Open AccessOn stability of a collinear libration point in the planar circular restricted photogravitational three-body problem in the cases of first and second order resonances
Author(s) -
B. S. Bardin,
Andrey N. Avdyushkin
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1959/1/012004
Subject(s) - planar , lagrangian point , libration (molecule) , instability , three body problem , stability (learning theory) , physics , point (geometry) , classical mechanics , circular orbit , equilibrium point , point particle , nonlinear system , order (exchange) , mathematics , mathematical analysis , geometry , mechanics , computer science , quantum mechanics , computer graphics (images) , finance , machine learning , economics
We deal with the planar circular photogravitational three-body problem. That is, we consider the motion of a particle under influence of gravitational and radiation forces acting from two bodies, which move in circular orbits. The stability of collinear point L 1 , which located on the line between the bodies, is investigated. By using the method of normal forms and applying theorems of KAM theory we perform a nonlinear stability study for parameter values corresponding to the cases of first and second order resonances. Rigorous conclusions on instability and stability in the sense of Lyapunov have been obtained.