Numerical determination of Lissajous trajectories in the restricted three-body problem

1987 ◽  
Vol 41 (1-4) ◽  
pp. 107-124 ◽  
Author(s):  
K. C. Howell ◽  
H. J. Pernicka
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Numerical Determination ◽  
Three Body Problem ◽  
Three Body ◽  
Lissajous Trajectories

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.

scholarly journals Asymmetric Periodic Orbits in the Three-Body Problem and Their Stability

1983 ◽  
Vol 74 ◽  
pp. 249-256
Author(s):  
A. Tsouroplis ◽  
C.G. Zagouras
Keyword(s):  
Periodic Solutions ◽  
Numerical Integration ◽  
Periodic Orbits ◽  
Body Problem ◽  
Numerical Determination ◽  
Three Body Problem ◽  
Stability Parameters ◽  
Variational Equations ◽  
Three Body

AbstractAn algorithm for the numerical determination of asymmetric periodic solutions of the planar general three body problem is described. The elements of the “variational” matrix which are used in this algorithm are computed by numerical integration of the corresponding “variational” equations. These elements are also used in the study of the linear isoenergetic stability. A number of asymmetric periodic orbits are presented and their stability parameters are given.

scholarly journals Orbital Stability in the Elliptic Restricted Three Body Problem

1978 ◽  
Vol 41 ◽  
pp. 333-337
Author(s):  
C.A. Williams ◽  
J.G. Watts
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Orbital Stability ◽  
Restricted Three Body Problem ◽  
Invariant Relation ◽  
Three Body Problem ◽  
Hill Stability ◽  
Elliptic Restricted Problem ◽  
Three Body

AbstractBased on the concept of orbital stability introduced by G. W. Hill, a method is presented to facilitate the determination of the orbital stability of solutions to the planar elliptic restricted problem of three bodies. The invariant relation introduced by Szebehely and Giacaglia (1964) contains an integral which is expanded here about a Keplerian solution to the problem. If the expansion converges, it can be used to determine the conditions for Hill stability. With it one can also define stability in a periodic sense.

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