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

Received 22 October 2022; accepted 02 December 2022; published 14 December 2022

2022, Vol. 18, no. 4, pp.  543-562

Author(s): Bardin B. S., Avdyushkin A. N.

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
Citation: Bardin B. S., Avdyushkin A. N., On Stability of the Collinear Libration Point $L_1^{}$ in the Planar Restricted Circular Photogravitational Three-Body Problem, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 4, pp.  543-562
DOI:10.20537/nd221202