Seminars

Many problems in astrodynamics and nonlinear control sit in an uncomfortable middle ground: the dynamics are too complex for closed-form solutions, yet purely numerical approaches can often obscure structure that is essential for prediction, design, and autonomy. This seminar explores how structure-preserving representations—in particular, frequency-based and Hamiltonian viewpoints—can bridge this gap.
We begin by revisiting a classical goal in dynamics: transforming nonlinear systems into coordinates where motion becomes simple, interpretable, and reusable. While invariant tori and action–angle variables provide this idealized picture for integrable systems, real multi-body and controlled systems rarely satisfy the assumptions required by strict perturbation theory. Rather than relying on exact integrability, we examine how quasi-periodic structure can be identified, approximated, and exploited directly from data.
We will discuss how these representations relate to classical normal-form and Hamilton–Jacobi constructions, and how they can be used to obtain semi-analytic descriptions of motion—even in unstable or non-integrable regimes. The same perspective naturally connects to optimal control, where Hamilton–Jacobi theory provides a unifying language for trajectory generation, value functions, and feedback synthesis. Throughout the talk, emphasis is placed on representation rather than rigor—why these structures persist in practice, how they can be computed and validated, and how they inform trajectory design in complex dynamical systems.