{
  "id": "2012.12166",
  "version": "v1",
  "published": "2020-12-22T17:00:04.000Z",
  "updated": "2020-12-22T17:00:04.000Z",
  "title": "Unifying the Hyperbolic and Spherical 2-Body Problem with Biquaternions",
  "authors": [
    "Philip Arathoon"
  ],
  "comment": "15 pages",
  "categories": [
    "math-ph",
    "math.DS",
    "math.MP"
  ],
  "abstract": "The 2-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions concerning the hyperbolic system by complexifying it and treating it as the complexification of a spherical system. In this way, results for the 2-body problem on the sphere are readily translated to the hyperbolic case. For instance, we implement this idea to completely classify the relative equilibria for the 2-body problem on hyperbolic 3-space for a strictly attractive potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-22T17:00:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F05",
      "70H33"
    ],
    "keywords": [
      "biquaternions",
      "holomorphic hamiltonian systems",
      "complex sphere",
      "natural description",
      "hyperbolic space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}