Trajectory Equivalence of the Two-Center Problem in the Flat Space, in Lobachevsky Space and on Sphere: Limit Passage (Part 1)
Keywords:
limit passage, constant curvature, Kepler’s problem, two-center problem, Lobachevsky spaceAbstract
The limit passage in the two-center problem in the Lobachevsky space and on a sphere is carried out as ( is a curvature of the corresponding space). The potentials and metrics in spaces under study are written in the gnomonic coordinates. It is shown that integrable problems of celestial mechanics (the Kepler problem and the two-center problem) pass one into another in spaces of constant curvature under changing two parameters: the space curvature and the distance between centers.References
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