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]

https://www.amazon.com/dp/0914098322/?tag=pfamazon01-20 on Amazon is enlightening, especially

It is quite clear that differential geometry is assumed. (Well, Spivak suggests that the first two volumes of "A Comprehensive Introduction to Differential Geometry" should be read before hand.)

There is a thorough discussion of Lagrangian and Hamiltonian mechanics from the differential geometric perspective.

and

There's an entire chapter (26 pages) dedicated to the Hamilton-Jacobi theory.

You can see the http://olivier.thill.perso.neuf.fr/books/bospphma.htm" online, where several pages can be previewed as well.

http://www.math.uga.edu/~shifrin/Spivak_physics.pdf" 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!