The First Limit Problem for 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. The equation has two parameters: e and μ. It is regular for 0 ≤ e < 1 and singular when e=1. For e→\infty we obtain three limit problems. Theirs bounded solutions were studied analytically and numerically. It was shown that for each fixed value of μ the solutions of the first limit problem from the one-parameter family with a periodic structure. The μ-depending families of odd bounded solutions were singled out. One of the families is twisted into the fractal spiral.