "doi": "10.3934/jgm.2009.1.461",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We discuss an extension of the Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the Hamilton--Jacobi theorem. Our intrinsic proof clarifies the difference from the conventional Hamilton-Jacobi theory for unconstrained systems. The proof also helps us identify a geometric meaning of the conditions on the solutions of the Hamilton-Jacobi equation that arise from nonholonomic constraints. The major advantage of our result is that it provides us with a method of integrating the equations of motion just as the unconstrained Hamilton--Jacobi theory does. In particular, we build on the work by Iglesias-Ponte, de Leon, and Martin de Diego so that the conventional method of separation of variables applies to some nonholonomic mechanical systems. We also show a way to apply our result to systems to which separation of variables does not apply.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-12-18T21:05:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F25",
      "70H06",
      "70H20",
      "37N05"
    ],
    "keywords": [
      "nonholonomic hamilton-jacobi equation",
      "integrability",
      "intrinsic proof clarifies",
      "conventional hamilton-jacobi theory",
      "hamilton-jacobi theorem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.3357O"
    }
  }
}