A Geometric Study of Solutions to Restricted Circular Double-Averaged Three-Body Problem

A geometric interpretation is given to the integrals of a restricted circular double-averaged three-body problem obtained by M.L. Lidov. A representation in specially chosen cylindrical and spherical coordinate systems makes the integrals more descriptive and their topological structure clearer. Fur...

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Bibliographic Details
Published in:Cosmic research 2001-11, Vol.39 (6), p.583-593
Main Author: Prokhorenko, V I
Format: Article
Language:English
Subjects:
Studies
Online Access:Get full text
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Summary:A geometric interpretation is given to the integrals of a restricted circular double-averaged three-body problem obtained by M.L. Lidov. A representation in specially chosen cylindrical and spherical coordinate systems makes the integrals more descriptive and their topological structure clearer. Further analysis involves a separation of variables and considers a finite size of a central body. It allows one to construct the boundaries within a domain of integral constants that split satellite orbits into two classes depending on a possible collision with the central body due to third-body perturbations. The first class includes the orbits that inevitably result in the collision with the central body; the orbits of the second class have nothing to do with the problem of collision with the central body.[PUBLICATION ABSTRACT]
ISSN:0010-9525
1608-3075
DOI:10.1023/A:1013057428421