### Abstract

This article considers the motion of a celestial body within the restricted three-body problem of the Sun-Earth system. The equations of controlled coupled attitude-orbit motion in the neighborhood of collinear libration point L_{1} are investigated. The translational orbital motion of a celestial body is described using Hill's equations of circular restricted three-body problem of the Sun-Earth system. Rotational orbital motion is described using Euler's dynamic equations and quaternion kinematic equation. We investigate the problem of stability of celestial body rotational orbital motion in relative equilibrium positions and stabilization of celestial body rotational orbital motion with proposed control laws in the neighborhood of collinear libration point L_{1}. To study stabilization problem, Lyapunov function is constructed in the form of the sum of the kinetic energy and special "kinematic function" of the Rodriguez-Hamiltonian parameters. Numerical modeling of the controlled rotational motion of a celestial body at libration point L_{1} is carried out. The numerical characteristics of the control parameters and rotational motion are given.

Original language | English |
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Title of host publication | Application of Mathematics in Technical and Natural Sciences |

Subtitle of host publication | 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017 |

Editors | MD Todorov |

Publisher | American Institute of Physics |

Number of pages | 8 |

Volume | 1895 |

ISBN (Electronic) | 9780735415799 |

DOIs | |

Publication status | Published - 12 Oct 2017 |

Event | 9th International Conference on Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS) - Albena Duration: 21 Jun 2017 → 26 Jun 2017 |

### Publication series

Name | AIP Conference Proceedings |
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Publisher | AMER INST PHYSICS |

Volume | 1895 |

ISSN (Print) | 0094-243X |

### Conference

Conference | 9th International Conference on Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS) |
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Country | Bulgaria |

City | Albena |

Period | 21/06/17 → 26/06/17 |

### Scopus subject areas

- Physics and Astronomy(all)

## Fingerprint Dive into the research topics of 'The research of the coupled orbital-attitude controlled motion of celestial body in the neighborhood of the collinear libration point L <sub>1</sub>'. Together they form a unique fingerprint.

## Cite this

_{1}. In MD. Todorov (Ed.),

*Application of Mathematics in Technical and Natural Sciences: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017*(Vol. 1895). [110007] (AIP Conference Proceedings; Vol. 1895). American Institute of Physics. https://doi.org/10.1063/1.5007413