J_2 invariant relative orbits via differential correction algorithm

作     者：Ming Xu Shijie Xu 

作者机构：School of Astronautics Beihang University Beijing 100083 China 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2007年第23卷第5期

页      面：585-595页

核心收录：

学科分类：08[工学] 0825[工学-航空宇航科学与技术] 

基　　金：The project supported by the Innovation Foundation of Beihang University for Ph.D.Graduates the National Natural Science Foundation of China(60535010) 

主　　题：Formation flying J2 invariant orbit Differential correction Formation configuration 

摘      要：This paper describes a practical method for finding the invariant orbits in Ja relative dynamics. Working with the Hamiltonian model of the relative motion including the J2 perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth＇s orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between J2 invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte-Carlo simulation.