Generalized Periodic Solutions to the Equation of Oscillations of a Satellite

We consider the generalized (rotational and oscillatory) odd 2$\pi$-periodic solutions to the equation of oscillations of a satellite in a plane of its elliptic orbit. We introduce a classification of the families of such solutions. The complete qualitative description of the set of generalized 2$\pi$-periodic solutions is given with all values of eccentricity e and inertial parameter $\mu$ including the limit values |e|=1 and |$\mu$|=\infty . The results are represented as graphs of the characteristics of the families in a new global coordinate system.