J2 invariant relative orbits via differential correction algorithm

• 来源期刊: 力学学报(英文版)
• 年，卷（期）: 2007,（5）
• 页码范围: 585-595
• 页数: 11页
• 语种: 英文

摘要

This paper describes a practical method for finding the invariant orbits in J2 relative dynamics. Working with the Hamiltonian model of the relative motion in cludingthe 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 configurationis proposed. The influences of measure errors on the invariantorbit are also investigated by the Monte-Carlo simulation.