Numerical Determination of Homoclinic and Heteroclinic Orbits at Collinear Equilibria in the Restricted Three-Body Problem with Oblateness

2006 ◽  
Vol 94 (2) ◽  
pp. 135-153 ◽  
Author(s):  
V. S. Kalantonis ◽  
C. N. Douskos ◽  
E. A. Perdios
Keyword(s):  
Body Problem ◽  
Heteroclinic Orbits ◽  
Restricted Three Body Problem ◽  
Numerical Determination ◽  
Three Body Problem ◽  
Homoclinic And Heteroclinic Orbits ◽  
Three Body

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

BIBECHANA ◽  
2015 ◽  
Vol 13 ◽  
pp. 18-22
Author(s):  
MAA Khan ◽  
MR Hassan ◽  
RR Thapa
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Variational Equations ◽  
First Order ◽  
Characteristic Exponents ◽  
Method Of Determination ◽  
The Stability ◽  
Three Body

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 

scholarly journals A New Kind of Periodic Orbit: The Three-Dimensional Asymmetric

1978 ◽  
Vol 41 ◽  
pp. 315-317 ◽  
Author(s):  
V. V. Markellos
Keyword(s):  
Periodic Orbit ◽  
Periodic Orbits ◽  
Body Problem ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

AbstractA great deal of human and computer effort has been directed in recent decades to the determination of the periodic orbits of the restricted three-body problem and the study of their properties for well known reasons of significance and feasibility.

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