Hamiltonian Formalism: Harmonic Oscillator

This lecture covers the Hamiltonian formalism applied to the harmonic oscillator, focusing on normal coordinates, the principle of least action, and the generation of new conserved quantities. The instructor explains how to derive the Lagrangian and Hamiltonian for the harmonic oscillator, emphasizing the isolation of the system and the generation of new quantities. The lecture also delves into solving the differential equations with partial derivatives and separating the variables to find the solution. The process involves identifying terms, manipulating equations, and solving for new dynamic variables. The lecture concludes with a detailed analysis of the Hamiltonian and the conservation of quantities.