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Which Mechanics book is the best for beginner in math major?

I am looking for suitable ways to learn mechanics in mathematician's perspective. I went through:

  • multivariable calculus from Spivak,
    • real analysis from Pugh,
    • differential equations from Hirsh/Smale/Devaney (mostly focusing on linear system, existence & uniqueness, nonlinear dynamical system, bifurcation, and brief touch on chaos) (so no application covered)
    • differential geometry from Pressley (but I hate pressley, so I am going to review through doCarmo)
  • topology from Willard (but not all of them)

The problem is I did not take freshman physics coures (because of annoying labs;;)

My goal is to be able to read Abraham/Marsden's Foundations of Mechanics or something of that level.

I was thinking of reading differential equations book's applications section first and... idk.

What books do you think is suitable for me to start learning classical mechanics?

P.S. Some people mentioned Arnold's Mathematical Methods of Classical Mechanics, but do you think it is self-contained in terms of physical intuition required?

  • $\begingroup$ Arnols's book is fantastic for those who know enough mathematics. It will definitely do the job. $\endgroup$ – DaniH Apr 1 '12 at 6:37
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    $\begingroup$ Related: physics.stackexchange.com/q/9165/2451 $\endgroup$ – Qmechanic Apr 1 '12 at 8:06
  • $\begingroup$ An alternative to the Abraham & Marsden might be Marsden & Ratiu, Introduction to Mechanics and Symmetry, amazon.com/… (according to the Amazon reviews, this is not a good book for self-study for at least one Engineer). $\endgroup$ – Peter Morgan Apr 1 '12 at 11:16
  • $\begingroup$ On the related question, people seem to mention Goldstein, but he does not relate mechanics to manifolds.... Do you think Goldstein is just for physicists? Or is it a good intermediate book before Abraham/Marsden? $\endgroup$ – chhan92 Apr 1 '12 at 19:04
  • $\begingroup$ Spivak has written a book Physics for Mathematicians: I. Mechanics which is, presumably, a multi-volume project. The first book may be precisely what you're after... $\endgroup$ – Alex Nelson Nov 5 '13 at 16:21

You cannot learn hysics from books on differential equations only.

Arnold is a nice book for mathematicians, but to pick up the way physicists think it is probably better to read in parallel a real physics books.

I think that Arnold together with Abraham/Marsden make a good combination.

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    $\begingroup$ My god, it's such a relief to see a real physicist expressing the view that Arnold's book is for mathematicians. I love The Variational Principles of Mechanics (Dover Books on Physics & Chemistry) [Paperback] Cornelius Lanczos, together with Goldstein's which goes to show that there isn't one physics book that can be entirely relied upon. $\endgroup$ – Larry Harson Apr 29 '12 at 23:32

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