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?