Which is the best book in modern theoretical classical mechanics?

camel_jockey

Hi!

I am a very mathematically-oriented physicist. Since I never plan in making contact with "dirty" mechanics like robotics, structural problems or force diagrams, I want a book that prepares me for the mathematical/theoretical foundations of mechanics so that I can transition more smoothly to string theory and quantum field theory - where the action, the Hamilton-Jacobi equations and symmetries/Noether currents are in focus. Is there any book which "has it all" ?

I was wondering if someone could recommend me a CONCISE, preferably short, book which fulfils this in the language of differential geometry etc. An internet PDF would also be of interest...

Many thanks!

deluks917

Mathematical Methods of Classical Mechanics by Arnold seems like a good choice for you.

The following webpage seems like it might be very usefull (it has two set of course notes):

http://math.ucr.edu/home/baez/classical/

lithis

Spivak’s Physics for Mathematicians, Mechanics I, perhaps? I haven’t read it, and it’s not short at 749 pages, but it sounds like something you might be looking for. A. Nelson’s review on Amazon is enlightening, especially

and

You can see the table of contents online, where several pages can be previewed as well.

Elementary Mechanics from a Mathematician’s Viewpoint is a 100-page PDF for some lectures Spivak gave; it is based on the first part of this book.

camel_jockey

Thanks! I am checking out the PDF now and will see if I have cash for Spivaks monster book!