scholarly journals Numerical determination of short-period Trojan orbits in the restricted three-body problem

1966 ◽  
Vol 71 ◽  
pp. 88 ◽  
Author(s):  
Edson F. Goodrich
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Numerical Determination ◽  
Three Body Problem ◽  
Short Period ◽  
Three Body

scholarly journals Equilibrium Points and Related Periodic Motions in the Restricted Three-Body Problem with Angular Velocity and Radiation Effects

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
E. A. Perdios ◽  
V. S. Kalantonis ◽  
A. E. Perdiou ◽  
A. A. Nikaki
Keyword(s):  
Angular Velocity ◽  
Body Problem ◽  
Equilibrium Points ◽  
Velocity Variation ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Long Period ◽  
Short Period ◽  
Three Body

The paper deals with a modification of the restricted three-body problem in which the angular velocity variation is considered in the case where the primaries are sources of radiation. In particular, the existence and stability of its equilibrium points in the plane of motion of the primaries are studied. We find that this problem admits the well-known five planar equilibria of the classical problem with the difference that the corresponding collinear points may be stable depending on the parameters of the problem. For all planar equilibria, sufficient parametric conditions for their stability have been established which are used for the numerical determination of the stability regions in various parametric planes. Also, for certain values of the parameters of the problem for which the equilibrium points are stable, the short and long period families have been computed. To do so, semianalytical expressions have been found for the determination of appropriate initial conditions. Special attention has been given to the continuation of the long period family, in the case of the classical restricted three-body problem, where we show numerically that periodic orbits of the short period family, which are bifurcation points with the long period family, are connected through the characteristic curve of the long period family.

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.

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