Real-life mechanical systems can usually be modeled as non-linear, non-periodic and non-autonomous dynamical systems. It is very important to have different tools to study these systems, and there are many classical procedures developed for this purpose. During the last decade, a new tool has been introduced, the Lagrangian Coherent Structures (LCS). They represent the most repelling and attracting structures of the phase space. Roughly speaking, LCS are particular manifolds that separate regions of space with distinctly different dynamics. In this thesis, algorithms to find the LCS of a system are presented and finally they will be applied in the Elliptic Restricted Three Body Problem in Astrodynamics in order to identify the Weak Stability Boundaries.

Dipartamento di Scienze e Tecnologie Aerospaziali,Politecnico di Milano