Hamilton-Jacobi Equation: Analytical Mechanics

This lecture covers the Hamilton-Jacobi equation in analytical mechanics, discussing the eigenvalues and eigenvectors of a matrix, the concept of constant of motion, and the separation of variables. It delves into the implications of integrable systems, deterministic chaos, and the loss of predictability. The instructor explains the significance of isolating variables, the conservation of constants of motion, and the integrability of systems. The lecture concludes with a detailed analysis of the Hamilton-Jacobi equation and its applications in various systems.