Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984azh....61..800i&link_type=abstract
(Astronomicheskii Zhurnal, vol. 61, July-Aug. 1984, p. 800-805) Soviet Astronomy (ISSN 0038-5301), vol. 28, July-Aug. 1984, p. 4
Astronomy and Astrophysics
Astronomy
1
Celestial Mechanics, Elliptical Orbits, Periodic Functions, Three Body Problem, Eccentric Orbits, Libration
Scientific paper
The existence of 6-pi periodic solutions of the differential equation of motion of the plane, restricted, elliptical three-body problem in complex form in the vicinity of a libration point is investigated. The approximate construction of the solutions is studied, and it is shown that the equation of this three-body problem for sufficiently small orbital eccentricity in the vicinity of the libration point has a continuum of 6-pi periodic solutions in the form of series in powers of the eccentricity. The process of determining the coefficients of the series which are solutions of the corresponding linear differential equations is stabilized. The convergence of these series can be proved by the ordinary principle of contractive mappings.
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