In elementary physics we learn to solve simple mechanics problems, such as motion with a constant force and the motion of the simple harmonic oscillator. These are important problems, since they can be solved exactly, making it easy to explore the solutions thoroughly. But in most real life applications the problems cannot be solved exactly. Then we must either make approximations or resort to numerical methods. In the past few years the advent of high speed computation has opened up the study of a whole new class of very interesting mechanics problems exhibiting chaotic solutions. In this lesson we will be exploring a deceptively simple mechanics problem that features chaotic behavior under certain conditions, namely the damped, driven anharmonic oscillator in one dimension. We will be solving for its motion using Maple.
A word about the organization of this document: The Maple commands are designed to work in the order given, starting with the first section and going to the last. For those of you who like to skip ahead, at the beginning of each section except for the first two, there is a command that allows you to initialize your Maple session for that section.
Carleton DeTar detar@physics.utah.edu