Classical Mechanics: Normal Modes for the Double Pendulum and the Eigenvalue Problem

This 31-minute tutorial from Dot Physics demonstrates how to find the normal modes of oscillation for the double pendulum by creating an eigenvalue problem using energy principles. Learn the mathematical "magic tricks" that make this complex physics problem solvable. The video provides a complete walkthrough of the process, connecting energy analysis to the eigenvalue formulation that reveals the system's natural oscillation patterns. Supplementary resources include a VPython Double Pendulum model code, a related video on normal modes with Python for a 2-mass/3-spring system, and additional content explaining the fundamental equations governing double pendulum motion.