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My review will be mostly comparing the book to Spivak's lecture notes. They are incredibly different.
The first ~430 pages are dedicated to Newtonian mechanics (including central potential, rigid body motion, and fictitious forces). I've noticed most physics textbooks just give this as "God given", but Spivak actually gives some intuition behind what's going on. This book is the perfect foil for Morin's "Introduction to Classical Mechanics".
The discussion of constraints is quite thorough. It begins with rigid body motion, and generalizes it in a beautiful way. Most other physics textbooks leave out any discussion of what to do with constraints (c.f. Arnold's "Mathematical Methods of Classical Mechanics" or even Goldstein).
Spivak discusses variational principles --- not just the principle of stationary action, but others too. Euler's equation derived from variation, Hamilton's principle, Maupertuis' principle of least action, Jacobi's version of the principle of least action, and symmetry in variational calculus. There is a minor typo on page 466 ("Jacobi's form of the principal [sic] of least action.") and 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. It's not completely abstract, it's amazingly grounded in physical intuition. There's an entire chapter (26 pages) dedicated to the Hamilton-Jacobi theory.
The only problem I have with the book is that classical field theory is not covered. Also gauge transformations are mentioned only once in passing. But this book is a wonderful introduction to mechanics for mathematicians, it will save a lot of frustration for mathematical physicists.
- Hardcover: 749 pages
- Publisher: Publish or Perish; first edition (December 6, 2010)
- Language: English
- ISBN-10: 0914098322
- ISBN-13: 978-0914098324
- Package Dimensions: 9.4 x 6.5 x 1.8 inches
- Shipping Weight: 2.8 pounds (View shipping rates and policies)
- Average Customer Review: 5 customer reviews
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Amazon Best Sellers Rank:
#519,282 in Books (See Top 100 in Books)
- #226 in Physics of Mechanics
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