论文标题
使用Koopman操作员理论，近似分析解决方案
Approximate Analytical Solution to the Zonal Harmonics Problem Using Koopman Operator Theory
论文作者
论文摘要
这项工作介绍了库普曼操作者理论的使用来为围绕非球体天体绕的卫星的区域谐波问题生成近似的分析解决方案。特别是，提出的解决方案直接提供了系统在纬向谐波的任何效果下的示意性演变，并且可以自动化以在近似溶液中获得任何准确性。此外，本文定义了一组修改的轨道元素，这些元素可应用于任何类型的轨道，并允许Koopman操作员具有快速的收敛性。在这方面，包括几个施用示例，表明所提出的方法可以在任何类型的轨道上使用，包括圆形，椭圆，抛物线和双曲线轨道。
This work introduces the use of the Koopman operator theory to generate approximate analytical solutions for the zonal harmonics problem of a satellite orbiting a non-spherical celestial body. Particularly, the solution proposed directly provides the osculating evolution of the system under the effects of any order of the zonal harmonics, and can be automated to obtain any level of accuracy in the approximated solution. Moreover, this paper defines a modified set of orbital elements that can be applied to any kind of orbit and that allows the Koopman operator to have a fast convergence. In that regard, several examples of application are included, showing that the proposed methodology can be used in any kind of orbit, including circular, elliptic, parabolic and hyperbolic orbits.
