Space Tether Dynamics and Stability of Equilibrium Positions under Different Perturbative Forces of General Nature in the Central Gravitational Field of Earth

Abstract

This paper presents an analysis of the stability of equilibrium positions of two artificial satellites system connected by light, flexible and elastic long tether under the combined effect of several classical perturbative forces in elliptical orbit. The tether may be either conducting or non-conducting. In this study, it is assumed to be non-conducting in nature. We have treated the problem with taking five perturbative forces acting simultaneously on the system. Among these perturbations, three perturbations exist due to the Earth’s influences: the geomagnetic field, shadows and oblateness. The other two perturbations are due to the elasticity of the cable and solar light pressure. The effect of air resistance is neglected considering the satellites as high-altitude satellites. To determine the stability of the satellites, the Lyapunov method has been used. The dynamical behaviours of the satellites are represented by differential equations. As anticipated, the Lyapunov method indicates that the equilibrium position is unstable. At last we have neglected the perturbative forces and treated the problem only under the effect of central gravitational field. The stability analysis is then carried graphically, and final conclusions are drawn.