Dynamics Near the Three-Body Libration Points via Koopman Operator Theory

TL;DR

This paper applies Koopman Operator theory to analyze and compute periodic orbits near libration points in the Circular Restricted Three-Body Problem, demonstrating high-accuracy solutions for orbit analysis and station-keeping.

Contribution

It introduces the use of Koopman Operator theory for computing and analyzing periodic orbits near libration points, offering a novel analytical approach in celestial mechanics.

Findings

High-accuracy analytical solutions for Lyapunov and Halo orbits

Effective application to station-keeping strategies

Demonstrates Koopman Operator's potential in orbital dynamics

Abstract

This paper investigates the application of the Koopman Operator theory to the motion of a satellite about a libration point in the Circular Restricted Three-Body Problem. Recently, the Koopman Operator has emerged as a promising alternative to the geometric perspective for dynamical systems, where the Koopman Operator formulates the analysis and dynamical systems in terms of observables. This paper explores the use of the Koopman Operator for computing both 2D and 3D periodic orbits near libration points. Further, simulation results show that the Koopman Operator provides analytical solutions with high accuracy for both Lyapunov and Halo orbits, which are then applied to a station-keeping application.