# Periodic and quasi-periodic orbit design based on the center manifold theory

Yuki Akiyama, Mai Bando, Shinji Hokamoto

Research output: Contribution to journalArticle

### Abstract

This paper proposes a new numerical method for finding libration point orbits in the vicinity of collinear libration points in the circular restricted three-body problem. The main advantage of this method is that it requires neither an initial guess nor complex algebraic manipulations for finding both quasi-periodic and periodic orbits. The proposed method consists of two steps: center manifold design and differential correction. The first step provides a quasi-periodic orbit parametrized by a single parameter vector. In the second step, the parameter vector in the first step is used to obtain an exact periodic orbit. This method is applied to find periodic and quasi-periodic orbits in the Sun-Earth restricted three-body problem around the L1 and L2 libration points.

Original language English 672-682 11 Acta Astronautica 160 https://doi.org/10.1016/j.actaastro.2019.02.029 Published - Jul 1 2019

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Orbits
Sun
Numerical methods
Earth (planet)

### All Science Journal Classification (ASJC) codes

• Aerospace Engineering

### Cite this

In: Acta Astronautica, Vol. 160, 01.07.2019, p. 672-682.

Research output: Contribution to journalArticle

title = "Periodic and quasi-periodic orbit design based on the center manifold theory",
abstract = "This paper proposes a new numerical method for finding libration point orbits in the vicinity of collinear libration points in the circular restricted three-body problem. The main advantage of this method is that it requires neither an initial guess nor complex algebraic manipulations for finding both quasi-periodic and periodic orbits. The proposed method consists of two steps: center manifold design and differential correction. The first step provides a quasi-periodic orbit parametrized by a single parameter vector. In the second step, the parameter vector in the first step is used to obtain an exact periodic orbit. This method is applied to find periodic and quasi-periodic orbits in the Sun-Earth restricted three-body problem around the L1 and L2 libration points.",
author = "Yuki Akiyama and Mai Bando and Shinji Hokamoto",
year = "2019",
month = "7",
day = "1",
doi = "10.1016/j.actaastro.2019.02.029",
language = "English",
volume = "160",
pages = "672--682",
journal = "Acta Astronautica",
issn = "0094-5765",
publisher = "Elsevier Limited",

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TY - JOUR

T1 - Periodic and quasi-periodic orbit design based on the center manifold theory

AU - Akiyama, Yuki

AU - Bando, Mai

AU - Hokamoto, Shinji

PY - 2019/7/1

Y1 - 2019/7/1

N2 - This paper proposes a new numerical method for finding libration point orbits in the vicinity of collinear libration points in the circular restricted three-body problem. The main advantage of this method is that it requires neither an initial guess nor complex algebraic manipulations for finding both quasi-periodic and periodic orbits. The proposed method consists of two steps: center manifold design and differential correction. The first step provides a quasi-periodic orbit parametrized by a single parameter vector. In the second step, the parameter vector in the first step is used to obtain an exact periodic orbit. This method is applied to find periodic and quasi-periodic orbits in the Sun-Earth restricted three-body problem around the L1 and L2 libration points.

AB - This paper proposes a new numerical method for finding libration point orbits in the vicinity of collinear libration points in the circular restricted three-body problem. The main advantage of this method is that it requires neither an initial guess nor complex algebraic manipulations for finding both quasi-periodic and periodic orbits. The proposed method consists of two steps: center manifold design and differential correction. The first step provides a quasi-periodic orbit parametrized by a single parameter vector. In the second step, the parameter vector in the first step is used to obtain an exact periodic orbit. This method is applied to find periodic and quasi-periodic orbits in the Sun-Earth restricted three-body problem around the L1 and L2 libration points.

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U2 - 10.1016/j.actaastro.2019.02.029

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EP - 682

JO - Acta Astronautica

JF - Acta Astronautica

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