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Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics) (Englisch) Gebundene Ausgabe – 1989


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Produktinformation

  • Gebundene Ausgabe: 520 Seiten
  • Verlag: Springer; Auflage: 2nd ed. 1989. Corr. 4th printing 1997 (1989)
  • Sprache: Englisch
  • ISBN-10: 0387968903
  • ISBN-13: 978-0387968902
  • Größe und/oder Gewicht: 15,6 x 3 x 23,4 cm
  • Durchschnittliche Kundenbewertung: 5.0 von 5 Sternen  Alle Rezensionen anzeigen (4 Kundenrezensionen)
  • Amazon Bestseller-Rang: Nr. 77.263 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)
  • Komplettes Inhaltsverzeichnis ansehen

Produktbeschreibungen

Pressestimmen

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

Synopsis

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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Einleitungssatz
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. Lesen Sie die erste Seite
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Die hilfreichsten Kundenrezensionen

2 von 2 Kunden fanden die folgende Rezension hilfreich Von Ein Kunde am 18. September 1999
Format: Gebundene Ausgabe
This book has theorems and proofs, unlike most mechanics books. Being a mathematics book, the objects are clearly defined and the hypothesis clearly stated. If you are a math student trying to understand physicists then this is clearly the best book to read. This is also a good place to find a motivated proof of the general Stokes' theorem for differential forms. The standard treatment defines d of a form and then magically proves stokes' theorem. Here it is done the other way around, and the mysterious definition of d is made into the theorem.
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4 von 5 Kunden fanden die folgende Rezension hilfreich Von Professor Joseph L. McCauley am 21. Dezember 2003
Format: Gebundene Ausgabe
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 Hase' in the field.
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5 von 6 Kunden fanden die folgende Rezension hilfreich Von Ein Kunde am 5. Mai 1999
Format: Gebundene Ausgabe
Throw away Goldstein. This book is the bible of classical mechanics
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2 von 3 Kunden fanden die folgende Rezension hilfreich Von Ein Kunde am 28. Januar 1998
Format: Gebundene Ausgabe
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!
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Die hilfreichsten Kundenrezensionen auf Amazon.com (beta)

Amazon.com: 17 Rezensionen
44 von 48 Kunden fanden die folgende Rezension hilfreich
The best, but challenging for not-mathematicians 21. Oktober 2001
Von Francesco Pedulla - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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.
42 von 47 Kunden fanden die folgende Rezension hilfreich
Encyclopedic 8. Mai 2002
Von Professor Joseph L. McCauley - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
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.
17 von 17 Kunden fanden die folgende Rezension hilfreich
Wonderful 26. Oktober 2007
Von Nicholas Hoell - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
This book is an excellent introduction to the world of classical physics for NON-PHYSICISTS. While some physicists will no doubt find it accessible, there is considerable reduction of physical concepts in order to get to the heart of the ideas underlying the formalism. Also, the material goes beyond what most physicists (non-theoreticians) will find practical.

He focuses largely on a geometric presentation, in the language of differential geometry, symplectic geometry, differential forms, Riemannian manifolds and includes a large amount of algebraic necessities. This is not a cookbook for learning how to solve classical mechanics, nor is it a math book per se, but it is a wonderful collection of introductions to a vast amount of useful mathematical formalism that permeates the physical literature. I would strongly recommend it to someone needing a thorough supplementary mechanics text, one that relies on very little physical insight and focuses on the geometric and algebraic structures underlying them.

The chapters are very well self-contained for the most part so you can skip to topics you find more appealing without feeling lost. Also, his presentation style is very clever, in case you're a fan of quick thinking and novel presentations (who isn't?).

The prerequisites are familiarity with somewhat advanced calculus and "mathematical maturity". Basic knowledge of group theory would also make it an easier read.
29 von 33 Kunden fanden die folgende Rezension hilfreich
little to say 24. Oktober 2000
Von Giuseppe A. Paleologo - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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. Besides, they convey insight and intuition: the opposite of Gallavotti's "the element of mechanics" (a very competent book, but obsessed with details). As all the great mathematicians, Arnold separates what's essential from what is not, what is interesting from what is pedantic. It The result is a challenging, wonderful book. I used it (partially) as a second year undergraduate text, and the teacher stressed in the first class that "if you understand Arnold you know classical mechanics". My advice is: get a good grasp of differential geometry and topology and of the tools of the trade (mathematical analysis, ODEs, PDEs) before studying it. Otherwise it will be still readable, but will not be fully appreciated. A last note: it's interesting that Stephen Smale, a mathematician whoshare many interests with V.I.Arnold and is equally illustrious, is another master of style and clarity. You may want to check his book on dynamical systems and his essays.
21 von 23 Kunden fanden die folgende Rezension hilfreich
The best ever book on classical mechanics. 28. Januar 1998
Von Ein Kunde - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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!
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