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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!

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    $\begingroup$ 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
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    $\begingroup$ 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
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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).

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