具有梯形凸壳的特殊平面五体中心构型的表征

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-03-31 DOI:10.1016/j.geomphys.2025.105494

Yangshanshan Liu , Shiqing Zhang

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引用次数: 0

摘要

我们用相互距离作为坐标来描述具有梯形凸壳的平面牛顿五体问题的一种中心构型；即，五个物体中的四个位于梯形的顶点，第五个物体位于平行边之一。我们证明了如果这个中心形存在，它是一个特定拉格朗日函数的唯一局部极小值。在数值上，我们证明了这个中心构型必须是一个等腰梯形，并且包含三个粒子的平行边比另一个短。此外，当第5质量减小到零时，主要结果仍然成立。在本文的最后，我们证明了极限情况是受限（4+1）体问题的中心构型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A characterization of a special planar 5-body central configuration with a trapezoidal convex hull

We use mutual distances as coordinates to characterize a kind of central configuration of the planar Newtonian 5-body problem with a trapezoidal convex hull; namely, four of the five bodies are located at the vertices of a trapezoid, and the fifth one is located on one of the parallel sides. We demonstrate that if this central configuration exists, it is a unique local minimum of a particular Lagrangian function. Numerically, we show that this central configuration must be an isosceles trapezoid, and the parallel side containing three particles is shorter than the other one. In addition, the main result remains true when the fifth mass decreases to zero. We show at the end of this paper that the limiting case is a central configuration of the restricted (4+1)-body problem.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity