• DocumentCode
    3526617
  • Title

    Riemannian metrics on 2D manifolds related to the Euler-Poinsot rigid body problem

  • Author

    Bonnard, Bernard ; Cots, Olivier ; Shcherbakova, Nataliya

  • Author_Institution
    Inst. de Math. de Bourgogne, Univ. de Bourgogne, Dijon, France
  • fYear
    2013
  • fDate
    10-13 Dec. 2013
  • Firstpage
    1804
  • Lastpage
    1809
  • Abstract
    The Euler-Poinsot rigid body problem is a well known model of left-invariant metrics on SO(3). In the present paper we discuss the properties of two related reduced 2D models: the sub-Riemanian metric of a system of three coupled spins and the Riemannian metric associated to the Euler-Poinsot problem via the Serret-Andoyer reduction.We explicitly construct Jacobi fields and explain the structure of conjugate loci in the Riemannian case and give the first numerical results for the spin dynamics case.
  • Keywords
    Jacobian matrices; numerical analysis; shear modulus; 2D manifolds; Euler-Poinsot rigid body problem; Jacobi fields; SO(3); Serret-Andoyer reduction; conjugate loci; coupled spins; left-invariant metrics; numerical results; spin dynamics; subRiemanian metrics; Equations; Jacobian matrices; Measurement; Optimal control; Standards; Trajectory; Vectors;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on
  • Conference_Location
    Firenze
  • ISSN
    0743-1546
  • Print_ISBN
    978-1-4673-5714-2
  • Type

    conf

  • DOI
    10.1109/CDC.2013.6760144
  • Filename
    6760144