KEPLER'S PROBLEM IN CONSTANT CURVATURE SPACES

被引：94

作者：

Kozlov, Valeri V. ^{[1
]}

Harin, Alexander O. ^{[1
]}

机构：

[1] Moscow State Univ, Dept Theoret Mech, Moscow 119899, Russia

来源：

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY | 1992年 / 54卷 / 04期

关键词：

Central field; closed orbits; spheroconical coordinates;

D O I：

10.1007/BF00049149

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

In this article the generalization of the motion of a particle in a central field to the case of a constant curvature space is investigated. We found out that orbits on a constant curvature surface are closed in two cases: when the potential satisfies Laplace-Beltrami equation and can be regarded as an analogue of the potential of the gravitational interaction, and in the case when the potential is the generalization of the potential of an elastic spring. Also the full integrability of the generalized two-centre problem on a constant curvature surface is discovered and it is shown that integrability remains even if elastic "forces" are added.

引用

页码：393 / 399

页数：7