scholarly journals New Periodic Orbits for the n-Body Problem

2006 ◽  
Vol 1 (4) ◽  
pp. 307-311 ◽  
Author(s):  
Cristopher Moore ◽  
Michael Nauenberg
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Fourier Coefficients ◽  
Three Dimensional ◽  
Inertia Tensor ◽  
Three Body Problem ◽  
Cubic Symmetry ◽  
Numerical Evidence ◽  
N Body Problem ◽  
Three Body

Since the discovery of the figure-eight orbit for the three-body problem [Moore, C., 1993, Phys. Rev. Lett., 70, pp. 3675–3679] a large number of periodic orbits of the n-body problem with equal masses and beautiful symmetries have been discovered. However, most of those that have appeared in the literature are either planar or are obtained from perturbations of planar orbits. Here we exhibit a number of new three-dimensional periodic n-body orbits with equal masses and cubic symmetry, including some whose moment of inertia tensor is a scalar. We found these orbits numerically, by minimizing the action as a function of the trajectories’ Fourier coefficients. We also give numerical evidence that a planar three-body orbit first found in [Hénon, M., 1976, Celest. Mech., 13, pp. 267–285], rediscovered by [Moore, 1993], and found to exist for different masses by [Nauenberg, M., 2001, Phys. Lett., 292, pp. 93–99], is dynamically stable.

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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