Mathematics – Logic
Scientific paper
Nov 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001cosre..39..583p&link_type=abstract
Cosmic Research, v. 39, Issue 6, p. 583-593 (2001).
Mathematics
Logic
Scientific paper
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.
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