The research of the coupled orbital-attitude controlled motion of celestial body in the neighborhood of the collinear libration point L 1

Research output

2 Citations (Scopus)

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 L1 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 L1. 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 L1 is carried out. The numerical characteristics of the control parameters and rotational motion are given.

Original languageEnglish
Title of host publicationApplication of Mathematics in Technical and Natural Sciences
Subtitle of host publication9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017
EditorsMD Todorov
PublisherAmerican Institute of Physics
Number of pages8
Volume1895
ISBN (Electronic)9780735415799
DOIs
Publication statusPublished - 12 Oct 2017
Event9th International Conference on Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS) - Albena
Duration: 21 Jun 201726 Jun 2017

Publication series

NameAIP Conference Proceedings
PublisherAMER INST PHYSICS
Volume1895
ISSN (Print)0094-243X

Conference

Conference9th International Conference on Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS)
CountryBulgaria
CityAlbena
Period21/06/1726/06/17

Scopus subject areas

  • Physics and Astronomy(all)

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  • Cite this

    Shmyrov, A., Shmyrov, V., & Shymanchuk, D. (2017). The research of the coupled orbital-attitude controlled motion of celestial body in the neighborhood of the collinear libration point L 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