{
  "id": "2405.07511",
  "version": "v1",
  "published": "2024-05-13T07:12:01.000Z",
  "updated": "2024-05-13T07:12:01.000Z",
  "title": "Bifurcation analysis of the problem of a \"rubber\" ellipsoid of revolution rolling on a plane",
  "authors": [
    "Alexander Kilin",
    "Elena Pivovarova"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "This paper is concerned with the problem of an ellipsoid of revolution rolling on a horizontal plane under the assumption that there is no slipping at the point of contact and no spinning about the vertical. A reduction of the equations of motion to a fixed level set of first integrals is performed. Permanent rotations corresponding to the rolling of an ellipsoid in a circle or in a straight line are found. A linear stability analysis of permanent rotations is carried out. A complete classification of possible trajectories of the reduced system is performed using a bifurcation analysis. A classification of the trajectories of the center of mass of the ellipsoid depending on parameter values and initial conditions is performed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-13T07:12:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J60",
      "70E18",
      "70E40",
      "70E50"
    ],
    "keywords": [
      "bifurcation analysis",
      "revolution rolling",
      "permanent rotations",
      "linear stability analysis",
      "horizontal plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}