{
  "id": "2004.09797",
  "version": "v1",
  "published": "2020-04-21T07:52:06.000Z",
  "updated": "2020-04-21T07:52:06.000Z",
  "title": "The Axisymmetric Central Configurations of the Four-Body Problem with Three Equal Masses",
  "authors": [
    "Emese Kővári",
    "Bálint Érdi"
  ],
  "comment": "16 pages, 8 figures, appeared in the open-access journal Symmetry (special issue: Astronomy and Symmetry)",
  "journal": "Symmetry, Vol. 12, No. 4, id. 648 (2020)",
  "doi": "10.3390/sym12040648",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In the studied axisymmetric case of the central four-body problem, the axis of symmetry is defined by two unequal-mass bodies, while the other two bodies are situated symmetrically with respect to this axis and have equal masses. Here, we consider a special case of the problem and assume that three of the masses are equal. Using a recently found analytical solution of the general case, we formulate the equations of condition for three equal masses analytically and solve them numerically. A complete description of the problem is given by providing both the coordinates and masses of the bodies. We show furthermore how the three-equal-mass solutions are related to the general case in the coordinate space. The physical aspects of the configurations are also studied and discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-21T07:52:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equal masses",
      "axisymmetric central configurations",
      "general case",
      "central four-body problem",
      "unequal-mass bodies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}