### Abstract

Periodic orbits around nonequilibrium points are generated systematically by using continuous low-thrust propulsion in the restricted three-body problem, with a mass ratio varying from 0 to 1/2. A continuous constant acceleration is applied to cancel the gravitational forces of two primary bodies and the centrifugal force at a nonequilibrium point, which is changed into an artificial equilibrium point. The equations of motion are linearized to analytically generate periodic orbits with constant acceleration. Then, periodic orbits around artificial equilibrium points which exist on the line connecting two primary bodies are investigated. The frequencies of these periodic motions are expressed by a parameter that is a function of the mass ratio and the position of the orbits around artificial equilibrium points. By choosing the frequencies of motions that are small-integer resonant, we have found the existence of points at which in-plane and out-of-plane motions are synchronized.

Original language | English |
---|---|

Pages (from-to) | 1131-1139 |

Number of pages | 9 |

Journal | Journal of Guidance, Control, and Dynamics |

Volume | 29 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2006 Sep 1 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Applied Mathematics
- Electrical and Electronic Engineering

### Cite this

*Journal of Guidance, Control, and Dynamics*,

*29*(5), 1131-1139. https://doi.org/10.2514/1.19079

**Periodic orbits with low-thrust propulsion in the restricted three-body problem.** / Morimoto, Mutsuko; Yamakawa, Hiroshi; Uesugi, Kuninori.

Research output: Contribution to journal › Article

*Journal of Guidance, Control, and Dynamics*, vol. 29, no. 5, pp. 1131-1139. https://doi.org/10.2514/1.19079

}

TY - JOUR

T1 - Periodic orbits with low-thrust propulsion in the restricted three-body problem

AU - Morimoto, Mutsuko

AU - Yamakawa, Hiroshi

AU - Uesugi, Kuninori

PY - 2006/9/1

Y1 - 2006/9/1

N2 - Periodic orbits around nonequilibrium points are generated systematically by using continuous low-thrust propulsion in the restricted three-body problem, with a mass ratio varying from 0 to 1/2. A continuous constant acceleration is applied to cancel the gravitational forces of two primary bodies and the centrifugal force at a nonequilibrium point, which is changed into an artificial equilibrium point. The equations of motion are linearized to analytically generate periodic orbits with constant acceleration. Then, periodic orbits around artificial equilibrium points which exist on the line connecting two primary bodies are investigated. The frequencies of these periodic motions are expressed by a parameter that is a function of the mass ratio and the position of the orbits around artificial equilibrium points. By choosing the frequencies of motions that are small-integer resonant, we have found the existence of points at which in-plane and out-of-plane motions are synchronized.

AB - Periodic orbits around nonequilibrium points are generated systematically by using continuous low-thrust propulsion in the restricted three-body problem, with a mass ratio varying from 0 to 1/2. A continuous constant acceleration is applied to cancel the gravitational forces of two primary bodies and the centrifugal force at a nonequilibrium point, which is changed into an artificial equilibrium point. The equations of motion are linearized to analytically generate periodic orbits with constant acceleration. Then, periodic orbits around artificial equilibrium points which exist on the line connecting two primary bodies are investigated. The frequencies of these periodic motions are expressed by a parameter that is a function of the mass ratio and the position of the orbits around artificial equilibrium points. By choosing the frequencies of motions that are small-integer resonant, we have found the existence of points at which in-plane and out-of-plane motions are synchronized.

UR - http://www.scopus.com/inward/record.url?scp=33749587598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749587598&partnerID=8YFLogxK

U2 - 10.2514/1.19079

DO - 10.2514/1.19079

M3 - Article

AN - SCOPUS:33749587598

VL - 29

SP - 1131

EP - 1139

JO - Journal of Guidance, Control, and Dynamics

JF - Journal of Guidance, Control, and Dynamics

SN - 0731-5090

IS - 5

ER -