Non-linear Oscillations
2nd Edition
Published on 1. August 1988
Book
Paperback/Softback
300 pages
978-0-19-856194-1 (ISBN)
Description
In this book, systems described in terms of non-linear ordinary differential equations are treated. An attempt is made to convey to engineers and physicists the basic ideas of the dynamic behaviour of non-linear systems and to provide a view of some of the phenomena and solution methods in non-linear oscillations. In this revised edition the author has updated the book, added a chapter on optimal control and new material on bifurcation theory and Hopf's theorem. Applications of the theory may be found not only in classical mechanics, but also in electronics, communications, biology and other branches of science.
More details
Edition
2nd Revised edition
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Oxford University Press
Target group
College/higher education
Professional and scholarly
Edition type
Revised edition
Illustrations
114 line illustrations, bibliography
ISBN-13
978-0-19-856194-1 (9780198561941)
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Schweitzer Classification
Persons
Content
Part 1 The mathematical pendulum as an illustration of linear and non-linear oscillations - systems which are similar to a simple linear oscillator: Undamped free oscillations of the pendulum; damped free oscillations; forced oscillations. Part 2 Liapounov stability theory and bifurcations: The concept of Liapounov stability; the direct method of Liapounov; stability by the first approximation; the Poincare map; the critical case of a conjugate pair of eigenvalues; simple bifurcation of equilibria and the Hopf bifurcation. Part 3: Self-excited oscillations in mechanical and electrical systems; analytical approximation methods for the computation of self-excited oscillations; analytical criteria for the existence of limit cycles; forced oscillations in self-excited systems; self-excited oscillations in systems with several degrees of freedom; Part 4 Hamiltonian systems: Hamiltonian differential equations in mechanics; canonical transformations; the Hamilton-Jacobi differential equation; canonical transformations and the motion; perturbation theory; Part 5 Introduction to the theory of optimal control: Control problems, controllability; the Pontryagin maximum principle; transversality conditions and problems with target sets; canonical perturbation theory in optimal control.