Forced oscillations of a satellite under the influence of light pressure and gravity forces

The relative motion of a spacecraft under the influence of gravitational forces and light pressure is considered. By spacecraft we mean a celestial body capable of reflecting light from the Sun. The orbital motion of the spacecraft is considered known. The spacecraft makes plane movements in a horizontal plane relative to its center of mass. The reflecting mirror can be placed perpendicular to the orbital plane.
The main problem solved in this paper is the study of the stability of eccentric oscillations. This technology is being rolled out gradually. First, the existence of oscillations of a given type is established. To do this, the implicit function theorem is applied in a standard way. The subsequent stability analysis is based on linear theory and is reduced to the consideration of systems in variations. The paper is concluded with consideration of the nonlinear case.