On Periodic Orbits in the Restricted Problem of Three Bodies in a Three Dimensional Coordinate System

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Authors

  • P. G. Deptt. of Maths, Bhagalpur University, Bhagalpur-7, Bihar ,IN

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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Published

1974-12-01

How to Cite

Choudhry, R. K. (1974). On Periodic Orbits in the Restricted Problem of Three Bodies in a Three Dimensional Coordinate System. The Journal of the Indian Mathematical Society, 38(1-4), 319–328. Retrieved from https://www.informaticsjournals.com/index.php/jims/article/view/16706

 

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.