UK Nonlinear News, August 2002
Cambridge University Press, 1 June 2000
When you think about experiments in nonlinear dynamics, the work of Libchaber, Mullin & Swinney usually springs to mind. If fluids is not your area, you may think of Roy for lasers or Winfree for biological problems. In all of these cases, the low dimensional theoretical ideas of nonlinear dynamics are being tested on infinite dimensional systems (the delay in the lasers allow them to qualify).
As far as I am aware, none of these authors has yet to write a book solely devoted to the experimental method. Moon has a great collection of experimental results to read through but of necessity the methodology can only be hinted at. By and large if you want to find out about how to do experiments in this area as well as how to integrate them with the theory, you have to go to the original papers.
Virgin´s book is an attempt to fill this gap by focusing attention on low dimensional mechanical systems. At a stroke, he has asked experimental questions directly of the theory in areas where it was originally developed. He has also done so in a way that can easily be followed and understood by readers. For that alone, he deserves enormous praise. He states that his (disparate) target audience is mechanical engineers, theoreticians and experimentalists in other areas. If he can convert the first group alone, then he will have achieved something formidable.
But it must be said that there are things wrong with the book which may well put off some of his target groups.
Mechanical engineers have of course moved away from (open loop) low dimensional systems a long time ago. Somehow the significant emphasis on mathematics, the relatively short discussions of experimental detail and the poor photographs of experimental apparatus make this book look as if it had been written by a theoretician (not so if he had made more of a fuss in the text about the website of the book - see below).
On the other hand, theoreticians will be appalled by the errors and omissions. For example, manifolds are never explained, some of the Latex is dreadful (I simply can't understand equations (3.7) - (3.11)) and just how many different vector notations does a book need? And just who or what is Liousville? A typo perhaps but in the index too?. Liouville the man, Louisville the city but Liousville?
The enormous strength of this book is the fact that Virgin has brought together real experimental results with nonlinear theory and found agreement. But these occasions are few and far between; to some extent Virgin has done himself few favours by downgrading his experimental achievements at the expense of the theory.
One final comment. There is a very good website associated with this book, at http://mems.egr.duke.edu/Nonlinear/Book.html.
Mentioned just once, in the Preface, the web site is a real treat. Fuzzy black and white pictures in the book appear with greater clarity and in full colour on the site. The whole thing is integrated with the book (including extra material in the form of downloadable videos) but you would never know it was there if you skipped the Preface. A second edition of this book should contain references throughout the text to this material, as and when it is needed. That really would make an impression on those target groups.
UK Nonlinear News thanks Cambridge University Press for providing a review copy of this book.
A listing of books reviewed in UK Nonlinear News is available.