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Which is the best book in modern theoretical classical mechanics?

  1. Oct 10, 2011 #1
    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!
     
  2. jcsd
  3. Oct 10, 2011 #2
    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/
     
  4. Oct 19, 2011 #3
    https://www.amazon.com/Physics-Mathematicians-Mechanics-Michael-Spivak/dp/0914098322/" on Amazon is enlightening, especially

    and

    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.
     
    Last edited by a moderator: May 5, 2017
  5. Oct 20, 2011 #4
    Thanks! I am checking out the PDF now and will see if I have cash for Spivaks monster book!
     
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