Bifurcations of planar to three-dimensional periodic orbits in the general three-body problem

1981 ◽  
Vol 25 (1) ◽  
pp. 3-31 ◽  
Author(s):  
V. V. Markellos
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Three Dimensional ◽  
Three Body Problem ◽  
Three Body

scholarly journals Numerical Investigation for Periodic Orbits in the Hill Three-Body Problem

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 72 ◽  
Author(s):  
Vassilis S. Kalantonis
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Numerical Study ◽  
Three Dimensional ◽  
Earth Satellite ◽  
Mission Design ◽  
Special Importance ◽  
Three Body Problem ◽  
Three Body ◽  
The Hill

The current work performs a numerical study on periodic motions of the Hill three-body problem. In particular, by computing the stability of its basic planar families we determine vertical self-resonant (VSR) periodic orbits at which families of three-dimensional periodic orbits bifurcate. It is found that each VSR orbit generates two such families where the multiplicity and symmetry of their member orbits depend on certain property characteristics of the corresponding VSR orbit’s stability. We trace twenty four bifurcated families which are computed and continued up to their natural termination forming thus a manifold of three-dimensional solutions. These solutions are of special importance in the Sun-Earth-Satellite system since they may serve as reference orbits for observations or space mission design.

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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