上海交通大学廖世俊团队近日研究了通用平面三体问题的周期轨道评述。相关论文于2025年6月23日发表在《中国科学：物理学 力学 天文学》杂志上。

三体问题仍然是科学界尚未解决的挑战。它是探索非线性动力学、天体物理学和轨道力学的基础模型。由于三体问题固有的混沌性质，周期轨道被视为构成系统支柱的主要框架，这为其动力学特性提供了至关重要的见解。在这篇综述中，研究组考察了平面三体问题周期轨道研究的历史和最新进展。 

他们概述了一般三体问题、数值周期轨道的定义和识别，以及用于对这些解进行分类的拓扑分类方法。此外，还描述了用于获得精确轨迹的干净数值模拟（CNS），以及具有不同初始配置、质量相等或不等、有或没有角动量的系统中周期轨道的分析和数值结果。该综述还涵盖了线性稳定性分析和开普勒第三定律扩展到通用三体问题等关键主题。最后，他们强调了几个悬而未决的问题和该领域未来研究的有前景的方向。

附：英文原文

Title: A review on periodic orbits of the general planar three-body problem

Author: Li, Xiaoming, Liao, Shijun

Issue&Volume: 2025-06-23

Abstract: The three-body problem continues to be an unsolved challenge in the scientific community. It serves as a foundational model for exploring nonlinear dynamics, astrophysics, and orbital mechanics. Due to the inherently chaotic nature of the three-body problem, periodic orbits are regarded as the primary framework that forms the backbone of the system, which provides crucial insights into its dynamical properties. In this review, we examine both historical and recent advances in the study of periodic orbits for the planar three-body problem. We provide an overview of the general three-body problem, the definition and identification of numerical periodic orbits, and the topological classification methods used to categorize these solutions. Additionally, we describe the clean numerical simulation (CNS) employed to obtain accurate trajectories, as well as both analytical and numerical results for periodic orbits in systems with different initial configurations, with equal or unequal masses, with or without angular momentum. The review also covers key topics such as linear stability analysis and the extension of Kepler’s third law to general three-body problems. Finally, we highlight several open questions and promising directions for future research in this field.

DOI: 10.1007/s11433-024-2686-6

Source: https://link.springer.com/article/10.1007/s11433-024-2686-6