On the dynamics of planar oscillations for a dumbbell satellite in $$\varvec{J_{2}}$$ J 2 problem

Abstract

In the present paper, we study regular and chaotic dynamics from planar oscillations of a dumbbell satellite under the influence of the gravity field generated by an oblate body, considering the effect of the zonal harmonic parameter \(J_{2}\). We theoretically show the existence of chaotic oscillations provided that the eccentricity becomes arbitrarily small, and the parameter \(J_{2}\) is of the same order of magnitude as the eccentricity. This is carried out by applying the so-called Melnikov method. Finally, for arbitrarily chosen values for the parameters involved in such a problem, we study the transition from regular to chaotic oscillations for a dumbbell satellite via the analysis of chaotic maps and Poincare surfaces of section, respectively.