{
  "annotation_id": "09f2f5df-a6e0-4d70-9718-17d318de2b60",
  "date_created": "2026-03-02T18:00:39.551000Z",
  "date_modified": "2026-03-02T18:00:39.551000Z",
  "file_hash": "e21623ae0107ae012a973dd8e2854527d74601c5dab058a0a9a2713dc87ef352",
  "private": false,
  "record": {
    "abstract": "The two-dimensional n-body problem of classical mechanics is a non-integrable\nHamiltonian system for n \u003e 2. Traditional numerical integration algorithms,\nwhich are polynomials in the time step, typically lead to systematic drifts in\nthe computed value of the total energy and angular momentum. Even symplectic\nintegration schemes exactly conserve only an approximate Hamiltonian. We\npresent an algorithm that conserves the true Hamiltonian and the total angular\nmomentum to machine precision. It is derived by applying conventional\ndiscretizations in a new space obtained by transformation of the dependent\nvariables. We develop the method first for the restricted circular three-body\nproblem, then for the general two-dimensional three-body problem, and finally\nfor the planar n-body problem. Jacobi coordinates are used to reduce the\ntwo-dimensional n-body problem to an (n-1)-body problem that incorporates the\nconstant linear momentum and center of mass constraints. For a four-body\nchoreography, we find that a larger time step can be used with our conservative\nalgorithm than with symplectic and conventional integrators.",
    "arxiv_id": "physics/0112084",
    "authors": [
      "Oksana Kotovych",
      "John C. Bowman"
    ],
    "categories": [
      "physics.comp-ph",
      "physics.class-ph"
    ],
    "doi": "10.1088/0305-4470/35/37/301",
    "title": "An Exactly Conservative Integrator for the n-Body Problem",
    "url": "https://arxiv.org/abs/physics/0112084"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "97d71611-a804-4acd-83f5-6ee23f60f39e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}