论文标题
$ s^2 $ ii上的三体相对平衡：扩展拉格朗日配置
Three-body relative equilibria on $S^2$ II: Extended Lagrangian configurations
论文作者
论文摘要
这是我们第一篇论文\ cite {pre}的自然延续，在该论文中，我们开发了一种新的几何技术，使我们能够研究两个球体上的相对平衡。我们考虑在$ \ mathbb {s}^2 $上的三个正质量的系统，这是在通用有吸引力的潜力的影响下移动的，这仅取决于群众之间的相互距离。我们将发现扩展的拉格朗日相对平衡的问题减少了对惯性张量的分析的问题，然后我们获得了更易于管理的等效惯性张量，使我们能够找到新的拉格朗日配置家族。
This is a natural continuation of our first paper \cite{pre}, where we develop a new geometrical technique which allow us to study relative equilibria on the two sphere. We consider a system of three positive masses on $\mathbb{S}^2$ moving under the influence of an generic attractive potential which only depends on the mutual distances among the masses. We reduce the problem of finding extended Lagrangian relative equilibria to the analysis of the inertia tensor, then we obtain a more manageable equivalent inertia tensor which allow us to find new families of Lagrangian configurations.
