Are there any intermediate mechanics books between Goldstein and Arnold?

[carllacan]

Hi.

I already had a first course on classical mechanics (lets say it was a Goldstein-level course) and I'd like to step up and read advanced, more "mathy" books. I've tried reading Arnold's book and it was frustratingly abstract.

Is there any other books that you could place between Goldstein and Arnold, in terms of formalism and difficulty?

Also, what would be the best way to prepare myself for Arnold's? That is, given that it appears to have been written for mathematicians, should I first get a solid understanding of topology or functional analysis?

Thanks.

 

[ShayanJ]

Hi
I checked Arnold's. I should say its not a book that contains "must-knows" of classical mechanics. I mean, of course there are interesting and important things in that book but a physicist doesn't have to know them. Instead of Arnold's, I suggest "Classical Dynamics:A contemporary approach" by Jose and Saletan.
But if you want to read Arnold's anyway, then you need some knowledge of differential geometry.

 

[carllacan]

Thanks, I had heard of Saletan, but I thought it was at the same level as Goldstein. I'll check it out.

I forgot to ask about "Structure and Interpretation of Classical Mechanics", by Sussman. It is written from a computer science point of view, using snippets of computer code (in Scheme) to maximize clarity. I would welcome opinions on its value, if anyone has any.

 

[ShayanJ]

Thanks, I had heard of Saletan, but I thought it was at the same level as Goldstein. I'll check it out.

Actually you're almost correct. But it seems to me that from place to place, you can find deeper explanations. Also Saletan and Jose cover more.

I forgot to ask about "Structure and Interpretation of Classical Mechanics", by Sussman. It is written from a computer science point of view, using snippets of computer code (in Scheme) to maximize clarity. I would welcome opinions on its value, if anyone has any.

I checked that too. It seems to me its more advanced than both Goldstein's and Saletan's. But the point is, it again contains things that you don't really need to know. If you ask me, to be able to apply classical mechanics broadly and effectively, Goldstein's and then Saletan's will do.