A Systematic Study of the Stability of Symmetric Periodic Orbits in the Planar, Circular, Restricted Three-Body Problem

2002 ◽  
pp. 239-255
Author(s):  
Alessandra Celletti ◽  
Andrea Chessa ◽  
John Hadjidemetriou ◽  
Giovanni Battista Valsecchi
Keyword(s):  
Periodic Orbits ◽  
Systematic Study ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Symmetric Periodic Orbits ◽  
The Stability ◽  
Three Body

scholarly journals LOCATION AND STABILITY OF THE TRIANGULAR POINTS IN THE TRIAXIAL ELLIPTIC RESTRICTED THREE-BODY PROBLEM

2021 ◽  
Vol 57 (2) ◽  
pp. 311-319
Author(s):  
M. Radwan ◽  
Nihad S. Abd El Motelp
Keyword(s):  
Linear Stability ◽  
Periodic Orbits ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Stability Regions ◽  
Triangular Points ◽  
Problem Frame ◽  
The Stability ◽  
Three Body

The main goal of the present paper is to evaluate the perturbed locations and investigate the linear stability of the triangular points. We studied the problem in the elliptic restricted three body problem frame of work. The problem is generalized in the sense that the two primaries are considered as triaxial bodies. It was found that the locations of these points are affected by the triaxiality coefficients of the primaries and the eccentricity of orbits. Also, the stability regions depend on the involved perturbations. We also studied the periodic orbits in the vicinity of the triangular points.

scholarly journals The Omega limit set of a family of chords

2019 ◽  
pp. 1-25 ◽  
Author(s):  
Edward Belbruno ◽  
Urs Frauenfelder ◽  
Otto van Koert
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Limit Behavior ◽  
Limit Set ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Contact Type ◽  
Symmetric Periodic Orbits ◽  
Three Body ◽  
Omega Limit Set

In this paper, we study the limit behavior of a family of chords on compact energy hypersurfaces of a family of Hamiltonians. Under the assumption that the energy hypersurfaces are all of contact type, we give results on the Omega limit set of this family of chords. Roughly speaking, such a family must either end in a degeneracy, in which case it joins another family, or can be continued. This gives a Floer theoretic explanation of the behavior of certain families of symmetric periodic orbits in many well-known problems, including the restricted three-body problem.

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