Extended state space approach for trajectory design in elliptic restricted three-body problem

Yuki Akiyama, Mai Bando, Shinji Hokamoto

Research output: Contribution to journalConference articlepeer-review


This paper presents novel methods to provide libration point orbits (LPOs) and invariant manifolds (IMs) associated with libration point orbits in the elliptic restricted three-body problem (ERTBP). First, we introduce an extended autonomous system to describe the ERTBP. By introducing an autonomous system which generates a periodic function and integrating it with the ERTBP which is non-autonomous, we can obtain the extended autonomous system. Then, the center manifold design method which can uniquely provide an LPO in the circular restricted three-body problem is applied to the ERTBP. Next, we present a design method for IMs in the ERTBP by using the local stability characteristics obtained by the state transition matrix along LPOs of the extended system. The proposed design methods are applied and verified for the Earth-Moon L1 ERTBP. We show various LPOs in the ERTBP by changing design parameters, and IMs associated with a libration point and an LPO.

Original languageEnglish
JournalProceedings of the International Astronautical Congress, IAC
Publication statusPublished - 2018
Event69th International Astronautical Congress: #InvolvingEveryone, IAC 2018 - Bremen, Germany
Duration: Oct 1 2018Oct 5 2018

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Astronomy and Astrophysics
  • Space and Planetary Science


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