标题： 三维空间中二体问题的最优约化 显示英文标题

标题： The Optimal Reduction of a 2-Body Problem in R^3

摘要： 在本文中，我们描述了两个物体系统在$\mathbb{R}^3$中的最优约化，其哈密顿量在旋转和平移下保持不变。 在这样做时，我们引入了参数化和图表，有助于给出显式表达式，以便处理约化过程的几何和动力学方面。 对于这个系统，Marsden-Weinstein 约化过程的标准假设仅部分满足，而最优约化可以轻易应用，我们研究了这两种约化过程之间的比较。 我们描述了在天文学中二元系统后牛顿哈密顿系统研究中的潜在应用。 显示英文摘要

摘要： In this paper we describe optimal reduction for the system of two bodies in $\mathbb{R}^3$ whose Hamiltonian is invariant under rotations and translations. In doing this, we introduce parametrizations and charts which help giving explicit expressions in order to deal with geometric and dynamical aspects of the reduction process. For this system, the standard assumptions of the Marsden-Weinstein reduction process are only partially satisfied while optimal reduction can be readily applied, and we study a comparison between those two reduction processes. We describe potential applications to the study of Post-Newtonian Hamiltonian systems for binary systems in astronomy.