{
  "abstract": "We discuss two models of a 3D torpedo in which the centre of mass $x$ moves only longitudinally, while the body may rotate about $x$. Although these are simple examples of left-invariant distributions on the Lie group $SE(3)$, they possess rich geometric structures. For the simplest model, we arrive at an abelian extension of a flat (3,5) path geometry, while adding tiny coupling, we obtain a non-trivial hyperbolic type codimension two CR geometry whose symmetry algebra is just $\\mathfrak{se}(3)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26439",
  "author_total": 2,
  "authors": [
    {
      "name": "Pavla Musilova"
    },
    {
      "name": "Jan Slovak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f0bs75msg0w25.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26439",
  "fulltext_url": null,
  "id": "f0bs75msg0w25",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26439",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7223017547",
  "pdf_url": "https://arxiv.org/pdf/2610.26439",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f0bs75msg0w25.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26439",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26439"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "From Chaplygin Sleigh to Torpedo: An~example of a~Cartan-Geometric View of Left-Invariant Nonholonomic Systems",
  "title_text": "From Chaplygin Sleigh to Torpedo: An~example of a~Cartan-Geometric View of Left-Invariant Nonholonomic Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/f0bs75msg0w25",
  "venue": "arXiv",
  "versions": []
}