{
  "abstract": "We develop a continuum theory for a fluid of elongated particles that advance along their own axes. The same kinematics is ideally shared by flocks of sheep, self-propelled rods, vehicular traffic, and turning flocks of birds. Within the framework of continua with vectorial microstructure, in which each point also carries an orientation, we impose the no-side-slip (skate) condition $\\vv=u\\,\\nn$ as an ideal, non-integrable internal constraint. We derive the pure equations of motion and the equation governing the constraint reaction from the principle of virtual power. Using a constitutive closure provided by the Ericksen-Leslie theory of nematic liquid crystals, we show how the constraint also shapes collective effects. It turns parabolic orientational diffusion into hyperbolic orientation-density waves and forbids any steady simple shear. It fixes the empirical Toner-Tu convective coefficient to the flow-alignment ratio measured in colloidal rollers, thereby providing a mechanical foundation for angular sound in micropolar active hydrodynamics. It also recovers the inertial spin model of bird flocks, with the addition of a banking force and a turn-density coupling. Finally, it recovers the classical macroscopic models of one-dimensional traffic flow, while describing steering, lateral tyre forces, and road geometry in two dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28380",
  "author_total": 1,
  "authors": [
    {
      "name": "Gaetano Napoli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bkrfw586k2qw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28380",
  "fulltext_url": null,
  "id": "2bkrfw586k2qw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28380",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.soft"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3104|Micro and Nano Robotics"
    ]
  ],
  "openalex": "W7204831365",
  "pdf_url": "https://arxiv.org/pdf/2608.28380",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bkrfw586k2qw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2608.28380",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28380"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Nonholonomic collective flows: velocity--orientation locking in a continuum with microstructure",
  "title_text": "Nonholonomic collective flows: velocity--orientation locking in a continuum with microstructure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/2bkrfw586k2qw",
  "venue": "arXiv",
  "versions": []
}