Mathematical Aspects of Classical and Celestial Mechanics

1 Basic Principles of Classical Mechanics

2 The n-Body Problem

3 Symmetry Groups and Order Reduction

4 Variational Principles and Methods

5 Integrable Systems and Integration Methods

6 Perturbation Theory for Integrable Systems

7 Non-Integrable Systems

8 Theory of Small Oscillations

9 Tensor Invariants of Equations of Dynamics

References.

V.I.Arnold

Famous 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

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

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. 1989

From 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,