Applications of Dynamical Systems Theory to Astrodynamics and Celestial Mechanics
The underlying dynamical structures that exist within multi-body systems can be leveraged to enable the design of trajectories for missions to interplanetary destinations and to further our understanding of natural celestial transport – both within our solar system and beyond. In contrast to the two-body problem, the dynamics within multi-body gravitational environments are nonlinear and chaotic, with no analytical solutions available. Accordingly, we leverage dynamical systems theory to identify and characterize any
fundamental solutions that exist (e.g. libration points, periodic orbits, quasi-periodic orbits, and manifolds) and to visualize a large set of trajectories (e.g. via Poincare maps). These techniques can be used within lower-fidelity dynamical models to rapidly and efficiently predict the characteristics of a diverse solution space in higher-fidelity environments. This seminar will outline applications of dynamical systems theory to: 1) trajectory design for both traditionally-large spacecraft and SmallSats; and 2) the study of natural celestial transport in binary systems.