Joint Subject Offering: 6.5160J, 8.351J, 12.620J

**Classical Mechanics:
A Computational Approach**

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Fall 2024: This is the last time this class will be offered!
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Jack Wisdom, wisdom@mit.edu, 54-414, x3-7730

Gerald Jay Sussman, gjs@mit.edu, 32-G514, x3-5874

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Content:
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We study the fundamental principles of classical analytical mechanics.

Subjects: The Lagrangian formulation. Action and variational principles. Hamilton's principle. Conserved quantities. Hamiltonian formulation and canonical equations. Surfaces of section. Canonical transformations and generating functions. Hamilton-Jacobi theory, Liouville's theorem and Poincare integral invariants. Poincare-Birkhoff and KAM theorems. Invariant curves. Canonical perturbation theory using Lie transforms. Nonlinear resonances. Resonance overlap and transition to chaos.

Ideas are illustrated and supported with examples from recent research.

We make extensive use of computing to capture methods, for simulation, and for symbolic analysis. Formulation in a computational framework encourages clear thinking and active exploration. }

This subject awards G-LEVEL Graduate Credit, however the subject is appropriate for undergraduates who have the prerequisite experience. Undergraduates are welcome.

Prerequisites: 8.01, 18.03, programming experience

Lectures: MWF at 1300 ET (1:00PM) in 54-823

Computer Lab: Wednesday evenings, 1900-2200 ET (7--10 PM), in 54-824.

Units: 3-3-6

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Teaching plan:
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Professors Jack Wisdom (EAPS) and Gerald Jay Sussman will teach this class entirely in person. We will run our evening laboratory, each Wednesday from 1900--2200 EDT (7:00PM--10:00PM). We expect students to actively participate in all of the meetings.

We also invite students individually and in groups to drop in to discuss problems with us at other times.

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Grades:
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This is an advanced class. There are no quizzes. Grades are entirely determined by the work that students do in weekly problem sets, attendance and participation in the class and in the laboratory, and some more extensive projects. In the evening laboratory we hang out with the students, engage in discussions, and we try to help with the weekly work. We encourage students to work together and help each other learn the material, but each student must prepare an individual report on the work done on the problem sets and projects. Each student must report on the help that they gave to and received from other students.

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Textbook:
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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 .

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

Don't Panic!: A guide for the perplexed (software setup).

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

We will also make our software available on Athena.

Our MIT Press book on differential geometry!

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