Dynamical Systems III: Mathematical Aspects Of Classical And Celestial Mechanics

by Vladimir I. Arnold

This work describes the fundamental principles, problems, and methods of classical mechanics. The authors have endeavored to give an exposition stressing the working apparatus of classical mechanics, rather than its physical foundations or applications. Chapter 1 is devoted to the fundamental mathematical models which are usually employed to describe the motion of real mechanical systems. Chapter 2 presents the n-body problem as a generalization of the 2-body problem. Chapter 3 is concerned with the symmetry groups of mechanical systems and the corresponding conservation laws. Chapter 4 contains a brief survey of various approaches to the problem of the integrability of the equations of motion. Chapter 5 is devoted to one of the most fruitful branches of mechanics - perturbation theory. Chapter 6 is related to chapters 4 and 5, and studies the theoretical possibility of integrating the equations of motion. Elements of the theory of oscillations are given in chapter 7. 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 "Encyclopaedia of Mathematical Sciences" addresses all mathematicians, physicists and enigneers.

Genres: Physics, Mathematics, Science

10 pages, Hardcover

First published November 1, 1993

About the author

Vladimir Igorevich Arnold (alternative spelling Arnol'd, Russian: Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010)[1] was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, classical mechanics and singularity theory, including posing the ADE classification problem, since his first main result—the partial solution of Hilbert's thirteenth problem in 1957 at the age of 19.