{
  "id": "2210.09105",
  "version": "v1",
  "published": "2022-10-17T13:54:54.000Z",
  "updated": "2022-10-17T13:54:54.000Z",
  "title": "New Role of Null Lagrangians in Derivation of Equations of Motion for Dynamical Systems",
  "authors": [
    "R. Das",
    "Z. E. Musielak"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.CD"
  ],
  "abstract": "The space of Null Lagrangians is the least investigated territory in dynamics since they are identically sent to zero by their Euler-Lagrange operator and thereby having no effects on equations of motion. A humble effort to discover the relevance of these Null Lagrangians in dynamics is made by introducing a generalized procedure (with respect to the recent procedure introduced by the authors of this paper) that takes advantage of the null-ness of these Lagrangians to construct non-standard Lagrangians that represent a range of interesting dynamical systems. By using the generalized procedure, derivation of equations of motion for a harmonic oscillator as well as for the Bateman and Duffing oscillators is presented. The obtained results demonstrate a new role played by the null Lagrangians and their corresponding non-standard Lagrangians in describing linear and nonlinear, and dissipative and non-dissipative dynamical systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-17T13:54:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "null lagrangians",
      "derivation",
      "generalized procedure",
      "construct non-standard lagrangians",
      "euler-lagrange operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}