Stretching in phase space and applications in general nonautonomous multi-body problems

Abstract

In the circular restricted three-body problem, periodic orbits, stable and unstable manifolds, chaotic regions, and other dynamical features have all proven useful for engineering applications. These phase-space structures can be identified because the system is autonomous in a rotating frame. In more complex multi-body and high-fidelity models, classic invariant sets are not readily identifiable and new approaches are required. The approach here exploits the anisotropy of the growth or decay of perturbations to the trajectories, building on recent ideas from the theory of hyperbolic Lagrangian coherent structures. The present framework yields a mechanism to construct transfers in multi-body systems. In particular, it is applied to a restricted four-body problem and transfers are constructed requiring smaller $$\varDelta v$$Δv values than are necessary to accomplish the corresponding shift in Jacobi constant values for the associated embedded three-body problems.