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Russian Journal of Nonlinear Dynamics, 2022, Volume 18, Number 4, Pages 543–562
DOI: https://doi.org/10.20537/nd221202
(Mi nd810)
 

Nonlinear physics and mechanics

On Stability of the Collinear Libration Point $L_1$ in the Planar Restricted Circular Photogravitational Three-Body Problem

B. S. Bardin, A. N. Avdyushkin

Moscow Aviation Institute, Volokolamskoye sh. 4, Moscow, 125080 Russia
References:
Abstract: The stability of the collinear libration point $L_1$ in the photogravitational three-body problem is investigated. This problem is concerned with the motion of a body of infinitely small mass which experiences gravitational forces and repulsive forces of radiation pressure coming from two massive bodies. It is assumed that the massive bodies move in circular orbits and that the body of small mass is located in the plane of their motion. Using methods of normal forms and KAM theory, a rigorous analysis of the Lyapunov stability of the collinear libration point lying on the segment connecting the massive bodies is performed. Conclusions on the stability are drawn both for the nonresonant case and for the case of resonances through order four.
Keywords: collinear libration point, photogravitational three-body problem, normal forms, KAM theory, Lyapunov stability, resonances.
Funding agency Grant number
Russian Foundation for Basic Research 20-31-90064
20-01-00637
This research was supported by the Russian Foundation for Basic Research under the scientific projects No. 20-31-90064 and 20-01-00637.
Received: 22.10.2022
Accepted: 02.12.2022
Bibliographic databases:
Document Type: Article
Language: english
Citation: B. S. Bardin, A. N. Avdyushkin, “On Stability of the Collinear Libration Point $L_1$ in the Planar Restricted Circular Photogravitational Three-Body Problem”, Rus. J. Nonlin. Dyn., 18:4 (2022), 543–562
Citation in format AMSBIB
\Bibitem{BarAvd22}
\by B. S. Bardin, A. N. Avdyushkin
\paper On Stability of the Collinear Libration Point $L_1$
in the Planar Restricted Circular Photogravitational
Three-Body Problem
\jour Rus. J. Nonlin. Dyn.
\yr 2022
\vol 18
\issue 4
\pages 543--562
\mathnet{http://mi.mathnet.ru/nd810}
\crossref{https://doi.org/10.20537/nd221202}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4527637}
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