Escape and capture in high-dimensional mathematical models and applications in space mission design

Abstract

This research project aims to investigate processes of escape and capture of trajectories in high dimensional mathematical models in order to explore their applications on Modern Space Mission Design in the Solar system. Our special interest is to study the dynamical structures of the spatial version of the circular restricted three body problem, whose phase space is six-dimensionional. In this context is important to identify, to detect, and to characterize the relevant invariant dynamical structures, in order to understand the role played by them in transport processes in the distinct regions of the physical space domain. In special, we aim to investigate two sets of invariant dynamical structures that are separatrices in transport processes in the phase space: (i) the stable and unstable manifolds of the central manifold of the collinear Lagrangian points, and (ii) the parabolic orbits, that are stable and unstable manifolds of periodic orbits in the infinity. Then, we will investigate the homoclinic and heteroclinic crossings of these manifolds, the formation of non-attractive chaotic invariant sets and the characterization of fractal escape basin boundaries. The potential applications of these dynamical structures will be explored in order to define new strategies and solutions for Space Mission Trajectory Design. Analytical and numerical tools of detection and analysis appropriate to high dimensional nonlinear Hamiltonian systems will be developed and implemented. Following, other more sophisticated mathematical models, such as the four-body bicircular model, can be studied. (AU)