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.

In this book we describe the basic principles, problems, and methods of cl- sical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth ?rst and foremost the ¿working¿ apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical - chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord- reduction theory for systems with symmetries, which is often used in appli- tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated.

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))