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Goldstein's mechanics


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In my opinion, the only problem of Goldstein's book is that the mathematical formalism used by the author differs very much from the formalism used in the modern research literature.

Today's papers speak in the language of "manifolds","symplectic geometry", "differential forms" etc. And this is much more than some new notation - it's completely new unifying framework for thinking.

So for all who is not afraid of mathematics, I would recommend to study this modern approach instead of tracking XIX century pathways.

The definitive book introducing this new approach is

Arnold V.I. "Mathematical foundations of classical mechanics",1989 (2ed)

The book is rather slim and the exercises are very useful.

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Tannin is right, differential and bracket geometry is the modern way of thinking.


The book by Arnold is cited in many papers, but I must confess that I have never read it. At some point I will get it out from the library.

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hmm, thanks all for the replies.


I don't think I have the mathmatical know-how to tackle a physics book that includes anything like differential geometry, and it also seems like a knowledge of the basics is important before going on to that kinda thing.


So I'll have to pick up a copy of goldsteins mechanics than. (also ajb I did have the equivalent of a freshman course in mechanics)

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  • 3 months later...

For all who are interested in gaining deeper insight into principles of mechanics (and eventually of most of the modern physics) I would like to recommend the book "Variational principles of mechanics" by C.Lanczos.

In his introduction the author states that the book is not written for "superhuman beings" but for EVERYONE, and he keeps his promise.

C. Lanczos was an assistant for A.Einstein and has many contributions in the field of mathematical physics.

I think that understanding (and not merely following) Goldstein is much easier after Lanczos. His explanation of variational calculus is superb.

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