Averaging of the equation of motion of a satellite with respect to its center of mass in degenerate cases: 1. Oscillations in the absolute frame of reference

The problem of attitude oscillations of a satellite with a small dynamic asymmetry in the plane of the orbit leads to a system degenerate to the fifth order from the point of view of the method of averaging. An explicit expression for the dominant term is obtained by integration in the complex plane. The recurrence procedure of calculating the higher approximations of the method of averaging is considered, as well as an approach to the analysis of the structure of derived expressions.