Hamiltonian Mechanics: Analytical Approach

This lecture covers the analytical approach to Hamiltonian mechanics, focusing on the harmonic oscillator and the Hamilton-Jacobi equation. It discusses the conservation of quantities, separation of variables, and the quadratic form of kinetic energy. The instructor explains the process of putting everything back together, the bias of examples, and the explicit appearance of certain terms. The lecture also delves into the complexities of potential functions and the ambiguity of certain quantities. It concludes with a detailed exploration of canonical transformations and the hidden effects on the temporal evolution of systems.