Courses:

Classical Mechanics: A Computational Approach >> Content Detail



Syllabus



Syllabus

MASSACHVSETTS INSTITUTE OF TECHNOLOGY
Joint Subject Offering: 6.946J, 8.351J, 12.620J

Classical Mechanics: A Computational Approach

Instructors:

Prof. Jack Wisdom
Prof. Gerald Jay Sussman

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, 6.001 or equivalent
Lectures
Three sessions / week
Computer Lab
Time to be arranged.
Units
3-3-6
Limited Enrollment
Permission of instructors required.


 



 








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