A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge Mathematical Library)

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Summary: A complete and scholarly book from one of THE experts
Review: This book is, or rather was , the first modern book on classical mechanics. I think the first edition was published in 1904 and at the time it represented just about all that was known about the subject. A serious student today could rightly ask why he/she should read such a old book ? Well the answer to that question is a not an esay one : however whilst I would never say it is an simple book it repays careful study. Anyone taking more modern courses based on Arnold or Abraham and Marsden would do well to have a copy of this book by their side.The problems are taken mainly from Cambridge Maths Tripos examinations and they form a useful adjunct to the main body of the text.All the major topics are coverd including the 2 and 3 body problem, small oscillations, stability,etc. Well worth a read.

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Summary: Integrability defined
Review: This is where I learned Liouville's integrability theorem for Hamiltonian systems, a key topic ignored by most modern texts on classical mechanics. Arnol'd covers it, but I found Arnol'd's more abstract lattice-based proof difficult to follow. Whittaker's text also contains many problems that are useful for a modern dynamics course. As a basis for understanding modern nonlinear dynamics, or for applications of mechanics, this old text is in many respects far better than the newer 'standard' mechanics texts by Landau-Lifshitz, and by Goldstein.

But take care: in a general discussion of integrability (conserved quantities) for general systems of odes early in the book, Whittaker does not distinguish local from global integrability. But then neither does Eisenhart in his book Continuous Groups, of the same era.

Rating:
Summary: The most detailed Dynamics Book Ever
Review: To put it mildly, this book is a frightening exercise to read. The biggest challenge faced by modern readers is that we seem to have lost certain mathematical skills and intuition compared with people in the very early 1900's. It takes enormous amounts of patience and effort to try and work through any of the proofs or derivations presented in this book.

However, Whittaker has presented just about every concept in classical dynamics that you could possibly want to know in an extremely elegant fashion. Concepts that you simply do not expect to see in a book written first in 1904 make an appearence here. This book is worth reading just to find out how the original mathematicicals that invented concepts view them. For exmaple, Whittakers use of Christoffel Symbols is the classical view that the early geometers like Levi-Civita probably had, without the modern terminology and viewpoint in temrs of connections on a manifold.

All in all this book is well worth the time and effort spent to read it, but be prepared to use up lots of paper in your attempts to convince yourself that a single proof is true.(Brush up your geometry before you even try to read this book)