### Abstract

In the restricted three body problem, each of the Lagrange points is in equilibrium between gravitational forces of the two primary bodies and centrifugal force in the rotating frame. A non-equilibrium point, which is not at Lagrange points, can be turned into an artificial equilibrium point (AEP) by canceling any residual acceleration at the non-equilibrium points with continuous control acceleration. This study describes an investigation of periodic orbits around the AEPs in the restricted three body problem. The non-linearized equations of motion in this problem are linearized around the AEPs, and periodic orbits are generated by simple constant control acceleration in three-dimensional space.

Original language | English |
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Title of host publication | Proceedings of SICE Annual Conference 2008 - International Conference on Instrumentation, Control and Information Technology |

Pages | 2607-2611 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2008 Dec 1 |

Externally published | Yes |

Event | SICE Annual Conference 2008 - International Conference on Instrumentation, Control and Information Technology - Tokyo, Japan Duration: 2008 Aug 20 → 2008 Aug 22 |

### Publication series

Name | Proceedings of the SICE Annual Conference |
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### Other

Other | SICE Annual Conference 2008 - International Conference on Instrumentation, Control and Information Technology |
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Country | Japan |

City | Tokyo |

Period | 08/8/20 → 08/8/22 |

### Fingerprint

### Keywords

- Artificial equilibrium point
- Restricted three body problem

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Control and Systems Engineering
- Computer Science Applications

### Cite this

*Proceedings of SICE Annual Conference 2008 - International Conference on Instrumentation, Control and Information Technology*(pp. 2607-2611). [4655106] (Proceedings of the SICE Annual Conference). https://doi.org/10.1109/SICE.2008.4655106

**Periodic orbits with constant control acceleration in the restricted three body problem.** / Morimoto, Mutsuko; Yamakawa, Hiroshi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of SICE Annual Conference 2008 - International Conference on Instrumentation, Control and Information Technology.*, 4655106, Proceedings of the SICE Annual Conference, pp. 2607-2611, SICE Annual Conference 2008 - International Conference on Instrumentation, Control and Information Technology, Tokyo, Japan, 08/8/20. https://doi.org/10.1109/SICE.2008.4655106

}

TY - GEN

T1 - Periodic orbits with constant control acceleration in the restricted three body problem

AU - Morimoto, Mutsuko

AU - Yamakawa, Hiroshi

PY - 2008/12/1

Y1 - 2008/12/1

N2 - In the restricted three body problem, each of the Lagrange points is in equilibrium between gravitational forces of the two primary bodies and centrifugal force in the rotating frame. A non-equilibrium point, which is not at Lagrange points, can be turned into an artificial equilibrium point (AEP) by canceling any residual acceleration at the non-equilibrium points with continuous control acceleration. This study describes an investigation of periodic orbits around the AEPs in the restricted three body problem. The non-linearized equations of motion in this problem are linearized around the AEPs, and periodic orbits are generated by simple constant control acceleration in three-dimensional space.

AB - In the restricted three body problem, each of the Lagrange points is in equilibrium between gravitational forces of the two primary bodies and centrifugal force in the rotating frame. A non-equilibrium point, which is not at Lagrange points, can be turned into an artificial equilibrium point (AEP) by canceling any residual acceleration at the non-equilibrium points with continuous control acceleration. This study describes an investigation of periodic orbits around the AEPs in the restricted three body problem. The non-linearized equations of motion in this problem are linearized around the AEPs, and periodic orbits are generated by simple constant control acceleration in three-dimensional space.

KW - Artificial equilibrium point

KW - Restricted three body problem

UR - http://www.scopus.com/inward/record.url?scp=56749175254&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56749175254&partnerID=8YFLogxK

U2 - 10.1109/SICE.2008.4655106

DO - 10.1109/SICE.2008.4655106

M3 - Conference contribution

AN - SCOPUS:56749175254

SN - 9784907764296

T3 - Proceedings of the SICE Annual Conference

SP - 2607

EP - 2611

BT - Proceedings of SICE Annual Conference 2008 - International Conference on Instrumentation, Control and Information Technology

ER -