Cylindrical Manifolds and Tube Dynamics in the Restricted Three-Body Problem

Shane D. Ross
Control and Dynamical Systems, California Institute of Technology
MC 107-81, Pasadena, CA 91125, USA. E-mail:


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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