On preservation of conditionally-periodic satellite librations in elliptic orbit with account of Solar light pressure (Q1876448)

The author considers planar librations of a satellite with its mass center moving in an elliptic orbit. Besides the gravitational force, the satellite is acted on by Solar light pressure. Rotation of a dynamically symmetrical satellite is taken as the unperturbed system. A direct application of KAM theorem is impossible because of nonanalyticity of the Hamiltonian. Using the reduction of the perturbed Hamiltonian system to a sequence of symplectic maps, and with the help of Moser's theorem on invariant curve, the existence of invariant tori and the fact that the action variables remain close to their initial values are proven. The vicinity of the limit case (the orbit eccentricity is equal to or approximately equal to 1) is also studied. In this case, the order of perturbation is supposed to be fixed. It turns out that in this case the action variables also preserve their values over asymptotically large time intervals.