Joint Subject Offering: 6.946J, 8.351J, 12.620J

**Classical Mechanics:
A Computational Approach**

Jack Wisdom, 54-414, x3-7730

Gerald Jay Sussman, 32G-514, 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 plan to consider the following topics: The Lagrangian formulation. Action, variational principles, and equations of motion. Hamilton's principle. Conserved quantities. Hamiltonian formulation and canonical equations. Surfaces of section. Chaos. Canonical transformations and generating functions. Hamilton-Jacobi theory, Liouville's theorem and Poincaré integral invariants. Canonical perturbation theory. Poincaré-Birkhoff and KAM theorems. Invariant curves. 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 G-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 2:00PM in room 34-304.

Computer Lab: Wednesday evenings, 7--10 PM, Room 14-0637.

Units: 3-3-6

Structure and Interpretation of Classical Mechanics, second edition, MIT Press, 2014, ISBN: 978-0-262-02896-7

Mechanics Book (HTML), second edition

Errata for the Mechanics Book, second edition . There are rewards for errors found (GJS).

Structure and Interpretation of Computer Programs, second edition (HTML)

Our MIT Press book on differential geometry!

**
Software for Differential Geometry
**
This software is now automatically available in our mechanics system,
if you get the latest version here.

**
Experimental Video Presentations
**
here.

We will make our software available on Athena.

If you want to install the software on your personal computers
see here.