Dynamics of a dumbbell satellite under the zonal harmonic effect of an oblate body

TL;DR

This paper analyzes how the zonal harmonic effect of an oblate body influences the dynamics of a dumbbell satellite, revealing periodic trajectories and reductions to classical equations under certain conditions.

Contribution

It demonstrates the impact of zonal harmonic parameters on satellite trajectories and extends classical theory by incorporating these effects using Lindstedt-Poincare's technique.

Findings

Pass trajectory of the satellite's center is periodic and differs from classical cases.

Equations of motion reduce to Beletsky's equation when zonal harmonic effect is zero.

The study applies Lindstedt-Poincare's method to prove these results.

Abstract

The aim of the present paper is to study the dynamics of a dumbbell satellite moving in a gravity field generated by an oblate body considering the effect of the zonal harmonic parameter. We prove that the pass trajectory of the mass center of the system is periodic and different from the classical one when the effect of the zonal harmonic parameter is non zero. Moreover, we complete the classical theory show- ing that the equations of motion in the satellite approximation can be reduced to Beletsky's equation when the zonal harmonic parameter is zero. The main tool for proving these results is the Lindstedt{Poincare's technique.