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MIT Electrical Engineering and Computer Science
EECS Event |
Monday, October 15, 2001
4:00 PM (refreshments 3:45)
Edgerton Hall, Room 34-101
EECS Colloquium
Abstract
There has recently been a remarkable revival of interest in classical mechanics. We now know that there is much more to it than previously suspected. The behavior of classical systems is surprisingly rich; derivation of the equations of motion, the focus of traditional presentations of mechanics, is just the beginning. Classical systems display a complicated array of phenomena such as nonlinear resonances, chaotic behavior, and transitions to chaos.
Classical mechanics is deceptively simple. It is surprisingly easy to get the right answer with fallacious reasoning or without the real understanding. To address this problem Jack Wisdom and I, with help from Hardy Mayer, have written a book with the title of this talk and are teaching a class at MIT that uses computational techniques to communicate a deeper understanding of Classical mechanics. We use computational algorithms to express the methods used to analyze dynamical phenomena. Expressing the methods in a computer language forces them to be unambiguous and computationally effective. Formulating a method as a computer-executable program and debugging that program is a powerful exercise in the learning process. Also, once formalized procedurally, a mathematical idea becomes a tool that can be used directly to compute results.
We present classical mechanics from an unusual perspective. We focus on understanding motion rather than deriving its equations. Recent discoveries in nonlinear dynamics appear throughout the presentation, rather than as an afterthought. We use a functional mathematical notation that allows precise understanding of fundamental properties of classical mechanics. We use computation to constrain notation, to capture and formalize methods, for simulation, and for symbolic analysis.
Gerald Jay Sussman is the Matsushita Professor of Electrical Engineering at MIT. He received the S.B. and the Ph.D. degrees in mathematics from MIT in 1968 and 1973, respectively. He has been involved in artificial intelligence research at M.I.T. since 1964. His research has centered on understanding the problem-solving strategies used by scientists and engineers, with the goals of automating parts of the process and formalizing it to provide more effective methods of science and engineering education. For further detail see http://www.swiss.ai.mit.edu/~gjs/biography.html.