The Critical Families of Periodic Solutions to the Equation of Oscillations of a Satellite

We consider the ordinary differential equation of the second order describing oscillations of a satellite in a plane of its elliptical orbit. There exists an infinite number of two-parameter families of odd 2$\pi$-periodic solutions to the equation. We have determined the domains of stability for four such families: K₁ - K₄. For this purpose we computed all one-parameter critical families of periodic solutions, which have the trace Tr = ±2. We have discovered the qualitative regularity in the structure of domains of stability of these families.