Canonical Transformations: Phase Portraits and Action Variables

This lecture covers canonical transformations, focusing on phase portraits and action variables. It explains the linear behavior of systems in phase space, the representation of trajectories, and the calculation of movement periods. The instructor demonstrates the relationship between variables and the determination of action variables. The lecture also delves into the Hamiltonian system, harmonic oscillators, and the significance of energy in action calculations. Through examples and equations, the lecture illustrates how to find explicit solutions and understand the behavior of systems under different transformations.