Analytical solutions around planar equilibria of three dipole problem

Proceeding with our investigation into the motion of a particle influenced by the electromagnetic field of three celestial bodies of a magnetic-dipole nature, we give here for the first time the analytical expressions of periodic solutions around a planar equilibrium point. These relations are serie...

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Bibliographic Details
Published in:Astrophysics and space science 1993-08, Vol.206 (1), p.71-89
Main Authors: DESINIOTIS, C. D, KAZANTZIS, P. G
Format: Article
Language:English
Subjects:
Astronomy
Celestial mechanics (including n-body problems)
Earth, ocean, space
Exact sciences and technology
Fundamental astronomy
Fundamental astronomy and astrophysics. Instrumentation, techniques, and astronomical observations
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Summary:Proceeding with our investigation into the motion of a particle influenced by the electromagnetic field of three celestial bodies of a magnetic-dipole nature, we give here for the first time the analytical expressions of periodic solutions around a planar equilibrium point. These relations are series expansions of second order power of a parameter epsilon in the vicinity of equilibria for the planar equations of motion. The above analytical expressions of periodic solutions give the first members of the family of periodic orbits which emanate from a stable equilibrium point. The whole family can then be calculated using a predictor-corrector algorithm.
ISSN:0004-640X
1572-946X
DOI:10.1007/BF00658384