Mathematical Methods of Classical Mechanics by V.I. Arnol'd

[Greg Bernhardt]

• Author: V.I. Arnol'd (Author), K. Vogtmann (Translator), A. Weinstein (Translator)
• Title: Mathematical Methods of Classical Mechanics
• Amazon Link: https://www.amazon.com/dp/1441930876/?tag=pfamazon01-20
• Prerequisities:
• Contents:

 

[Group_Complex]

This is one of the most beautiful mathematical physics texts out there.

 

[andrien]

this is the text which starts with the idea of an affine space.somewhat tough as compared to Goldstein.

 

[dextercioby]

If you think Herbert Goldstein wrote in 800 pages is last edition all there is to write about non-quantum mechanics, there you are for a big surprise. There are at least 800 pages more to write about, and 400 of them you can find in this gem-book which I whole-heartedly recommend for anyone doing graduate studies in physics.

 

[thegreenlaser]

Not sure if I'm supposed to start a new thread or ask this here...

I'm an engineering/physics student (senior undergrad) trying to self-study to get a better grounding in Lagrangian/Hamiltonian mechanics. Is this book accessible as a "mature" introduction to advanced mechanics, or is it more for people who already know the stuff and just want to frame it more mathematically? Put another way, am I better off working through something like Goldstein first and then coming to this book, or should I start with this book right away?

 

[WannabeNewton]

Definitely use something like Goldstein or Calkin first. You won't learn physics from Arnold's book, you'll just learn how to make the physics more mathematically rigorous. Personally I find the former to be much more important and interesting than the latter. Cheers.

 

[lurflurf]

^Yes Goldstein and Arnold complement each other quite well. I don't agree that the purpose of Arnold is to dress mechanics up with rigor. I think Arnold is uninterested in doing that. The book gives a different way of thinking conceptually about mechanics. Arnold has an interesting perspective. I would warn against becoming too enamoured with Arnolds approach as some readers do. It is not the one true way.

If you think Herbert Goldstein wrote in 800 pages is last edition all there is to write about non-quantum mechanics, there you are for a big surprise.

I actually think of Goldstein as a quantum mechanics book. It seems a bit more interested in laying a foundation for later study of quantum mechanics than doing classical mechanics for its own sake. Not that there is anything wrong with that.

 

[R136a1]

I actually think of Goldstein as a quantum mechanics book.

Yes, exactly! It's like how think of Spivak's calculus actually being an algebraic geometry book.
Those textbook authors try to trick us!