Foundations Of Mechanics (on Demand Printing Of 30102)
Foundations Of Mechanics (on Demand Printing Of 30102)By: Ralph Abraham 
Lowest New Price: $80.00List Price: $92.00 Average Customer Rating: 4.5 out of 5 Description:In the Spring of 1966, I gave a series of lectures in the Princeton University Department of Physics, aimed at recent mathematical results in mechanics, especially the work of Kolmogorov, Arnold, and Moser and its application to Laplace’s question of stability of the solar system. Mr. Marsden’s notes of the lectures, with some revision and expansion by both of us, became this book.Although the lectures were attended equally by mathematicians and physicists, our goal was to make the subject available to the nonspecialists. Therefore, the mathematical background assumed was dictated by the physics graduate students in the audience. Hoping this would be typical of the people interested in this subject, I have made the same assumptions in the book.Thus, we take for granted basic undergraduate calculus and linear algebra, and a limited amount of classical analysis, point set topology, and elementary mechanics. Then we begin with modern advanced calculus, and go on to a complete and self-contained treatment of graduate level classical mechanics.--From the Preface to the First Edition Publisher: Westview Press Customer Review: 4 out of 5 The rest of the book is dedicated to dynamical systems, including a fac-simile of a paper of Kolmogorov. However, the topics could be trated with less fuss (as, for example, in the marvellous little and sadly out-of-print book of David Ruelle). Customer Review: 5 out of 5 Photographs of mathematicians from Gauss and Legendre right up to the most venerable living mathematicians are included in a picture gallery at the front of the book. This is excellent. The book requires as a beginning, all the material regarding the Hamiltonian and Lagrangian formulations of mechanics - which means you won't have a clue about what the book is saying until you have got somewhat beyond the second year at university. Then the authors start discussing topology, and the ideas which are necessary to re-formulate ideas in quite different clothing. This is very hard - the reader really needs to know about very hard mathematics. Ideas about point set topology are essential because the subject matter encompasses chaotic behaviour and the many body problem. Newtons equations (and this surprises many people) lead to large systems of non-linear equations - and the general theory of the solution of such systems leads almost inevitably to poincare point sets, winding numbers, and so forth. The theory of integral operators (see Kranoselsky, et al) has long been couched in these terms. Get this by all means, and prepare to have a hard journey ahead. I should mention that many parts of the book are quite readable and the authors go out of their way to reach the reader as far as possible. It's actually a physically large book, it would be probably better to get the hard back edition if it's available. Customer Review: 4 out of 5 All necessary background is self-contained. However, the book is difficult and I would not recommend it as a first learning text. For that I would send you to Frankel's _The Geometry of Physics_. --> Find out more about "Foundations Of Mechanics (on Demand Printing Of 30102)" at Amazon.com or Order Now |
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