Study of the stability of the perturbed solutions of the restricted three body problem

Authors

  • MAA Khan Teacher of Maths, Muslim Higher School, Bhagalpur-812002
  • MR Hassan Dept. of Mathematics, S.M. College, Bhagalpur, T.M.B. University, Bhagalpur – 812007
  • RR Thapa Dept. of Mathematics, P.G. Campus, Tribhuvan University, Biratnagar

DOI:

https://doi.org/10.3126/bibechana.v13i0.13321

Keywords:

Characteristic equations, Characteristic exponents, Complex plane, Poincare's implicit function

Abstract

In this paper we have been examined the stability of the perturbed solutions of the restricted three body problem. We have been restricted ourselves only to the first order variational equations. Our variational equations depend on the periodic solutions. Here the applications of the method of Fuchs and Floquet Proves to be complicated and hence we have been preferred Poincare's Method of determination of the characteristic exponents. With the determination of the characteristic exponents we have been abled to conclude regarding the stability of the generating solution. We have obtained that the motions are unstable in all the cases. By Poincare's implicit function theorem we have concluded that the stability would remain the same for small value of the parameter m and in all types of motion of the restricted three-body problem.

BIBECHANA 13 (2016) 18-22

 

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Published

2015-12-03

How to Cite

Khan, M., Hassan, M., & Thapa, R. (2015). Study of the stability of the perturbed solutions of the restricted three body problem. BIBECHANA, 13, 18–22. https://doi.org/10.3126/bibechana.v13i0.13321

Issue

Section

Research Article