{
  "id": "0711.2488",
  "version": "v2",
  "published": "2007-11-15T19:23:38.000Z",
  "updated": "2008-05-20T16:55:24.000Z",
  "title": "Controllability properties of a class of systems modeling swimming microscopic organisms",
  "authors": [
    "Mario Sigalotti",
    "Jean-Claude Vivalda"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, with Stokes equations governing the surrounding fluid. The action of the cilia is described by a set of controlled velocity fields on the surface of the organism. The first contribution of the paper is the proof that such a system is generically controllable when the space of controlled velocity fields is at least three-dimensional. We also provide a complete characterization of controllable systems in the case in which the organism has a spherical shape. Finally, we offer a complete picture of controllable and non-controllable systems under the additional hypothesis that the organism and the fluid have densities of the same order of magnitude.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-05-20T16:55:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "systems modeling swimming microscopic organisms",
      "controllability properties",
      "couples newtons laws driving",
      "controlled velocity fields",
      "model couples newtons laws"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2488S"
    }
  }
}