论文标题
平衡点及其在平面等边限制的四体问题中的线性稳定性：审查和新结果
Equilibrium points and their linear stability in the planar equilateral restricted four-body problem: A review and new results
论文作者
论文摘要
在这项工作中，我们重新审视平面限制了四体问题，以研究三个具有不均质量的重体产生的重力下的无限质量的动力学，形成了等边三角形构型。我们统一了有关此问题平衡点的存在和线性稳定性的已知结果，该结果已作为相对平衡或平面限制$（3 + 1）$ - 身体问题的中心配置。这是朝这个方向上的第一次尝试。进行系统的数值研究以获得质量空间中的共振曲线。我们使用这些曲线来回答有关线性稳定性和不稳定性域之间现有边界的问题。讨论了稳定域内发现的稳定点总数的表征。
In this work, we revisit the planar restricted four-body problem to study the dynamics of an infinitesimal mass under the gravitational force produced by three heavy bodies with unequal masses, forming an equilateral triangle configuration. We unify known results about the existence and linear stability of equilibrium points of this problem which have been obtained earlier, either as relative equilibria or a central configuration of the planar restricted $(3 + 1)$-body problem. It is the first attempt in this direction. A systematic numerical investigation is performed to obtain the resonance curves in the mass space. We use these curves to answer the question about the existing boundary between the domains of linear stability and instability. The characterization of the total number of stable points found inside the stability domain is discussed.
