Three-dimensional bifurcations of periodic solutions around the triangular equilibrium points of the restricted three-body problem

1991 ◽  
Vol 51 (4) ◽  
pp. 349-362 ◽  
Author(s):  
E. Perdios ◽  
C. G. Zagouras ◽  
O. Ragos
Keyword(s):  
Periodic Solutions ◽  
Body Problem ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

Resonant Three-Dimensional Periodic Solutions About the Triangular Equilibrium Points in the Restricted Problem

1983 ◽  
Vol 74 ◽  
pp. 235-247 ◽  
Author(s):  
C.G. Zagouras ◽  
V.V. Markellos
Keyword(s):  
Periodic Solutions ◽  
Restricted Problem ◽  
Body Problem ◽  
Equilibrium Points ◽  
Mass Parameter ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Special Values ◽  
Three Body

AbstractIn the three-dimensional restricted three-body problem, the existence of resonant periodic solutions about L4 is shown and expansions for them are constructed for special values of the mass parameter, by means of a perturbation method. These solutions form a second family of periodic orbits bifurcating from the triangular equilibrium point. This bifurcation is the evolution, as μ varies continuously, of a regular vertical bifurcation point on the corresponding family of planar periodic solutions emanating from L4.

scholarly journals Approximate Analytical Periodic Solutions to the Restricted Three-Body Problem with Perturbation, Oblateness, Radiation and Varying Mass

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 110
Author(s):  
Fabao Gao ◽  
Yongqing Wang
Keyword(s):  
Periodic Solutions ◽  
Body Problem ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
The Third ◽  
Velocity Surface ◽  
Solution Point ◽  
Zero Velocity Surface ◽  
Three Body

Against the background of a restricted three-body problem consisting of a supergiant eclipsing binary system, the two primaries are composed of a pair of bright oblate stars whose mass changes with time. The zero-velocity surface and curve of the problem are numerically studied to describe the third body’s motion area, and the corresponding five libration points are obtained. Moreover, the effect of small perturbations, Coriolis and centrifugal forces, radiative pressure, and the oblateness and mass parameters of the two primaries on the third body’s dynamic behavior is discussed through the bifurcation diagram. Furthermore, the second- and third-order approximate analytical periodic solutions around the collinear solution point L3 in two-dimensional plane and three-dimensional spaces are presented by using the Lindstedt-Poincaré perturbation method.

Stability of equilibrium points in the generalized perturbed restricted three-body problem

2010 ◽  
Vol 331 (2) ◽  
pp. 511-519 ◽  
Author(s):  
Jagadish Singh ◽  
Jessica Mrumun Begha
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Stability Of Equilibrium ◽  
Three Body
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