II: Dynamical Systems and Chaos
The second part of this course will include a discussion of dynamical systems theory and chaos. Our main vehicle for this discussion will be the motion of the one-dimensional driven, damped pendulum.
Thumbnail: A double rod pendulum animation showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions. (Public Domain; Catslash).