{
  "annotation_id": "a1df6c73-0904-4bf9-8ca5-03a0f62e6e08",
  "date_created": "2026-03-02T18:00:36.429000Z",
  "date_modified": "2026-03-02T18:00:36.429000Z",
  "file_hash": "975f9adbf60b8dcbe6f10a8a5291eb439e2636544edc11d8399de89b0652dcc4",
  "private": false,
  "record": {
    "abstract": "In this paper, we propose a novel algebraic and geometric description for the\ndissipative dynamics. Our formulation bears some similarity to the Poisson\nstructure for non-dissipative systems. We develop a canonical description for\nconstrained dissipative systems through an extension of the Dirac brackets\nconcept, and we present a new formula for calculating Dirac brackets. This\nformula is particularly useful in the description of dynamical systems with\nmany second-class constraints. After presenting the necessary formal background\nwe illustrate our method on several examples taken from particle dynamics,\ncontinuum media physics and wave mechanics.",
    "arxiv_id": "physics/0110065",
    "authors": [
      "Sonnet Q H Nguyen",
      "Lukasz A Turski"
    ],
    "categories": [
      "physics.class-ph",
      "math-ph",
      "math.MP",
      "physics.flu-dyn",
      "physics.gen-ph"
    ],
    "doi": "10.1088/0305-4470/34/43/312",
    "journal_ref": "Journal of Physics A: Math. Gen. 34, No. 43, 9281-9302, 2001",
    "title": "On the Dirac Approach to Constrained Dissipative Dynamics",
    "url": "https://arxiv.org/abs/physics/0110065"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8e235e87-3202-4d1b-9b71-a654d4148252",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}