{
  "id": "2210.01740",
  "version": "v1",
  "published": "2022-10-04T17:01:30.000Z",
  "updated": "2022-10-04T17:01:30.000Z",
  "title": "Periodic oscillations in the restricted Hip-Hop 2N+1 body problem",
  "authors": [
    "Andres Rivera",
    "Oscar Perdomo",
    "Nelson Castaneda"
  ],
  "comment": "12 pages, 5 figures",
  "categories": [
    "math.DS",
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "We prove the existence of periodic solutions of the restricted $(2N+1)$-body problem when the $2N$-primaries move on a periodic Hip-Hop solution and the massless body moves on the line that contains the center of mass and is perpendicular to the base of the antiprism formed by the $2N$-primaries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-04T17:01:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F10",
      "37C27",
      "34A12"
    ],
    "keywords": [
      "body problem",
      "periodic oscillations",
      "restricted hip-hop",
      "periodic hip-hop solution",
      "periodic solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}