{
  "id": "2303.09102",
  "version": "v1",
  "published": "2023-03-16T06:18:52.000Z",
  "updated": "2023-03-16T06:18:52.000Z",
  "title": "Symmetries and first integrals for variational ODEs with delay",
  "authors": [
    "V. A. Dorodnitsyn",
    "R. V. Kozlov",
    "S. V. Meleshko"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A Lagrangian formalism for variational second-order delay ordinary differential equations (DODEs) is developed. The Noether operator identity for a DODE is established, which relates the invariance of a Lagrangian function with the appropriate variational equations and the conserved quantities. The identity is used to formulate Noether-type theorems that give the first integrals for DODE with symmetries. Relations between the invariance of the variational second-order DODEs and the invariance of the Lagrangian functions are also analyzed. Several examples illustrate the theoretical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-16T06:18:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first integrals",
      "variational odes",
      "variational second-order delay ordinary differential",
      "second-order delay ordinary differential equations",
      "symmetries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}