Survey of Recent Results on Weak Stability Boundaries and Applications
A region of transitional stability in the three-body problem has proved to have interesting mathematical properties and also important applications to several fields. This region, called the weak stability boundary, was first discovered for its use in providing a methodology for computing new types of low energy transfers. Up to recently, understanding it’s underlying structure has been elusive. Recent results on understanding the mathematical structure of this region are presented as well as associated dynamics. This includes both numerical and theoretical results indicating the underlying complicated structure of invariant hyperbolic manifolds. Associated resonance dynamics are described. Recent applications are described within the field of astronomy on a theory for the origin of the Moon and also on the minimal energy transfer of solid material between planetary systems.
KeywordsInvariant Manifold Planetary System Jacobi Constant Weak Stability Boundary Ballistic Capture
I would like to thank Telespazio and, in particular, Ettore Perozzi for the invitation to attend the workshop at Fucino in October 2007 on Novel Spaceways for Scientific and Exploration Missions. This work is partially supported by grants from NASA and the AISR program.
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