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Mathematical Methods of Classical Mechanics
 
 
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Mathematical Methods of Classical Mechanics (Hardcover)

de V.I. Arnol'd (Author), K. Vogtmann (Translator), A. Weinstein (Translator) "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..." En savoir plus
5.0étoiles sur 5  Voir tous les commentaires (9 évaluations de client)
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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


Product Description

In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
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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. Lire la première page
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Plat recto | Droit d'auteur | Table des matières | Extrait | Index | Plat verso
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9 évaluations
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5.0étoiles sur 5 (9 évaluations de client)
 
 
 
 
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5.0étoiles sur 5 Best book on CM, Fév 26 2004
Par Janosch Lenzi (Firenze, Fi Italy) - Voir tous mes commentaires
(REAL NAME)   
This review is from: Mathematical Methods of Classical Mechanics (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.
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5.0étoiles sur 5 Encyclopedic, Mai 8 2002
Par Professor Joseph L. McCauley "Joseph L. McCauley" (Austria+Texas) - Voir tous mes commentaires
(TOP 1000 REVIEWER)   
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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5.0étoiles sur 5 The best, but challenging for not-mathematicians, Oct. 21 2001
Par Francesco Pedulla (Rome, ITALY) - Voir tous mes commentaires
(REAL NAME)   
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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 		 Commentaires client les plus récents

5.0étoiles sur 5 After reading Arnold
After reading Arnold, I know no other authors of classical mechanics.
Publié le Fév 15 2001 par Li-yu-xuan

5.0étoiles sur 5 Clear and to the point
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... Read more
Publié le Déc 28 2000

5.0étoiles sur 5 little to say
This book is an example of great scientific writing style. Not all the epsilon and deltas are spelled out, and yet the the proofs are nowhere short of rigorous. Read more
Publié le Oct. 24 2000 par Giuseppe A. Paleologo

5.0étoiles sur 5 Great for mathematicians trying to understand physicists.
This book has theorems and proofs, unlike most mechanics books. Being a mathematics book, the objects are clearly defined and the hypothesis clearly stated. Read more
Publié le Sep 18 1999

5.0étoiles sur 5 A Masterpiece. The Best Book on Classical Mechanics.
Throw away Goldstein. This book is the bible of classical mechanics
Publié le Mai 5 1999

5.0étoiles sur 5 The best ever book on classical mechanics.
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... Read more
Publié le Janv. 28 1998

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