Lecture
This lecture covers Lyapunov stability theory applied to the simple pendulum system. Starting with the definition of a smoky, bounded set, the instructor explains the asymptotic stability of the system when the energy function is zero. Through examples of the simple pendulum, the lecture demonstrates the application of Lyapunov stability theory in analyzing the system's behavior. The lecture further delves into the concept of candidate Lyapunov functions and their role in determining the system's stability. By examining the invariant sets and equilibrium points, the lecture concludes with insights into the local stability of the system and the conditions for stability.