Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics)
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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
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I feel the most vital portions of this book are the appendices. They provide introductions to subjects which are important for researchers, one being on contact manifolds (Contact structures) which are important when one has an odd-dimensional manifold. Other topics are dynamical system symmetries and normal forms and to many fields they are still relevant for researchers.
I would suggest this book for those who seek a deeper mathematical understanding of Mechanics, so can be seen as the step beyond Goldstein for example. Compared to other books of Geometric Mechanics it is docile. Walter Thirring's book "Classical Mathematical Physics" is actually more rigorous and Prop-Proof based. If someone wishes to dive even deeper, one can check out Souriau's "Structure of Dynamical Systems" or the mammoth tome "Foundations of Mechanics" by Ralph Abraham and John Marsden.
For dynamical systems and nonlinear dynamics researchers, this is a great book to mature mathematical tools and ideas.
There are many other books on classical mechanics, some of them stronger than this one in some respects but this is the book to read if you do not want or can't consult a whole library. Foundations of Mechanics by Abraham and Marsden is a colossal treatise that certainly seeks to be a reference work rather than a textbook, it can be useful as a place to look for details you cannot find in the appendices of Arnold's book; Introduction to Mechanics and Symmetry by Marsden and Ratiu is more accessible, the historical comments and abundance of examples are very interesting or/and enlightening, however the order and choice of material is somewhat puzzling, it is inevitable to compare it with Arnold's brilliant layout: one begins with Newtonian/Galileian approach and subsequently those methods are refined and generalized with the Lagrangian and Hamiltonian formalisms.
Very worth mentioning are the appendices which constitute almost half of the current edition of Arnold's book: one can find there from an intuitive discussion of Riemannian geometry and the generalization to finite and infinite dimensional Lie groups, made by Arnold in the sixties, of Euler's equations for the rigid body, to discussions of the now so popular momentum maps, Poisson structures, Kähler manifolds, KdV equations and a bit of KAM theory.
Do not expect this book to give you (as a previous reviewer wrote) all the epsilons and deltas and explicit formulae you might be used to find in a textbook, the arguments are very concise and sometimes the proofs are cryptic but very often the intuitive idea and the geometrical insight of a proposition is all that is required to produce a rigorous proof and that's exactly what this book gives you.
Top international reviews
It uses more sophisticated mathematics than Landau, but covers the same topics - and some more.
An absolute must-read.
La carta sembra quella delle risme più economiche, la stampa è quella ottenibile dopo una serie di più scansioni e stampe successive. Alcuni caratteri sono a malapena leggibili.
La rilegatura è pessima: i fogli non sono cuciti, ma solo incollati. Il libro si apre a fatica e la copertina sembra distaccarsi dalle pagine da un momento all'altro.
Ho letto che in molti hanno avuto problemi simili relativamente a libri Springer acquistati da Amazon. Sembra siano stampati su richiesta.
Non comprerò mai più un libro Springer da Amazon, se non a un prezzo stracciato.
Cette évaluation concerne seulement la qualité de l'impréssion et la reliure. L'ouvrage mérite bien plus de 5 étoiles.
Escogieron un papel muy barato y la impresión es de muy mala calidad.
El libro tiene una enorme cantidad de ejemplos en caracteres pequeños que no se pueden leer debido a la mala impresión; la mayoría de estos están incompletos.
Al ser el papel de tan mala calidad, el libro es demasiado grueso para el número de páginas que lo constituyen, y, además, el empastado, que se supone es de pasta gruesa, está mal elegido para el grosor que tiene el libro.
Esta versión no tiene nada que ver con la que se imprimía antes, por lo que el precio es totalmente injusto para la calidad del libro haciéndolo al menos 3 veces más caro de lo que uno recibe.