Analysis of Equilibrium Points of the Three Body
Problem for the Formation of Rotational of
Dumbbell-shaped Body
Masatoshi. Hirabayashi1，Osamu. Mori2,3
Mutsuko. Y. Morimoto3，and Jun’ichiro. Kawaguchi2,3
1 The University of Tokyo,
2 Institute of Space and Astronautics Science (ISAS) / JAXA
3 JAXA Space Exploration Center (JSPEC)/JAXA
E-mail: m?hirabayashi@isas.jaxa.jp
Abstract
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.
Keyword: Itokawa, rubble-pile, and three-body problem
制限三体問題を用いた回転するダンベル形状天体の安定性に関する解析
平林　正稔1，森　治2,3
森本　睦子3，川口　淳一郎2,3
1 東京大学　大学院,
2 宇宙科学研究本部(ISAS) / 宇宙航空研究開発機構(JAXA),
3 月惑星探査センター(JSPEC) / JAXA
概要
本稿では，ダンベル形状の物体まわりの，質量の無視できる質点（以降，第三質点と呼ぶ）の運動の
安定性について考察する．ダンベル形状物体は，二つの有限質量質点が剛棒で接合されている物体
（以降，二質点と呼ぶ）であると模擬できる．この問題は，制限三体問題の特別な問題であると考え
ることができる．二つの自由度が存在するため，本稿では，この二つの自由度を無次元角速度，無次
元質量で表現した．これによれば，二質点を通る直線上に3 つ，またこの二質点の垂直二等分線上に
2 つで，計5 つの平衡点が存在する．また，これらの平衡点のうち，垂直二等分線上の二質点にはさ
まれた点において安定な領域があることが示される．