Non-linear Planar Oscillation of a Satellite in Elliptical orbit under the Influence of External Forces of General Nature.

The present work is devoted to the analysis of nonlinear planar oscillation of a satellite launched into an elliptical orbit under the influence of external forces of general nature such as accretion and tidal effects, etc. These forces are considered in the form of a frictional force and a periodic force. Throughout the discussion the Bogoliubov-Krylov-Mitropolsky method is used. The analysis regarding the stability of the stationary planar oscillation of a satellite near the resonance frequency shows that discontinuity occurs in the amplitude of the oscillation at a frequency of the external periodic force which is less than the frequency of the natural oscillation. This discontinuity in the amplitude of oscillation may cause noticeable change in the orbital parameters of the satellite.