论文标题
在平面三体问题中的某些共线配置上
On some collinear configurations in the planar three-body problem
论文作者
论文摘要
在本文中，我们进一步研究了平面牛顿三体问题，重点是共线构型，其中三个物体或它们的速度是对齐的。我们提供了蒙哥马利结果的独立证明，表明除了拉格朗日解决方案之外，所有负能量解决方案均对零角动量案例产生了syzygies，即位置的共线构型。作者先前探讨了有限解决方案的广义syzygies的概念，包括速度对齐。在这项研究中，我们扩大了范围，以涵盖负能量案例并提供新的界限。我们的方法基于基本的Sturm-Liouville理论和三体问题的Wintner-Conley“线性”形式，如Albouy和Chenciner的作品中所述。
In this paper, we further investigate the planar Newtonian three-body problem with a focus on collinear configurations, where either the three bodies or their velocities are aligned. We provide an independent proof of Montgomery's result, stating that apart from the Lagrange solution, all negative energy solutions to the zero angular momentum case result in syzygies, i.e., collinear configurations of positions. The concept of generalised syzygies, inclusive of velocity alignments, was previously explored by the author for bounded solutions. In this study, we broaden our scope to encompass negative energy cases and provide new bounds. Our methodology builds upon the elementary Sturm-Liouville theory and the Wintner-Conley "linear" form of the three-body problem, as previously explored in the works of Albouy and Chenciner.
