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S.D. Ross, W.S. Koon (Control and Dynamical Systems, Caltech), M.W. Lo (Navigation and Mission Design, Jet Propulsion Laboratory), J.E. Marsden (Control and Dynamical Systems, Caltech)
The dynamics of comets and other solar system objects which have a three-body energy close to that of the collinear libration points are known to exhibit a complicated array of behaviors such as rapid transition between the interior and exterior Hill's regions, temporary capture, and collision. The invariant manifold structures of the collinear libration points for the restricted three-body problem, which exist for a range of energies, provide the framework for understanding these transport phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold "tubes" associated to libration point orbits are the phase space conduits transporting material to and from the smaller primary body (e.g., Jupiter), and between primary bodies for separate three-body systems (e.g., Saturn and Jupiter).
This point of view has worked well in describing the planar circular restricted three-body problem. The current work seeks to extend the results to three degrees of freedom.
This work was supported by the National Science Foundation Grant No. KDI/ATM-9873133 under a contract with the Jet Propulsion Laboratory, NASA.