three body problem, Lagrangian equilibrium point, libration, degree of freedom, equation of motion, stability, mathematical analysis, dumbbell-shaped body, restricted three body problem, RTBP, rod-connected restricted three body problem, RCRTBP
University of Tokyo Graduate School
Japan Aerospace Exploration Agency Institute of Space and Astronautical Science
Japan Aerospace Exploration Agency JAXA Space Exploration Center
Japan Aerospace Exploration Agency Institute of Space and Astronautical Science
出版者
宇宙航空研究開発機構宇宙科学研究本部
出版者（英）
Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency (JAXA/ISAS)
雑誌名
第17回アストロダイナミクスシンポジウム講演後刷り集 2007
雑誌名(英)
Proceedings of 17th Workshop on JAXA Astrodynamics and Flight Mechanics
This paper describes the stability of the Rotational Dumbbell shaped body. This problem, defined as the Rod-Connected Restricted Three Body Problem, is the special case of the Restricted Three-Body Problem, characterized by three bodies: two primary bodies connected each other by a rigid stick; and a mass-free body. While the Restricted Three-Body problem has only one degree of freedom, there are two degrees of freedom in this problem. By setting properly two parameters, described as the non-dimensional angular velocity and the mass ratio, both positions of equilibriums and stable regions are determined. In this paper, the stability in any type of those non-dimensional values is analyzed. There are five equilibriums and three stable points. Of these equilibriums, three points are along the line passing through two primary bodies, and the other two points are along the perpendicular bisector between two primary bodies. In addition, those stable points are comprised of two points which are along the perpendicular bisector between two primary bodies and a point which is along the line segment between two primary bodies.
Analysis of equilibrium points of the three body problem for the formation of rotational of dumbbell-shaped body
