论文标题
$ \ mathbb {s}^2 $ i的三体相对平衡：欧拉配置
Three-body relative equilibria on $\mathbb{S}^2$ I: Euler configurations
论文作者
论文摘要
使用角动量的特性，我们开发了一种新的几何技术来研究一个$ 3 $的系统 - 具有正质量的身体的相对平衡，在两个球体的影响下，仅取决于身体之间的相互距离，在两个球体上移动。使用上述技术，我们对三个物体的相对平衡进行分析，当时它们在相同的大地测量（Euler构型）上移动时。
Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential depending only on the mutual distances among the bodies. With the above techniques we do an analysis of the relative equilibria for the case of three bodies when they are moving on the same geodesic (Euler configurations).
