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.

本文研究了 Koopman 算子理论在圆受限三体问题中卫星绕平动点运动的应用。最近，Koopman 算子已成为动态系统几何透视的一种有前途的替代方案，其中 Koopman 算子根据可观察量来制定分析和动态系统。本文应用Koopman算子计算平动点附近的二维和三维周期轨道，得到正交多项式动力学的完整谱分析。此外，仿真结果表明，Koopman 算子为李雅普诺夫和晕轨道提供了高精度的解析解。然后将 Koopman 解决方案应用于站点保持应用程序，