The topology of the regularized integral surfaces of the 3-body problem
The topology of the regularized integral surfaces of the 3-body problem
复制标题
三体问题正则化积分曲面的拓扑
DOI：
10.1016/0022-0396(72)90038-1
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发表时间：
1972
期刊：
影响因子：
--
通讯作者：
R. Easton
中科院分区：
文献类型：
--
作者：
R. Easton
动量，角动量和能量的积分表面的平面三体问题被认为是。确定了穿过隔离块的轨道的端点。它示出，这种识别具有独特的扩展到一个识别，它对进入块的轨道的端点，并结束在一个二进制碰撞与离开块的轨道的端点，并来自一个二进制碰撞。正则化的问题是表明交叉轨道的端点的识别具有连续的、唯一的扩展。得到了三体问题的正则化相空间，以及由三体运动方程诱导流动的问题的正则化积分曲面。最后描述了这些曲面的拓扑结构。
Momentum, angular momentum, and energy of integral surfaces in the planar three-body problem are considered. The end points of orbits which cross an isolating block are identified. It is shown that this identification has a unique extension to an identification which pairs the end points of orbits entering the block and which end in a binary collision with the end points of orbits leaving the block and which come from a binary collision. The problem of regularization is that of showing that the identification of the end points of crossing orbits has a continuous, unique extension. The regularized phase space for the three-body problem was obtained, as were regularized integral surfaces for the problem on which the three-body equations of motion induce flows. Finally the topology of these surfaces is described.