# Mathematical Aspects of Classical and Celestial Mechanics

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Oktober 2006

## Beschreibung

### Beschreibung

This work describes the fundamental principles, problems, and methods of classical mechanics. The main attention is devoted to the mathematical side of the subject. The authors have endeavored to give an exposition stressing the working apparatus of classical mechanics. The book is significantly expanded compared to the previous edition. The authors have added two chapters on the variational principles and methods of classical mechanics as well as on tensor invariants of equations of dynamics. Moreover, various other sections have been revised, added or expanded. The main purpose of the book is to acquaint the reader with classical mechanics as a whole, in both its classical and its contemporary aspects. The book addresses all mathematicians, physicists and engineers. From the reviews of the previous editions: "... 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, Nov. 1989.### Inhaltsverzeichnis

Basic Principles of Classical Mechanics.- The n-Body Problem.- Symmetry Groups and Order Reduction.- Variational Principles and Methods.- Integrable Systems and Integration Methods.- Perturbation Theory for Integrable Systems.- Non-Integrable Systems.- Theory of Small Oscillations.- Tensor Invariants of Equations of Dynamics.### Portrait

V.I.ArnoldFamous author of various Springer books in the field of dynamical systems, differential equations, hydrodynamics, magnetohydrodynamics, classical and celestial mechanics, geometry, topology, algebraic geometry, symplectic geometry, singularity theory

1958 Award of the Mathematical Society of Moscow1965 Lenin Award of the Government of the U.S.S.R.1976 Honorary Member, London Mathematical Society1979 Honorary Doctor, University P. and M. Curie, Paris1982 Carfoord Award of the Swedish Academy1983 Foreign Member, National Academy, U.S.A.1984 Foreign Member, Academy of Sciences, Paris1987 Foreign Member, Academy of Arts and Sciences, U.S.A.1988 Honorary Doctor, Warwick University, Coventry1988 Foreign Member, Royal Soc. London, GB1988 Foreign Member, Accademia Nazionale dei Lincei, Rome, Italy1990 Member, Academy of Sciences, Russia1990 Foreign Member, American Philosophical Society1991 Honorary Doctor, Utrecht1991 Honorary Doctor, Bologna1991 Member, Academy of Natural Sciences, Russia1991 Member, Academia Europaea1992 N.V. Lobachevsky Prize of Russian Academy of Sciences1994 Harvey Prize Technion Award1994 Honorary Doctor, University of Madrid, Complutense1997 Honorary Doctor, University of Toronto, Canada2001 Wolf Prize of Wolf Foundation

V.V.Kozlov

Famous Springer author working in the field of general principles of dynamics, integrability of equations of motion, variational methods in mechanics, rigid body dynamics, stability theory, non-holonomic mechanics, impact theory, symmetries and integral invariants, mathematical aspects of statistical mechanics, ergodic theory and mathematical physics.

1973 Lenin Komsomol Prize (the major prize for young scientists in USSR)1986 M.V. Lomonosov 1st Degree Prize (the major prize awarded by M.V. Lomonosov Moscow State University)1988 S. A. Chaplygin Prize of Russian Academy of Sciences1994 State Prize of the Russian Federation1995 Member, Russian Academy of Natural Sciences2000 S.V. Kovalevskaya Prize of Russian Academy of Sciences2000 Member, Academy of Sciences, Russia2003 Foreign member of the Serbian Science Society

A.I.Neishtadt

Neishtadt is also Springer Author, working in the field of perturbation theory (in particular averaging of perturbations, adiabatic invariants), bifurcation theory, celestial mechanics

2001 A.M.Lyapunov Prize of Russian Academy of Sciences (joint with D.V.Anosov))

### Pressestimmen

From the reviews of the previous editions: "... As an encyclopaedia article, this book does not seek to serve as a textbook, nor to replace the original articles whose results it describes. 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, Nov. 1989 "This is a book to curl up with in front of a fire on a cold winter's evening. ..." SIAM Reviews, Sept. 1989From the reviews of the third edition:

"Mathematical Aspects of Classical and Celestial Mechanics is the third volume of Dynamical Systems section of Springer's Encyclopaedia of Mathematical sciences. ... if you wanted an idea of the broad scope of classical mechanics, this is a good place to visit. One advantage of the present book is that the authors are particularly skilled in balancing rigor with physical intuition. ... The authors provide an extensive bibliography and a well-selected set of recommended readings. Overall, this is a thoroughly professional offering." (William J. Satzer, MathDL, January, 2007)

"The new edition is a considerable updating of the last. ... it is a reference for experts that will pull them back from their narrow subarea of expertise, give them a vast overview of what other experts know, and send them to the references if they actually want to be able to use something. ... In conclusion, this is a book that every mathematical library must own and that many experts will want to have on their shelves." (James Murdock, SIAM Review, Vol. 49 (4), 2007)

"This book is the third English edition of an already classical piece devoted to classical mechanics as a whole, in its traditional and contemporary aspects ... . The book is significantly expanded with respect to its previous editions ... enriching further its already important contribution of acquainting mathematicians, physicists and engineers with the subject. ... New chapters on variational principles and tensor invariants were added, making the book more self-contained. ... Its purpose is to serve as a detailed guide on the subject ... ." (Ernesto A. Lacomba, Mathematical Reviews, Issue 2008 a)

EAN: 9783540282464

ISBN: 3540282467

Untertitel: Originaltitel: Matematicheskie Aspekty Klassicheskoj i Nebesnoj Mekhaniki.
'Encyclopaedia of Mathematical Sciences'.
3rd ed. 2006.
Book.
Sprache: Englisch.

Verlag: Springer

Erscheinungsdatum: Oktober 2006

Seitenanzahl: 536 Seiten

Übersetzer/Sprecher: Übersetzt von E. Khukhro

Format: gebunden

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