{
  "id": "2203.14930",
  "version": "v1",
  "published": "2022-03-28T17:33:09.000Z",
  "updated": "2022-03-28T17:33:09.000Z",
  "title": "Equal masses Eulerian relative equilibria on a rotating meridian of S^2",
  "authors": [
    "Toshiaki Fujiwara",
    "Ernesto Pérez-Chavela"
  ],
  "comment": "20 pages, 5 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "Relative equilibria on a rotating meridian on $\\mathbb{S}^2$ in equal-mass three-body problem under the cotangent potential are determined. We show the existence of scalene and isosceles relative equilibria. Almost all isosceles triangles, including equilateral, can form a relative equilibrium, except for the two equal arc angles $\\theta = \\pi/2$. For $\\theta\\in (0,2\\pi/3)\\setminus \\{\\pi/2\\}$, the mid mass must be on the rotation axis, in our case, at the north or south pole of $\\mathbb{S}^2$. For $\\theta\\in (2\\pi/3,\\pi)$, the mid mass must be on the equator. For $\\theta=2\\pi/3$, we obtain the equilateral triangle, where the position of the masses is arbitrary. When the largest arc angle $a_\\ell$ is in $a_\\ell\\in (\\pi/2,a_c)$, with $a_c=1.8124...$, two scalene configurations exist for given $a_\\ell$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-28T17:33:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F07",
      "70F15"
    ],
    "keywords": [
      "relative equilibrium",
      "equal masses eulerian relative equilibria",
      "rotating meridian",
      "largest arc angle",
      "equal-mass three-body problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}