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JOURNALS // Theoretical and Applied Mechanics // Archive

Theor. Appl. Mech., 2023 Volume 50, Issue 1, Pages 25–38 (Mi tam124)

The behavior of a satellite trajectory near the equilibrium points of Sun-Earth system and its control

Lina A. Shalby, Noha A. Ali

Department of Mathematics, Faculty of Women, Ain Shams University, Cairo, Egypt

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 $l_2$-method at $L_1$ as an example.

Keywords: circular restricted three body problem, Lagrange points, stability, chaos.

MSC: Primary 58F13; Secondary 70F07

Received: 16.08.2022
Accepted: 12.02.2023

Language: English

DOI: https://doi.org/10.2298/TAM220816003S



© Steklov Math. Inst. of RAS, 2024