am 21. Dezember 2003
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.
am 18. September 1999
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.
am 28. Januar 1998
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!