Dynamical Systems III
By: edited by Vladimir I. Arnold
Series: Encyclopaedia of Mathematical Sciences -- 3; Encyclopaedia of Mathematical Sciences -- 3
Publisher: Springer Berlin Heidelberg
Published: 1988
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 294
ISBN-13: 9783662025376; 9783662025352
Subjects: Global analysis (Mathematics); Physics
Description: 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.
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Table of contents: title: Contents: Basic Principles of Classical Mechanics; title: The n-Body Problem; title: Symmetry Groups and Reduction (Lowering the Order); title: Integrable Systems and Integration Methods; title: Perturbation Theory for Integrable Systems; title: Nonintegrable Systems; title: Theory of Small Oscillations; title: Comments on the Bibliography; title: Recommended Reading; title: Bibliography; title: Index.