Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics) [Hardcover]

V. I. Arnold (Author), A. Weinstein (Author), K. Vogtmann (Author)

Book Description

Publication Date: May 16, 1989 | ISBN-10: 0387968903 | ISBN-13: 978-0387968902 | Edition: 2nd

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Editorial Reviews

Review

Second Edition V.I. Arnol’d Mathematical Methods of Classical Mechanics "The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising . . . The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview." —AMERICAN MATHEMATICAL MONTHLY

Language Notes

Text: English (translation)
Original Language: Russian

Product Details

• Hardcover: 525 pages
• Publisher: Springer; 2nd edition (May 16, 1989)
• Language: English
• ISBN-10: 0387968903
• ISBN-13: 978-0387968902
• Product Dimensions: 9.3 x 6.3 x 1.1 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (14 customer reviews)
• Amazon Best Sellers Rank: #418,978 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

21 of 21 people found the following review helpful:

5.0 out of 5 stars The best ever book on classical mechanics., January 28, 1998

By A Customer

This review is from: Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics) (Hardcover)

Written by a great mathematician of our time, Vladimir Arnol'd, this truly outstanding book represents classical mechanics from a unifying geometrical point of view and is a "must-to-read" book for any graduate student working in the field. Proofs are wonderfully clear and concise, problems are refreshingly stimulating, ideas are beautifully intuitive. Buy this book now and you will get a long time good friend and teacher!

36 of 41 people found the following review helpful:

5.0 out of 5 stars Encyclopedic, May 8, 2002

By 

Professor Joseph L. McCauley "Joseph L. McCauley" (Austria+Texas) - See all my reviews

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This review is from: Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics) (Hardcover)

Extremely stimulating, uses Galileo to motivate Newton's laws instead of postulating them. Treatment of Bertrand's theorem is beautiful, but contains one error (took me 2 years before I realized where..). However, I know of only one physicist who successully worked out all the missing steps and taught from this book. I know mathematicians who have cursed it. I used/use it for inspiration. The treatment of Liouville's integrability theorem, I found too abstract, found the old version in Whittaker's Analytical Dynamics to be clearer (Arnol'd might laugh sarcastically at this claim!)--for an interesting variation, but more from the standpoint of continuous groups, see the treatment in ch. 16 of my Classical Mechanics (Cambridge, 1997). In my text I do not restrict the discussion of integrability/nonintegrability to Hamiltonian systems but include driven dissipative systems as well. Another strength of Arnol'd: his discussion of caustics, useful for the study of galaxy formation (as I later learned while doing work in cosmology). Also, I learned from Arnol'd that Poisson brackets are not restricted to canonical systems (see also my ch. 15). I guess that every researcher in nonlinear dynamics should study Arnol'd's books, he's the 'alte Hasse' in the field.

14 of 14 people found the following review helpful:

5.0 out of 5 stars Best book on CM, February 26, 2004

By 

Janosch Lenzi (Firenze, Fi Italy) - See all my reviews
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This review is from: Mathematical Methods of Classical Mechanics Hb (Graduate Texts in Mathematics,) (Hardcover)

Best book on CM (based most on symplectic formulation). Extremely clear if one has enough patience to follow exactly the author's way and to work out the proposed stimulating problems. Contains an original way of introducing differential forms, integration of differential forms and homology/De Rahm's thm.: you fully get in the subject in few pages ! The first part does not make use of symplectic formalism but is also quite original and stimulating. The level is last yr. undergr. 1st yr. graduate. Very useful if used with E. ott (Chaos in Dynamical Systems) for studying nonlinear dynamics.