Classical Mechanics

John Baez

Here are some course notes and homework problems for a mathematics graduate course on classical mechanics. There are two versions of the course:

The second course reviews a lot of basic differential geometry. But, if you'd like to study these courses on your own and don't feel comfortable with manifolds, vector fields, differential forms and vector bundles, you might try the following texts, in rough order of increasing sophistication:

Everyone should read some books on classical mechanics, too! Here's the physicist's bible of classical mechanics — a great new version of the book I used as an undergrad:

And here's a famous book that's closer to the style of this course:

There are LaTeX and encapsulated Postscript files of all the material below if for some bizarre reason you want them. However, we reserve all rights to these, except for Toby's stuff.

Lagrangian approach

In the Spring of 2005 we started with the Lagrangian approach to classical mechanics, with a heavy emphasis on action principles. We then derived the Hamiltonian approach from that.
Derek Wise took notes, and Blair Smith converted them into LaTeX, adding extra material and creating this book:

These versions have some typos that are fixed in this newer version; however, a bunch of pictures are ugly in the newer version — something I will fix when I figure out how.

Here are Derek's original hand-written notes:

You can find errata for these notes here. If you find more errors, please email me!

Hamiltonian approach

In the Winter of 2008 we started with Newton's laws and quickly headed towards the Hamiltonian approach to classical mechanics, focusing on Poisson manifolds rather than symplectic manifolds. Alex Hoffnung created lecture notes in TeX, available below. These need intensive polishing before they become a book — or part of a book.

Here are the course notes:

Lagrangian approach: © 2005 John Baez, Derek Wise and Blair Smith
Hamiltonian approach: © 2008 John Baez and Alex Hoffnung