5 Set oriented numerical methods in space mission design

Abstract

This chapter discusses the set oriented numerical methods in space mission design. New techniques for the design of energy efficient trajectories for space missions have been proposed which are based on the circular restricted three-body problem as the underlying mathematical model. These techniques exploit the structure and geometry of certain invariant sets and associated invariant manifolds in phase space in order to systematically construct efficient flight paths. A new paradigm for the construction of energy efficient trajectories for spacecraft is currently emerging. It heavily bases on concepts and techniques from the theory and numerical treatment of dynamical systems. The basic strategy is the following: Instead of a two-body problem, as in more classical approaches, one considers a restricted three-body problem as the mathematical model for the motion of the spacecraft. This enables one to exploit the intricate structure and geometry of certain invariant sets and their stable and unstable manifolds in phase space—which are not present in two-body problems—as candidate regions for energy efficient trajectories.