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!

  • 3
    $\begingroup$ 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. $\endgroup$ – Matt E Oct 14 '10 at 2:23
  • 1
    $\begingroup$ 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. $\endgroup$ – Jyotirmoy Bhattacharya Oct 14 '10 at 6:55
  • $\begingroup$ Smale's name is associated more with (classical) dynamical systems than classical mechanics per se. $\endgroup$ – T.. Oct 15 '10 at 16:17

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).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy