Lecture 26
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FLOQUET THEORY: This lecture introduces Floquet theory for characterizing the stability of periodic orbits in a dynamical system. It also introduces the concept of flow maps and Poincare sections for the analysis of periodic solutions.
Lecture 27
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THE PENDULUM AND FLOQUET THEORY: This lecture considers the pendulum whose support is periodically driven at a given frequency. Such a scenarios allows for stabilization of the pendulum in the upright position.
Lecture 28
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DATA-DRIVEN FLOQUET THEORY: This lecture considers a modern perspective on what can be done with Poincare maps and Floquet theory. Specifically, we use a data-driven method for nonlinear Floquet theory.