The Noisy Pendulum, by M. Gitterman
The Noisy Pendulum, by M. Gitterman, Singapore, World Scientific, 2008, 120 pp., £25.00 (hardback), ISBN 978 981 283 299 3. Scope: monograph. Level: undergraduate, graduate and general reader.
The pendulum provides the simplest model for the description of nonlinear dynamical behaviour. Although this would have been a matter of concern for the many generations whose time was set by the harmonic motion of the pendulum of a grandfather clock, this aspect of pendulum dynamics has ensured that careful attention is given to its elucidation. However, the behaviour of the pendulum has implications for a number of other physical phenomena whose dynamics, as shown in this book, are isomorphic to that of the pendulum: e.g. Brownian motion, charge density waves and parametric resonance. The author also points to use of the model of the noisy pendulum in chemical reaction; biophysics; super-ionic conductors; plasma physics; surface diffusion; polymer dynamics and more. Placed in that wider context the author's motivation for compiling a ‘pendulum dictionary’ becomes very clear.
The author indicates the target audience as being ‘researchers working in different fields where the pendulum model is applicable’ and also expresses the hope that ‘teachers and students will find some useful material in the book’. As someone who initiates a course in nonlinear dynamics with a study of the simple pendulum this reviewer can confirm that he has found a lot of useful material in the book. However, this is not a text book – no examples and exercises are included.
The book is relatively short but nevertheless the author treats the subject whilst only assuming prior knowledge of basic mechanics and differential equations. For this reason it is expected that this book would be enjoyably read by anyone with such a background and hence the audience may be slightly broader than expected by the author. Nevertheless, one would expect that it will be the targeted research audience which will derive the greatest benefit from this book.
The development of the subject matter is clear and methodical. The treatment begins with the familiar discussion of the simple pendulum. Significantly the author uses the term ‘mathematical pendulum’ thus explicitly signifying the nature of the approach. However, the physical significance of the behaviour is made clear. Having recovered the dynamics of the basic pendulum action the treatment is extended by adding to the physical aspects which are included. Clearly from the book's title we expect to have the role of noise carefully explicated and indeed this is done. Then, with a view to drawing out the nonlinear dynamics, the effects of driving the pendulum are considered leading to a discussion of deterministic chaos in this simple mechanical system. The behaviour of the inverted pendulum is also examined.
The description of the mathematical aspects is clear and succinct. The presentation is aided by a number of very clear diagrams and an index is available to guide the reader when necessary. Although not highly germane, one may remark that the book is very well produced and has an attractive cover – by which it is fair to judge the content of this book.
© 2010, K. Alan Shore