The Limit Problems for the Equation of Oscillations of a Satellite

We consider the ordinary differential equation of the second order, which describes oscillations of a satellite with respect to its mass center moving along an elliptic orbit with eccentricity e. The equation has two parameters: e and µ. It is regular for 0 ≤ e < 1 and singular when e = 1. For $e \to $ 1 we obtain three limit problems. Their bounded solution to the first limit problem form a two-dimensional (2D) continuous invariant set with a periodic structure. Solutions to the second limit problem form 2D and 3D manifolds. The µ-depending families of odd bounded solutions are singled out. One of the families is twisted into a self-similar spiral. To obtain the limit families of the periodic solutions to the original problem match together the odd bounded solutions to the first and the second limit problem. The point of conjunction is described by the third (the basic) limit problem. The limit families are very close to prelimit ones computed in earlier studies.