Arguably, the applicability of a mathematical theory (or its links with other well established parts of this science) is what makes it important. This book serves to justify in this sense the study of ordinary differential equations, calculus of variations, Riemannian geometry, symplectic geometry, Lie groups and Lie algebras, manifold theory as well as other more specialized subjects such as integrable systems or catastrophe theory.
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.
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Top reviews from other countries
Seungwoo Park
deteriorated printing quality, but understandable for the price I paid
Reviewed in Italy on June 1, 2023Cliente Amazon
Want to know classical mechanics and the math behind it?
Reviewed in Brazil on July 18, 2017
Lars Sørensen
This is almost a natural continuation of the excellent book "Mechanics" by Landau
Reviewed in the United Kingdom on November 26, 2013
Raul Lopez Rivera
Excelente obra, pero mal impresa.
Reviewed in Mexico on June 3, 2019Cliente Amazon
Contenuto del libro ottimo. Carta, rilegatura e stampa pessime
Reviewed in Italy on May 8, 2018