{
  "id": "1109.6056",
  "version": "v2",
  "published": "2011-09-27T22:38:29.000Z",
  "updated": "2012-09-12T16:57:01.000Z",
  "title": "Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints",
  "authors": [
    "Melvin Leok",
    "Tomoki Ohsawa",
    "Diana Sosa"
  ],
  "comment": "44 pages, 3 figures",
  "journal": "Journal of Mathematical Physics 53, 072905 (2012)",
  "doi": "10.1063/1.4736733",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SG"
  ],
  "abstract": "We extend Hamilton-Jacobi theory to Lagrange-Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer to the generalized Hamilton-Jacobi equation as the Dirac-Hamilton-Jacobi equation. For non-degenerate Lagrangian systems with nonholonomic constraints, the theory specializes to the recently developed nonholonomic Hamilton-Jacobi theory. We are particularly interested in applications to a certain class of degenerate nonholonomic Lagrangian systems with symmetries, which we refer to as weakly degenerate Chaplygin systems, that arise as simplified models of nonholonomic mechanical systems; these systems are shown to reduce to non-degenerate almost Hamiltonian systems, i.e., generalized Hamiltonian systems defined with non-closed two-forms. Accordingly, the Dirac-Hamilton-Jacobi equation reduces to a variant of the nonholonomic Hamilton-Jacobi equation associated with the reduced system. We illustrate through a few examples how the Dirac-Hamilton-Jacobi equation can be used to exactly integrate the equations of motion.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-12T16:57:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70H20",
      "70H45",
      "37J60",
      "70F25",
      "45.20.Jj",
      "02.30.Sa",
      "02.40.Yy"
    ],
    "keywords": [
      "nonholonomic constraints",
      "degenerate lagrangian systems",
      "hamiltonian systems",
      "degenerate nonholonomic lagrangian systems",
      "weakly degenerate chaplygin systems"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2012,
      "month": "Jul",
      "volume": 53,
      "number": 7,
      "pages": 2905
    },
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JMP....53g2905L"
    }
  }
}