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Cybernetics and Systems Analysis

, Volume 53, Issue 3, pp 333–345 | Cite as

Mathematical Model of Interaction of a Symmetric Top with an Axially Symmetric External Field

  • S. I. ZubEmail author
  • S. S. Zub
  • V. S. Lyashko
  • N. I. Lyashko
  • S. I. Lyashko
CYBERNETICS

Abstract

A symmetric top is considered, which is a particular case of a mechanical top that is usually described by the canonical Poisson structure on T*SE (3). This structure is invariant under the right action of the rotation group SO(3), but the Hamiltonian of the symmetric top is invariant only under the right action of the subgroup S 1, which corresponds to the rotation of the symmetric top around its axis of symmetry. This Poisson structure is obtained as the reduction T* SE (3) / S 1. A Hamiltonian and motion equations are proposed that describe a wide class of interaction models of the symmetric top with an axially symmetric external field.

Keywords

mathematical model of a symmetric top Poisson reduction symplectic leaf Kirillov–Kostant–Souriau 2-form relative equilibrium energy-momentum method 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • S. I. Zub
    • 1
    Email author
  • S. S. Zub
    • 2
  • V. S. Lyashko
    • 3
  • N. I. Lyashko
    • 4
  • S. I. Lyashko
    • 2
  1. 1.National Scientific Center “Institute of Metrology,” Ministry of Economic Development and Trade of UkraineKharkivUkraine
  2. 2.Taras Shevchenko National University of KyivKyivUkraine
  3. 3.P. L. Shupyk National Medical Academy of Postgraduate EducationKyivUkraine
  4. 4.V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of UkraineKyivUkraine

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