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


Ross, Shane David (2004) Cylindrical Manifolds and Tube Dynamics in the Restricted Three-Body Problem. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KHYT-A428.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:astrodynamics; dynamical astronomy; symbolic dynamics; trajectory generation; transition state
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Control and Dynamical Systems
Awards:Everhart Distinguished Graduate Student Lecturer Award, 2004.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Marsden, Jerrold E.
Thesis Committee:
  • Marsden, Jerrold E. (chair)
  • Scheeres, Daniel
  • Lo, Martin
  • Murray, Richard M.
Defense Date:7 April 2004
Non-Caltech Author Email:sdross (AT)
Record Number:CaltechETD:etd-05182004-154045
Persistent URL:
Ross, Shane David0000-0001-5523-2376
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1854
Deposited By: Imported from ETD-db
Deposited On:19 May 2004
Last Modified:04 Feb 2021 01:26

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