Mathematical Aspects of Classical and Celestial Mechanics

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 Moscow 1965 Lenin Award of the Government of the U.S.S.R. 1976 Honorary Member, London Mathematical Society 1979 Honorary Doctor, University P. and M. Curie, Paris 1982 Carfoord Award of the Swedish Academy 1983 Foreign Member, National Academy, U.S.A. 1984 Foreign Member, Academy of Sciences, Paris 1987 Foreign Member, Academy of Arts and Sciences, U.S.A. 1988 Honorary Doctor, Warwick University, Coventry 1988 Foreign Member, Royal Soc. London, GB 1988 Foreign Member, Accademia Nazionale dei Lincei, Rome, Italy 1990 Member, Academy of Sciences, Russia 1990 Foreign Member, American Philosophical Society 1991 Honorary Doctor, Utrecht 1991 Honorary Doctor, Bologna 1991 Member, Academy of Natural Sciences, Russia 1991 Member, Academia Europaea 1992 N.V. Lobachevsky Prize of Russian Academy of Sciences 1994 Harvey Prize Technion Award 1994 Honorary Doctor, University of Madrid, Complutense 1997 Honorary Doctor, University of Toronto, Canada 2001 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 Sciences 1994 State Prize of the Russian Federation 1995 Member, Russian Academy of Natural Sciences 2000 S.V. Kovalevskaya Prize of Russian Academy of Sciences 2000 Member, Academy of Sciences, Russia 2003 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))

• 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.

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, 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)