具有SU（2）Poisson结构的空间中心力问题
Central force problem in space with SU(2) Poisson structure
摘要：
在三维空间中考虑有心力问题，其中空间坐标之间的Poisson括号是SU（2）李代数的Poisson括号。结果表明，在吸引幂律势中，只有开普勒势的所有束缚态都是闭合轨道。给出了开普勒势下路径方程的解析解。结果表明，除了开普勒势，与普通空间相反，所有的势，几乎所有的圆轨道是封闭的，是非幂律的。对于非幂律势的路径方程的数值解的例子。
英文摘要：
The central force problem is considered in a three dimensional space in which the Poisson bracket among the spatial coordinates is the one by the SU(2) Lie algebra. It is shown that among attractive power-law potentials it is only the Kepler one that all of its bound-states make closed orbits. The analytic solution of the path equation under the Kepler potential is presented. It is shown that except the Kepler potential, in contrast to ordinary space, all of the potentials for which all of the almost circular orbits are closed are non-power-law ones. For the non-power-law potentials examples of the numerical solutions of the path equations are presented.
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