三角形运动几何与三体问题研究
Kinematic geometry of triangles and the study of the three-body problem
摘要：
这本专著描述了一个黎曼几何减少方法的三体问题。基本定理在引言部分介绍，而它们的证明在后面的章节中提供，在这些章节中对特定主题进行了更详细的分析。其基本思想是将质量三角形的运动学和动力学分别约化为表示SO（3）-同余类和相似类的同余模空间和形空间，特别是导出了质量三角形运动的欧拉方程，推广了经典的刚体运动的欧拉方程。最后几章研究了在上述几何条件下的牛顿三重碰撞运动，并在特殊情况下分析了它们的形状曲线。
英文摘要：
This monograph describes a Riemannian geometric reduction approach to the three-body problem. The fundamental theorems are presented in the introductory part, whereas their proofs are provided in later chapters where specific topics are analyzed in more detail. The basic idea is to reduce the kinematic and dynamics of mass triangles to the congruence moduli space and the shape space, representing SO(3)-congruence and similarity classes respectively.In particular, the Euler equations for mass triangle motions are worked out, generalizing the classical Euler equations for rigid body motions. The last chapters are devoted to the study of Newtonian triple collision motions, in the above geometric setting, and their shape curves are analyzed in special cases.
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