Within the phase space of the planar circular restricted three-body problem, stable and unstable manifolds of periodic orbits with a S x R (cylindrical) geometry are shown to exist. The periodic orbits considered reside in bottleneck regions of the energy manifold, separating large zones associated with motion about one mass, the other mass, or both masses.The cylinders have the physical property that all motion through the bottleneck in which the periodic orbit resides must occur through the interior of these surfaces. The cylinders thus mediate the global transport of test particles between large zones of the energy surface which are separated by the bottlenecks.By elucidating the structuring role of the cylinders, we provide a new language for discussing some important problems in celestial mechanics. Furthermore, we propose that these cylindrical structures are the natural objects of study for the design of space mission trajectories which take advantage of three-body effects.
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机译：在平面圆形受限三体问题的相空间内，显示出具有S x R（圆柱）几何形状的周期轨道的稳定和不稳定流形。所考虑的周期性轨道位于能量流形的瓶颈区域中，它们将与围绕一个质量，另一质量或这两个质量的运动相关的大区域分隔开。圆柱体的物理特性是，所有通过周期性轨道所在的瓶颈的运动都必须发生在这些表面的内部。因此，圆柱体在能量表面的大区域之间（通过瓶颈隔开）介导了测试粒子的整体传输。通过阐明圆柱体的结构作用，我们提供了一种新的语言来讨论天体力学中的一些重要问题。此外，我们认为这些圆柱结构是利用三体效应设计空间任务轨迹的自然对象。
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