Rolling Coin, Bicycles, Fish, Chaplygin Swimmer - Small Oscillations About Equilibrium
Explore analytical dynamics in this comprehensive lecture covering nonholonomic systems and small oscillations about equilibrium. Delve into fascinating examples like rolling coins, bicycle stability, and fish locomotion. Learn how to calculate critical speeds for rolling objects and understand the principles behind self-stabilizing bicycles. Discover the analogy between nonholonomic rolling systems and aquatic animals, and investigate the mysterious behavior of rattlebacks. Master the concept of small oscillations in N-degree freedom systems, including normal modes and natural frequencies. Apply Taylor series expansions to analyze potential energy functions and solve eigenvalue problems to determine system behavior. Gain valuable insights into complex dynamical systems and their applications in engineering and physics.