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Dynamical Systems III

Dynamical Systems III
Catalogue Information
Field name Details
Dewey Class 530.1
Title Dynamical Systems III ([EBook]) / edited by Vladimir I. Arnold.
Added Personal Name Arnold, Vladimir Igorevic , 1937-2010. editor.
Other name(s) SpringerLink (Online service)
Publication Berlin, Heidelberg : Springer , 1988.
Physical Details XIV, 294 pages, 3 illus. : online resource.
Series Encyclopaedia of mathematical sciences 0938-0396 ; ; 3
ISBN 9783662025352
Summary Note This work describes the fundamental principles, problems, and methods of elassical mechanics focussing on its mathematical aspects. The authors have striven to give an exposition stressing the working apparatus of elassical mechanics, rather than its physical foundations or applications. This appara­ tus is basically contained in Chapters 1, 3,4 and 5. Chapter 1 is devoted to the fundamental mathematical models which are usually employed to describe the motion of real mechanical systems. Special consideration is given to the study of motion under constraints, and also to problems concerned with the realization of constraints in dynamics. Chapter 3 is concerned with the symmetry groups of mechanical systems and the corresponding conservation laws. Also discussed are various aspects of the theory of the reduction of order for systems with symmetry, often used in applications. Chapter 4 contains abrief survey of various approaches to the problem of the integrability of the equations of motion, and discusses some of the most general and effective methods of integrating these equations. Various elassical examples of integrated problems are outlined. The material pre­ sen ted in this chapter is used in Chapter 5, which is devoted to one of the most fruitful branches of mechanics - perturbation theory. The main task of perturbation theory is the investigation of problems of mechanics which are" elose" to exact1y integrable problems.:
Contents note 1. Basic Principles of Classical Mechanics -- 2. The n-Body Problem -- 3. Symmetry Groups and Reduction (Lowering the Order) -- 4. Integrable Systems and Integration Methods -- 5. Perturbation Theory for Integrable Systems -- 6. Nonintegrable Systems -- 7. Theory of Small Oscillations -- Comments on the Bibliography -- Recommended Reading.
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