{
  "annotation_id": "9b795ad0-df45-4b3f-b6fd-c94af4a3952b",
  "date_created": "2026-03-02T18:00:42.671000Z",
  "date_modified": "2026-03-02T18:00:42.671000Z",
  "file_hash": "01e664d276b2b10fbddef9826ac1a999e828d1c985ea11255bf5f8eb62151d83",
  "private": false,
  "record": {
    "abstract": "The Kustaanheimo-Stiefel (KS) transformation maps the non-linear and singular\nequations of motion of the three-dimensional Kepler problem to the linear and\nregular equations of a four-dimensional harmonic oscillator. It is used\nextensively in studies of the perturbed Kepler problem in celestial mechanics\nand atomic physics. In contrast to the conventional matrix-based approach, the\nformulation of the KS transformation in the language of geometric Clifford\nalgebra offers the advantages of a clearer geometrical interpretation and\ngreater computational simplicity. It is demonstrated that the geometric algebra\nformalism can readily be used to derive a Lagrangian and Hamiltonian\ndescription of the KS dynamics in arbitrary static electromagnetic fields. For\norbits starting at the Coulomb centre, initial conditions are derived and a\nframework is set up that allows a discussion of the stability of these orbits.",
    "arxiv_id": "physics/0301017",
    "authors": [
      "T. Bartsch"
    ],
    "categories": [
      "physics.class-ph"
    ],
    "doi": "10.1088/0305-4470/36/25/305",
    "journal_ref": "J. Phys. A 36, 6963 (2003)",
    "title": "The Kustaanheimo-Stiefel transformation in geometric algebra",
    "url": "https://arxiv.org/abs/physics/0301017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1e3ad7f8-913f-4bf2-8045-31f445574f22",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}