Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I read that Smale recast classical mechanics in terms of symplectic geometry. I know a bit about classical mechanics but nothing about symplectic geometry.

Are there any writings from Smale on this which I could read?

And also what other books or texts are there which cover this?

Thank you!

share|cite|improve this question
My understanding is that this goes back before Smale; more precisely, the Hamilton--Jacobi formulation of classical mechanics in terms of canonical coordinates is (I believe) the original inspiration for symplectic geometry. (The phase space in classical mechanics is naturally a symplectic manifold.) If you do a Google search for "geometry and physics text" you find many references discussing this material. Probably others will leave specific suggestions here. – Matt E Oct 14 '10 at 2:23
I'm also trying to learn more about this area. A basic book that gives wonderful intuition is Arnold's Mathematical Methods of Classical Mechanics. I've also seen Marsden & Ratiu's Introduction to Mechanics and Symmetry mentioned but haven't read it myself. – Jyotirmoy Bhattacharya Oct 14 '10 at 6:55
Smale's name is associated more with (classical) dynamical systems than classical mechanics per se. – T.. Oct 15 '10 at 16:17
up vote 2 down vote accepted

I'd recommend Foundations of Mechanics by Abraham and Marsden. It's a huge book, with a very rigorous treatment of mechanics. Altough Smale is not an author, he's heavily cited in the book (by the way, the book provides an excellent bibliography).

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.