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Mathematical Methods of Classical Mechanics Hardcover – Sep 23 1997


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Product Details

  • Hardcover: 519 pages
  • Publisher: Springer; 2nd ed. 1989. Corr. 4th printing 1997 edition (Sept. 23 1997)
  • Language: English
  • ISBN-10: 0387968903
  • ISBN-13: 978-0387968902
  • Product Dimensions: 2.9 x 16.6 x 24.1 cm
  • Shipping Weight: 862 g
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (8 customer reviews)
  • Amazon Bestsellers Rank: #181,843 in Books (See Top 100 in Books)
  • See Complete Table of Contents


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First Sentence
In this chapter we write down the basic experimental facts which lie at the foundation of mechanics: Galileo's principle of relativity and Newton's differential equation. Read the first page
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Format: 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.
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Format: Hardcover
Arnold shines for clarity, completeness and rigour. But, at the same time, he requires a remarkable intellectual effort on the part of the reader (at least a physicist or an engineer). Some readers might see this as a book of math rather than physics, but that would not be fair: Arnold always stresses the geometrical meaning and the physical intuition of what he states or demonstrates. You can take full advantage from the effort of reading this book only if you master a wide range of mathematical topics: essentially differential geometry, ODEs and PDEs and some topology. That's not always true for engineer or physics students at the beginning graduate level. For that kind of readers, Goldstein is a much better fit. Arnold can (and maybe should) be read afterwards.
On the other hand, the exercises, although not very numberous, are very well conceived and help a lot to deepen the comprehension of the text. Also, the order of the topics is linear and very effective from a didactic point of view. The exposition is clear, concise and always goes straight to the point. Thanks to these features, it is one of the most effective books for self-teaching I ever happened to read.
From a physical point of view, the domain of applications is essentially limited to discrete systems. Furthermore, the electromagnetism and relativity are not even cited, although they can be viewed as the logical completion of classical mechanics (see, for example, Goldstein). But the extreme generality of the approach largely balance the more restricted physical domain. In my opinion, the best book you can read on the topics.
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By Li-yu-xuan on Feb. 15 2001
Format: Hardcover
After reading Arnold, I know no other authors of classical mechanics.
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By A Customer on Dec 28 2000
Format: Hardcover
I approached reading this book with a certain amount of trepidation. I thought that like with many mechanics books, I will be forced to put it down after page three because the struggle of continuing is too onerous. Surprising, I have gotten past chapter 5 and wish to continue. In other words Arnold does not expect too much from the reader. Contains some formal proofs but not enough dull you interest in the subject. Also unlike many mechanics books it is not filled with endless pompous writing (e.g Goldstein, and Salatan ) but gets directly to the point. Also I like the way the problems are presented. After every couple of paragraphs a problem (of not too great of difficulty) is given for the reader to try. This promotes reinforcement of the subject material. Some of the solutions are given and I only wish I had them all. In short the best advanced classical mechanics book I have come across.
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