Nonlinear stability of the triangular libration points for the photo gravitational elliptic restricted problem of three bodies

1990 ◽  
Vol 48 (4) ◽  
pp. 299-317 ◽  
Author(s):  
Vijay Kumar ◽  
R. K. Choudhry
Keyword(s):  
Nonlinear Stability ◽  
Restricted Problem ◽  
Libration Points ◽  
Triangular Libration Points ◽  
Elliptic Restricted Problem

scholarly journals Nonlinear Stability of the Triangular Libration Points for Radiating and Oblate Primaries in CR3BP in Nonresonance Condition

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Nutan Singh ◽  
A. Narayan
Keyword(s):  
Resonance Frequency ◽  
Radiation Pressure ◽  
Nonlinear Stability ◽  
Equilibrium Points ◽  
Kam Theory ◽  
Boundary Region ◽  
Libration Points ◽  
Triangular Libration Points ◽  
Nonresonance Condition ◽  
The Stability

This paper investigates the existence of resonance and nonlinear stability of the triangular equilibrium points when both oblate primaries are luminous. The study is carried out near the resonance frequency, satisfying the conditionsω1=ω2,  ω1=2ω2, andω1=3ω2in circular cases by the application of Kolmogorov-Arnold-Moser (KAM) theory. The study is carried out for the various values of radiation pressure and oblateness parameters in general. It is noticed that the system experiences resonance atω1=2ω2,  ω1=3ω2for different values of radiation pressures and oblateness parameter. The caseω1=ω2corresponds to the boundary region of the stability for the system. It is found that, except for some values of the radiation pressure, and oblateness parameters and forμ≤μc=0.0385209, the triangular equilibrium points are stable.

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