Day 164: Action-Angle Variables — The Geometry of Integrable Systems

Learning Objectives

• •Define action variables as phase space integrals and compute them for standard systems
• •Construct angle variables as canonical conjugates to actions
• •State and interpret the Liouville-Arnold theorem for integrable systems
• •Apply the Bohr-Sommerfeld quantization rule J = nℏ
• •Understand adiabatic invariance and its applications
• •Visualize motion on invariant tori and connect to KAM theory

Today's Schedule (7 hours)