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

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 dynamic systems, where the Koopman operator formulates the analysis and dynamic systems in terms of observables. This paper applies the Koopman operator for computing both two-dimensional and three-dimensional periodic orbits near libration points, obtaining the complete spectral analysis of the dynamics with orthogonal polynomials. Further, simulation results show that the Koopman operator provides analytical solutions with high accuracy for both Lyapunov and halo orbits. The Koopman solution is then applied to a station-keeping application, where a new particle filter and a nonlinear model predictive controller are developed.