Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists [Hardcover]

J. M. T. Thompson (Author), H. B. Stewart (Author)

Book Description

ISBN-10: 0471909602 | ISBN-13: 978-0471909606 | Publication Date: August 1986 | Edition: 1

Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists J. M. T. Thompson, FRS, University College, London H. B. Stewart, Brookhaven National Laboratory This book is the first comprehensive, systematic account of nonlinear dynamics and chaos, one of the fastest-growing disciplines of applicable mathematics. It is highly illustrated and written in a clear, comprehensible style, progressing gently from the most elementary to the most advanced ideas while requiring little previous knowledge of mathematics. Examples of applications to a wide variety of scientific fields introduce concepts of instabilities, bifurcations and catastrophes, and particular attention is given to the vital new ideas of chaotic behaviour and unpredictability in deterministic systems. This is a book for systems analysts, for mathematicians, and for all those in any field of science or technology who use computers to model systems which change over time. Contents Preface 1 Introduction Part I Basic Concepts of Nonlinear Dynamics 2 An overview of nonlinear phenomena; 3 Point attractors in autonomous systems; 4 Limit cycles in autonomous systems; 5 Periodic attractors in driven oscillators; 6 Chaotic attractors in forced oscillators; 7 Stability and bifurcations of equilibria and cycles Part II Iterated Maps as Dynamical Systems 8 Stability and bifurcation of maps; 9 Chaotic behaviour of one- and two-dimensional maps Part III Flows, Outstructures, and Chaos 10 The geometry of recurrence; 11 The Lorenz system; 12 Rössler’s band; 13 Geometry of bifurcation Part IV Applications in the Physical Sciences 14 Subharmonic resonances of an offshore structure; 15 Chaotic motions of an impacting system; 16 The particle accelerator and Hamiltonian dynamics; 17 Experimental observations of order and chaos References and Bibliography Index

Product Details

• Hardcover: 392 pages
• Publisher: John Wiley & Sons; 1 edition (August 1986)
• Language: English
• ISBN-10: 0471909602
• ISBN-13: 978-0471909606
• Product Dimensions: 9.1 x 6.1 x 1.2 inches
• Shipping Weight: 1.5 pounds
• Average Customer Review: 3.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,920,093 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

3 of 4 people found the following review helpful:

4.0 out of 5 stars Good Introduction To Chaos, March 26, 2004

By 

Scott Rodriguez (Piqua, OH United States) - See all my reviews

This review is from: Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists (Hardcover)

The book is complex enough to provide good information on NLD, chaos, and the associated differential equations, but not so complex you can't get a firm working grasp of the subject. Lots of nice illustrations, clearly and concisely explained. Bifurcations, attractors and all that jazz is in there too if you want to make your own Poincare maps (also explained). I used the information from the book to generate visualizations of an externally excited system moving in and out of different modes of vibration. Such a techinique is not directly explaned in the text, but a good read of the first few chapters will provide the tools to do so. Recommended.

2 of 5 people found the following review helpful:

2.0 out of 5 stars Not that good, February 6, 2005

By 

Janosch Lenzi (Firenze, Fi Italy) - See all my reviews
(REAL NAME)   

This review is from: Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists (Hardcover)

This book contains some standard topics treated on an elementary way. Unfortunatelly mathemathical formalism is almost left out.
The approach to the subject is pretty popular.
I think one is going to invest her/his own time in a better way by working first on V.I.Arnold's "Classical Mechanics" (symplectic formalism) then going on with E. Ott's "Chaos" (one of the best on the subject, but Lichtenberg-Liebermann is also a good one, in my opinion) and, finally, taking a look into some parts of Arnold's "Geometrical methods of ODE". More stuff is available on the Web (arxiv.org --> recent abstracts and new approaches on dynamical systems in Physics). This is a good way to gain a technical basis instead of a popular one.