Families of Periodic Solutions of the Beletskii Equation

We give a survey of achievements in the study of planar periodic oscillations and rotations of a satellite around its masscenter that moves along the elliptic orbit in the central gravitational field. These oscillations and rotations are described by the ordinary differential (Beletskii) equation of the second order with periodic coefficients and two parameters. The equation is equivalent to the periodic Hamiltonian system with one degree of freedom and has a singularity. It appeared that two-parameter families of generalized periodic solutions of the simple equation have the unexpectedly complicated structure. In particular, near the singularity of the equation these families form the very complicated structures of a new type.