Invariant Manifolds, Material Transport and Space Mission Design

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


The dynamics of comets and other solar system objects which have a three-body energy close to that of the collinear Lagrange 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 Lagrange points for the restricted three-body problem, which exist for a range of energies, provide the framework for understanding these complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold "tubes" associated to Lagrange point orbits are the phase space structures that provide a conduit for orbits travelling to and from the smaller primary body (e.g., Jupiter), and between primary bodies for separate three-body systems (e.g., Saturn and Jupiter). One can also use this methodolgy to design interesting and versatile space missions which use very little fuel. Combining this detailed knowledge of phase space transport with control and optimal control techniques provides a powerful tool for space mission design.

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