›› 2013, Vol. 33 ›› Issue (1): 30-36.doi: 10.3780/j.issn.1000-758X.2013.01.005

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Kinetic Characteristics and Continuation Algorithm of Periodic Families

LIU Lei1,2,LIU Yong1,2,CAO Jianfeng1,2,TANG Geshi1,2,HU Songjie1,2   

  1. (1 Science and Technology on Aerospace Flight Dynamics Laboratory, Beijing 100094) (2  Beijing Aerospace Control Center, Beijing 100094)
  • Received:2012-06-12 Revised:2012-10-23 Online:2013-02-25 Published:2013-02-25

Abstract: Study on halo orbit period and scope of kinetic characteristics is the premise of halo orbit applications. For the applications and some numerical issues on a big halo orbit and a whole halo family, considering the wide applications of the libration points in the Sun-Earth/Moon and Earth-Moon system, the kinetic characteristics and the continuation algorithm of periodic families were studied under the circular restricted three-body problem. The method of numerical halo family determination by the continuation algorithm was presented.  Influences of family parameter selection on family determination were analyzed. Finally, the halo families with a large scope were given in the Sun-Earth/Moon and Earth-Moon system, together with their kinetic characteristics of orbit periods and locations. The results show that the family parameter of x is preferable for an L1 halo family and the y velocity or T is preferable for L2. The method is fit for the numerical halo family determination in any three-body system, especially for those under perturbations by a simple modification of state transition matrix.

Key words: Three-body problem, Libration point, Halo orbit, Continuation algorithm, Orbit design, Deep space exploration