{
  "id": "1907.04726",
  "version": "v1",
  "published": "2019-07-10T13:52:30.000Z",
  "updated": "2019-07-10T13:52:30.000Z",
  "title": "Characterization of the critical points for the free energy of a Cosserat problem",
  "authors": [
    "Petre Birtea",
    "Ioan Casu",
    "Dan Comanescu"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.OC"
  ],
  "abstract": "Using the embedded gradient vector field method we explicitly compute the list of critical points of the free energy for a Cosserat body model. We also formulate necessary and sufficient conditions for critical points in the abstract case of the special orthogonal group $SO(n)$. Each critical point is then characterized using an explicit formula for the Hessian operator of a cost function defined on the orthogonal group. We also give a positive answer to an open question posed in L. Borisov, A. Fischle, P. Neff, \"Optimality of the relaxed polar factors by a characterization of the set of real square roots of real symmetric matrices\", ZAMM (2019), namely if all local minima of the optimization problem are global minima. We point out a few examples with physical relevance, in contrast to some theoretical (mathematical) situations that do not hold such a relevance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-10T13:52:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "74A30",
      "74A60",
      "74G05",
      "74G65",
      "74N15",
      "53B21"
    ],
    "keywords": [
      "critical point",
      "free energy",
      "cosserat problem",
      "characterization",
      "embedded gradient vector field method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}