The behavior of a satellite trajectory near the equilibrium points of sun-earth system and its control

Abstract

In this paper, the behavior of a satellite trajectory near the equilibrium points of the Sun-Earth system is studied. The equations describing the motion of the satellite in the circular restricted three body problem for the Sun-Earth system, are discussed for their ordinary differential equations form, and Lagrange points are determined. Then, the stability is studied at each Lagrange point. The trajectories of a satellite starting its motion near Lagrange points are illustrated, showing the stability and instability behavior. Finally, the unstable trajectory is controlled by using ??2-method at ??1 as an example.