Rigorous Physics Books on Classical Mechanics

Question

I'm a mathematician that would like to read some books of physics. However, trying to read some texts I'm getting confused many times because the lack of mathematical rigor, at least at a formal level.

I am thus looking for rigorous differential geometric treatments of physical topics, wherever applicable. The only ones that I've found are the books/notes of Leon A. Takhtajan, but I would like to know if there are some more books at a similar level of rigour. In particular, I would like some recommendations on rigorous differential geometric treatments of classical mechanics.

Answer 1

Perhaps one of the nicest differential geometric accounts on classical mechanics, written by a mathematician and for mathematicians is,

• Spivak's Physics for Mathematicians: Mechanics I which covers classical mechanics from the ground-up using the language of differential geometry.

It contains several historical and philosophical nuggets that would also give the working mathematician a rough idea about how physicists think about and approach a problem. Some other great books are,

• Fasano and Marmi's Analytical Mechanics, which contains some good chapters on statistical mechanics, chaos and ergodic theory in addition to classical mechanics built from the ground-up.
• Arnold's Mathematical Methods of Classical Mechanics is a classic and concise text that is a must-have reference for those with an interest in the mathematical physics of classical mechanics.
• Thirring's Classical Mathematical Physics is an authoritative and concise text that not only presents classical mechanics, but also field theory in rigorous fashion.

Hope these books can be of help to you :)