{
  "abstract": "The linearity of the Stokes equations organises the hydrodynamic response of a rigid particle into a hierarchy of resistance operators, coupling successive truncations of the ambient-flow jet to moments of the surface traction. Since the work of Kelvin and Larmor, it has been known that this response does not resolve particle geometry faithfully: bodies with discrete rotational symmetry may be indistinguishable from bodies of revolution (Brenner's helicoidal symmetry) and a chiral body may respond isotropically, as in Kelvin's isotropic helicoid. We regard the resistance operators as elements of finite-dimensional O(3)-representation spaces and use character formulae to determine, at every level of the hierarchy, which point-group symmetries are hydrodynamically distinguishable and the dimension of each invariant space. This yields an explicit nested sequence of hydrodynamic symmetry-group sets, from the translation-force level to the quadratic-flow level. The framework reveals hydrodynamic classes that no shape can realise geometrically, gives helicoidal symmetry a level-dependent definition, and shows that polyhedral symmetry becomes visible in a strict order: tetrahedral symmetry in shear, octahedral symmetry through the stresslet, and icosahedral symmetry in quadratic flow. Projecting the resistance operators onto force- and torque-free motion provides symmetry-based parameter counts and a constructive route to the corresponding dynamical normal forms. We thereby complete the Jeffery-Bretherton-Ishimoto classification, characterise all hydrodynamic classes producing Jeffery dynamics, and identify chiral tetrahedral and octahedral normal forms that can generate irregular full-attitude dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.23907",
  "author_total": 1,
  "authors": [
    {
      "name": "Clément Moreau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/btbfbf01crvmm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.23907",
  "fulltext_url": null,
  "id": "btbfbf01crvmm",
  "issns": [],
  "landing_url": "https://hal.science/hal-05829077v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
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    ],
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    ],
    [
      "hal",
      "1.math.math-mp"
    ],
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      "hal",
      "1.phys.phys"
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      "hal",
      "2.phys.phys.phys-flu-dyn"
    ],
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      "openalex",
      "3104|Micro and Nano Robotics"
    ]
  ],
  "openalex": "W7204246892",
  "pdf_url": "https://hal.science/hal-05829077/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/btbfbf01crvmm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "hal-05829077",
      "source": "hal",
      "url": "https://hal.science/hal-05829077v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mp",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "hal:2.phys.phys.phys-flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "The Stokes resistance of an arbitrary particle: a classification of hydrodynamic symmetries",
  "title_text": "The Stokes resistance of an arbitrary particle: a classification of hydrodynamic symmetries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/btbfbf01crvmm",
  "venue": "HAL",
  "versions": []
}