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

Yuki Akiyama, Mai Bando, Shinji Hokamoto

Research output: Contribution to journalConference article

Abstract

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 L 1 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
Volume2018-October
Publication statusPublished - Jan 1 2018
Event69th International Astronautical Congress: #InvolvingEveryone, IAC 2018 - Bremen, Germany
Duration: Oct 1 2018Oct 5 2018

Fingerprint

three body problem
design method
libration
Orbits
trajectory
Trajectories
trajectories
orbits
Moon
matrix
periodic functions
moon
Earth (planet)

All Science Journal Classification (ASJC) codes

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

Cite this

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title = "Extended state space approach for trajectory design in elliptic restricted three-body problem",
abstract = "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 L 1 ERTBP. We show various LPOs in the ERTBP by changing design parameters, and IMs associated with a libration point and an LPO.",
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T1 - Extended state space approach for trajectory design in elliptic restricted three-body problem

AU - Akiyama, Yuki

AU - Bando, Mai

AU - Hokamoto, Shinji

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N2 - 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 L 1 ERTBP. We show various LPOs in the ERTBP by changing design parameters, and IMs associated with a libration point and an LPO.

AB - 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 L 1 ERTBP. We show various LPOs in the ERTBP by changing design parameters, and IMs associated with a libration point and an LPO.

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