Mathematics
Scientific paper
Sep 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005cosre..43..361r&link_type=abstract
Cosmic Research, Volume 43, Issue 5, pp.361-368
Mathematics
Scientific paper
A hydrodynamic analogy for the solution to a satellite version of the restricted three-body problem is considered with allowance made for precession of the disturbing body orbit. Applying, in the first approximation, the analytical solution to a doubly averaged equation system obtained in 1961 by M.L. Lidov, we consider the precession of the disturbing body orbit as some disturbing factor. The appropriate model enables us to describe the general pattern of integral curves in the entire area of their existence as a picture of flow lines of the potential motion of some fictitious homogeneous incompressible fluid. For the synthesis of an adequate mathematical model, a method similar to the Pade approximation is used. The obtained model and its discrete continual analog allow us to present, in a pictorial form, the disturbance of orbits under the effect of precession of the disturbing body orbit.
Prokhorenko V. I.
Rabinovich B. I.
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