{
  "annotation_id": "c5722945-b41f-42b6-abd0-50ead875b62f",
  "date_created": "2026-02-17T05:53:20.020000Z",
  "date_modified": "2026-02-17T05:53:20.020000Z",
  "file_hash": "07eca95e9c8a3f7b8eadd9c654242d3935279dd4b1bba4466db4c80275311336",
  "private": false,
  "record": {
    "abstract": "In this paper we consider reduction of the stochastic Hamilton-Pontryagin principle formulated on the Pontryagin bundle of a manifold $Q$. We prove that a stochastic action invariant under the free and proper action of a Lie group $G$ drops to a reduced variational principle expressed in terms of variables of the Pontryagin bundle of the reduced space $Q/G$, the associated adjoint bundle $\\tilde{\\mathfrak{g}}:= (Q\\times \\mathfrak{g})/G$ and its dual bundle $\\tilde{\\mathfrak{g}}^*$. This provides a stochastic analogue of the deterministic implicit Lagrange-Poincar\\\u0027e reduction. The stochastic Euler-Lagrange equations drop to a set of stochastic horizontal and vertical Lagrange-Poincar\\\u0027e equations on $T(Q/G)\\oplus T^*(Q/G)\\oplus\\tilde{\\mathfrak{g}}\\oplus\\tilde{\\mathfrak{g}}^*$. As examples, we consider stochastic perturbations of the rigid body with a rotor, as well as a Kaluza-Klein description of stochastic perturbations of a charged particle in a magnetic field.",
    "arxiv_id": "2601.08994",
    "authors": [
      "Archishman Saha"
    ],
    "categories": [
      "math-ph",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Stochastic Implicit Lagrange-Poincar\\\u0027e Reduction",
    "url": "https://arxiv.org/abs/2601.08994",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "97e86b55-f619-45e4-b942-3ea6aaa57134",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}