MAE5790-1 Course introduction and overview
1:16:31MAE5790-2 One dimensional Systems
1:16:44MAE5790-3 Overdamped bead on a rotating hoop
1:13:12MAE5790-4 Model of an insect outbreak
1:15:16MAE5790-5 Two dimensional linear systems
1:15:20MAE5790-6 Two dimensional nonlinear systems fixed points
1:07:17MAE5790-7 Conservative Systems
1:17:13MAE5790-8 Index theory and introduction to limit cycles
1:13:55Testing for Closed Orbits
1:16:52Van der Pol Oscillator
1:05:58Averaging Theory for Weakly Nonlinear Oscillators
1:16:08Bifurcations in Two-Dimensional Systems
46:54Hopf Bifurcations in Aeroelastic Instabilities and Chemical Oscillators
1:07:57Global Bifurcations of Cycles
1:16:23Chaotic Waterwheel
1:14:12Waterwheel Equations and Lorenz Equations
1:12:42Chaos in the Lorenz Equations
1:16:36Strange Attractor for the Lorenz Equations
1:13:48One-Dimensional Maps
1:14:35Universal Aspects of Period Doubling
1:11:56Feigenbaum's Renormalization Analysis of Period Doubling
1:15:59Renormalization: Function Space and a Hands-On Calculation
1:08:32Chaotic Waterwheel
This lecture introduces the chaotic waterwheel, deriving its governing equations through continuity and torque balance. It demonstrates a miraculous exact decoupling of a three-dimensional subsystem, utilizing the orthogonality of Fourier modes.
Schematic diagram of the waterwheel. Video of waterwheel in action. Derivation of governing equations for the waterwheel. Contuinuity equation and torque balance. Amplitude equations. Using orthogonality of the Fourier modes. A miracle: Exact decoupling of a three-dimensional subsystem from the rest of the modes.
Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 9.0, 9.1.
Global Bifurcations of Cycles
Next · Lecture 16Waterwheel Equations and Lorenz Equations