On Periodic Orbits in the Restricted Problem of Three Bodies in a Three Dimensional Coordinate System
Abstract
This paper is an extension of paper [1] which also studies the existence of periodic orbits in the restricted problem of three bodies in a three dimensional coordinate system. Instead of taking p20 = g30 = P30 = 0 for the generating solution as in [1], we have chosen the following conditions:
(i) P20 ≠0, q30 = P30 = 0
and (ii) P20 ≠0, q30 ≠0, P30 = 0(n)
The existence of periodic orbits is studied in both cases, using the same variables and the same method as in [1]. Our study will be restricted only to the first approximation.
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Copyright (c) 1974 Ram Kishore Choudhry
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
R. K. CHOUDHRY, On a class of periodic orbits in the restricted problem of three bodies in a three dimensional coordinate system, Progress of Mathematics. Vol. 2, No. 1 (1968), 128-133.
G. N. DUBOSHIN. Celestial Mechanics (Analytical and qualitative methods), Moscow (Russian), 1964.
H. T. H. PIAGQIO, An elementary treatise on differential equations and their applications, G. Bell & sons. London (1950).
H. HANCOCK, Elliptic Integrals, Dover Publications, New York (1958).
V. G. DEMIN, A new class of periodic solutions in the restricted problem of three bodies, Bulletin ITA, No. 10(93), (Russian), 1960.