The Second Limit Problem for the Equation of Oscillations of a Satellite.
Abstract:
This preprint is an immediate continuation of the preprint №124, 1995.
We consider the ordinary differential equation of the second order describing oscillations of a satellite in a plane of its elliptical orbit. The equation has two parameters: e and μ. It is regular for 0 ≤ e < 1 and singular when e=1. For e→1 we obtain three limit problems. It was shown that for each fixed value of μ the solutions of the second limit problem form the one- and two-parameter families. The μ-depending families of odd bounded solutions were singled out. Gluing together the odd bounded solutions of the first and the second limit problem we obtain the limit families of periodic solutions of the original problem.
