Classical Mechanics for Mathematician

[chhan92]

Hi!
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?

 

[A. Bahat]

V.I. Arnold's Mathematical Methods of Classical Mechanics sounds like it would be suitable. You'll finally get to see those differential forms from Spivak in action!

 

[chhan92]

But is Arnold self-contained in terms of physical intuition?
Do you think Arnold is readable without freshman-level physical knowledge?

 

[Petek]

I haven't looked at this book, but https://www.amazon.com/dp/0914098322/?tag=pfamazon01-20 by Spivak may be what you're looking for. (http://www.mathpop.com/mechanics1.htm has an offer to send you the Preface and Table of Contents of the book.)

 

[sponsoredwalk]

Here's an idea if you want to do the basics of mechanics with more of an emphasis on calculus than most introductory approaches - Mix:
http://www.pa.msu.edu/courses/phy233b/VideoLectures.html
http://www.pa.msu.edu/courses/2010fall/PHY321/VideoLectures/
with reading both https://www.amazon.com/dp/0201073927/?tag=pfamazon01-20 & https://www.amazon.com/dp/0070843570/?tag=pfamazon01-20 (http://archive.org/details/SchaumsTheoryAndProblemsOfTheoreticalMechanics).
I'd take notes from the video in the first link first, then the second link, then read the corresponding section of Symon finally doing the schaums sections & Symon's problems together last. it'd be a good idea to go through the Yale videos as well. Then you could go onto Lagrangian https://www.amazon.com/dp/0070692580/?tag=pfamazon01-20 & Arnol'd without that soul-destroying headache. If you want to really rush things then at least watch the videos before going on as they are the best ones I've found & do the most out of all the basic ones I've seen.

 

[A. Bahat]

I completely forgot about Spivak--also an excellent suggestion! Ideally you could compare these two books in a library and see which one you prefer.

 

[Snicker]

Classical mechanics is has a very strong geometric flavor. That is, you can learn a lot of pretty mathematics by learning classical mechanics.I would strongly recommend either Mathematical Methods of Classical Mechanics by V.I. Arnold or An Treatise on the Analytical Dynamics of Particles and Rigid Bodies by E.T. Whittaker (out of copyright/print; legally available on-line here).

After that, purchase Dynamical Systems IV: Symplectic Geometry and Its Applications. There is also a really nice set of lecture notes by "www.math.princeton.edu/~acannas/Papers/symplectic.pdf" .