MIT Department of Electrical Engineering & Computer Science

EECS Fall 1995 Catalog Supplement

6.946J Variational Mechanics: A Computational Approach(H)

MW F 11, 26-168
Prerequisites: 8.01, 18.03, 6.001 or equivalent
Limited enrollment - permission of instructors required
Computer lab to be arranged
3-3-6
Profs. Gerald Sussman and Jack Wisdom, NE43-408, x5874 and 54-414, x7730

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 plan to consider the following topics: the Langrangian 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; cantori; nonlinear resonances; resonance overlap and transition to chaos; properties of chaotic motion; transport, diffusion, mixing; symplectic integration; adiabatic invariants; many-dimensional systems; Arnold diffusion.

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.