{
  "id": "1211.2682",
  "version": "v1",
  "published": "2012-11-12T16:24:29.000Z",
  "updated": "2012-11-12T16:24:29.000Z",
  "title": "Swimming as a limit cycle",
  "authors": [
    "Henry O. Jacobs"
  ],
  "comment": "24 pages, 4 figures, submitted",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP",
    "math.SG",
    "physics.bio-ph"
  ],
  "abstract": "Steady swimming can be characterized as both periodic and stable. These characteristics are the very definition of limit cycles, and so we ask \"Can we view swimming as a limit cycle?\" In this paper we will find that the answer is \"yes\". We will define a class of dissipative systems which correspond to the passive dynamics of a body immersed in a Navier-Stokes fluid (i.e. the dynamics of a dead fish). Upon performing reduction by symmetry we will find a hyperbolically stable fixed point which corresponds to the stability of a dead fish in stagnant water. Given a periodic force on the shape of the body we will invoke the persistence theorem to assert the existence of a loop which approximately satisfies the exact equations of motion. If we lift this loop with a phase reconstruction formula we will find that the lifted loops are not loops, but stable trajectories which represent regular periodic motion reminiscent of swimming.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-12T16:24:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37L15",
      "92B99",
      "74F10"
    ],
    "keywords": [
      "limit cycle",
      "represent regular periodic motion reminiscent",
      "phase reconstruction formula",
      "correspond",
      "navier-stokes fluid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.2682J"
    }
  }
}