Journal of Astronautics ›› 2020, Vol. 41 ›› Issue (2): 154-165.doi: 10.3873/j.issn.1000-1328.2020.02.004

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Analytical Solutions for Relative Motion in the Circular Restricted Three Body Problem

ZHOU Jing, HU Jun, ZHANG Bin   

  1. 1.Beijing Institute of Control Engineering, Beijing 100190, China; 2.National Laboratory of Space Intelligent Control, Beijing 100190, China
  • Received:2019-05-20 Revised:2019-06-25 Online:2020-02-15 Published:2020-02-25

Abstract: Aiming at the problem of relative motion near the collinear libration points in the circular restricted three-body problem of the Earth-Moon system, which is of great value both in theory and applications, a general method is proposed for the relative motion near the periodic/quasi-periodic orbits in the vicinity of the collinear libration points. Based on the first-order analytical solutions, the precise orbits are obtained through differential correction approach. The monodromy matrix is analyzed and then six modes of relative motion are extracted by referencing the Floquet theory. The relative motion can be described as a linear combination of these modes and then the approximate analytical solutions are obtained. The simulations of these modes and relative motion with Halo orbits, Lissajous orbits and Lyapunov orbits as the reference orbits respectively in the vicinity of Earth-Moon L1 points are made and the validity of the six modes and the analytical solutions for relative motion is proved.

Key words: Circular restricted three-body problem, Collinear libration points, Periodic/quasi-periodic orbits, Monodromy matrix, Modes analysis, Relative motion

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