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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