{
  "abstract": "We study a Purcell three-link microswimmer whose joints are \\emph{odd-elastic}: the torsional stiffness is non-Hermitian, its antisymmetric part $k_o$ injecting mechanical work so that the internal elastic drift is non-conservative. Our main finding is a sharp separation between geometry and cost --- odd elasticity is invisible to the control geometry of the swimmer and visible only in the energy of a manoeuvre. The mechanism is a single algebraic fact: the drift lies in the span of the two control vector fields, so the system is feedback-equivalent to a driftless one and the odd modulus enters the bracket structure only through the scalar $\\det\\textbf{K}=k^2+k_o^2$. From this we deduce that the abnormal extremals of the energy problem are unchanged by $k_o$, that the swimmer is globally controllable for every non-reciprocity with no threshold, and that its nilpotent model is the Cartan $(2,3,5)$ sub-Riemannian structure, deformed only by the metric scaling $g_χ=(1+χ^2)g_0$. The odd modulus acts solely on the cost: casting the optimal-steering problem in sub-Finsler (Randers) form, we prove that a prescribed reorientation is strictly cheaper for either sign of $k_o$. Full Resistive-Force-Theory simulations confirm the analysis and reveal that at isotropic drag the swimmer becomes a pure rotator, turning without translating.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.02777",
  "author_total": 3,
  "authors": [
    {
      "name": "Rossella Attanasi"
    },
    {
      "name": "Gaetano Napoli"
    },
    {
      "name": "Marta Zoppello"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c2pshwfhjp0f8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.02777",
  "fulltext_url": null,
  "id": "c2pshwfhjp0f8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.02777",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3104|Micro and Nano Robotics"
    ]
  ],
  "openalex": "W7172502762",
  "pdf_url": "https://arxiv.org/pdf/2608.02777",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c2pshwfhjp0f8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2608.02777",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.02777"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Odd elasticity in a three-link microswimmer: feedback equivalence, global controllability, and the cost of non-reciprocity",
  "title_text": "Odd elasticity in a three-link microswimmer: feedback equivalence, global controllability, and the cost of non-reciprocity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/c2pshwfhjp0f8",
  "venue": "arXiv",
  "versions": []
}