A Computational Approach
Jack Wisdom, 54-414, x3-7730
Gerald Jay Sussman, 32-385, x3-5874
We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.
We will consider the following topics: The Lagrangian formulation. Action, variational principles, and equations of motion. Hamilton's principle. Conserved quantities. Rigid bodies and tops. Hamiltonian formulation and canonical equations. Surfaces of section. Chaos. Canonical transformations and generating functions. Liouville's theorem and Poincaré integral invariants. Poincaré-Birkhoff and KAM theorems. Invariant curves and cantori. Nonlinear resonances. Resonance overlap and transition to chaos. Properties of chaotic motion.
Ideas will be illustrated and supported with physical examples. We will make extensive use of computing to capture methods, for simulation, and for symbolic analysis.
This subject awards H-LEVEL Graduate Credit, however the subject is appropriate for undergraduates who have taken the prerequisites. Undergraduates are welcome.
Prerequisites: 8.01, 18.03, programming experience
Lectures: MWF at 11 AM in room 54-317.
Computer Lab: Wednesday evenings, 7--10 PM, Room 14-0637.
MIT Press Mechanics Book
Mechanics Book (HTML)
Errata for Mechanics Book
Structure and Interpretation of Computer Programs (HTML)
Red Tape Memo
Edwin cheat sheet
Supplementary notes on Differential Geometry
Experimental Software for Differential Geometry This software is now automatically available in our mechanics system, if you get the latest version here.
Notes on the Poincare equations lecture
Notes on the Poincare equations
Code investigating constraints
Animation of motion of islands in Henon map (Courtesy of Alex Schwendner)
We will provide access to computers that run our software.
If you want to install the software on your personal computers see here.