THE RESTRICTED THREE-BODY PROBLEM: THEORETICAL FOUNDATIONS, STABILITY ANALYSIS, AND MODERN MODELING APPROACHES
Keywords:
Artificial intelligence, celestial mechanics, Lagrange points, Lyapunov method, numerical modeling, stability analysis.Abstract
This article explores one of the fundamental problems in classical mechanics — the restricted three-body problem. The theoretical foundations of the problem, including Lagrange and Euler points, the equations of motion, and their properties, are analyzed. Furthermore, the paper presents a stability analysis using the Lyapunov method and numerical modeling techniques. Modern approaches such as artificial intelligence-based models, numerical computation algorithms, and their practical applications are also discussed. The findings highlight the significance of this complex problem in celestial mechanics, astrodynamics, and other related fields.
References
Szebehely, V. (1967). Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press.
Murray, C. D., & Dermott, S. F. (1999). Solar System Dynamics. Cambridge University Press.
Roy, A. E. (2005). Orbital Motion (4th ed.). Institute of Physics Publishing.
Alligood, K. T., Sauer, T. D., & Yorke, J. A. (1996). Chaos: An Introduction to Dynamical Systems. Springer.
Battin, R. H. (1999). An Introduction to the Mathematics and Methods of Astrodynamics. AIAA Education Series.
Hairer, E., Nørsett, S. P., & Wanner, G. (1993). Solving Ordinary Differential Equations I: Nonstiff Problems (2nd ed.). Springer.
Korshunova, N. A., & Azimov, D. M. (2014). Analytical solutions for impulsive arcs in a two-fixed-center field. Acta Astronautica, 102, 23–31. https://doi.org/10.1016/j.actaastro.2014.05.016
Ruzmatov, M. I., Azimov, D. M., & Korshunova, N. A. (2023). A new class of intermediate impulsive arcs in the restricted three-body problem. Advances in Space Research, 71(2), 456–465. https://doi.org/10.1016/j.asr.2023.01.017.
