Lagrangian - Bead on a Driven Hoop vs. Bead on a Free Hoop

Explore the fascinating comparison between a bead's motion on a driven rotating hoop and a freely rotating hoop in this 28-minute physics video. Delve into the Lagrangian mechanics behind these systems, building upon Andy Rundquist's work. Examine the detailed derivation for a driven rotating hoop and access the accompanying Python code to further enhance your understanding of these complex physical phenomena.