Earth-to-moon low energy transfer using time-dependent invariant manifolds

This paper investigates time-dependent invariant manifolds in the Sun-Earth-Moon bicircular problem (BCP) using Lagrangian coherent structures (LCSs) as substitutes. LCSs, which are defined as ridges of finite-time Lyapunov exponent (FTLE) fields, are proving to be excellent platforms for studies of stable and unstable manifolds in flows with arbitrary time dependence. A preliminary assertion of this paper is achieved numerically: timedependent invariant manifolds in the BCP are not only separatrices, but also invariant sets. Dichotomy is utilized to extract LCSs for the purpose of improving computational efficiency. A series of LCSs, with regularly spaced energy, are then extracted to illustrate the configuration of time-dependent invariant manifold on specified section. Finally, the application on constructing Earth-Moon low energy transfer in non-autonomous system is presented.