Geodesic
The behavior of a satellite trajectory near the equilibrium points of Sun-Earth system and its control
Theoretical and applied mechanics, Tome 50 (2023) no. 1

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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 $l_2$-method at $L_1$ as an example.
Keywords: circular restricted three body problem, Lagrange points, stability, chaos 
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Lina A. Shalby; Noha A. Ali. The behavior of a satellite trajectory near the equilibrium points of Sun-Earth system and its control. Theoretical and applied mechanics, Tome 50 (2023) no. 1. http://geodesic.mathdoc.fr/item/TAM_2023_50_1_a3/