MICZ-Kepler: Dynamics on the cone over SO(n)

被引:2
|
作者
Montgomery, Richard [1 ]
机构
[1] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA
来源
REGULAR & CHAOTIC DYNAMICS | 2013年 / 18卷 / 06期
基金
美国国家科学基金会;
关键词
Kepler problem; MICZ-K system; co-adjoint orbit; Sternberg phase space; symplectic reduction; superintegrable systems; YANG-MILLS FIELD; CLASSICAL PARTICLE;
D O I
10.1134/S1560354713060038
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We show that the n-dimensional MICZ-Kepler system arises from symplectic reduction of the "Kepler problem" on the cone over the rotation group SO(n). As a corollary we derive an elementary formula for the general solution of the MICZ-Kepler problem. The heart of the computation is the observation that the additional MICZ-Kepler potential, |I center dot|(2)/r (2), agrees with the rotational part of the cone's kinetic energy.
引用
收藏
页码:600 / 607
页数:8
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