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

被引：1
|
作者：
Zub S.I. [1 ]
Zub S.S. [2 ]
Lyashko V.S. [3 ]
Lyashko N.I. [4 ]
Lyashko S.I. [2 ]
机构：
[1] National Scientific Center “Institute of Metrology,” Ministry of Economic Development and Trade of Ukraine, Kharkiv
[2] Taras Shevchenko National University of Kyiv, Kyiv
[3] P. L. Shupyk National Medical Academy of Postgraduate Education, Kyiv
[4] V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv
来源：
Cybernetics and Systems Analysis | 2017年 / 53卷 / 3期
关键词：
energy-momentum method; Kirillov–Kostant–Souriau; 2-form; mathematical model of a symmetric top; Poisson reduction; relative equilibrium; symplectic leaf;
D O I：
10.1007/s10559-017-9933-7
中图分类号：
学科分类号：
摘要：
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. © 2017, Springer Science+Business Media New York.
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页码：333 / 345
页数：12
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