Customer Reviews

Classical Dynamics (Dover Books on Physics)

5 star:		(1)
4 star:		(4)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

This book can be compared with Walter Rudin's Principles of Mathematical Analysis in that it is very terse and the reader must sit with pencil and paper to fill in many details, both in the theory and example problems. It is the case that this process actively engages the reader into the subject and permits a deeper, fuller understanding than just reading the results and final equations. Having less detail in the theory is understandable, but I've found that the example problems are equally as difficult to follow; this makes it increasingly tough to solve his problems (though once I solve a problem, I feel a great sense of accomplishment) On problems: the problems are very well thought out and complement the theoretical section of the text quite well.

Chronologically, "Classical Dynamics" was Donald Greewood's second major publication on Analytical Dynamics, covering more advanced topics than the ones in "Principles of Dynamics," whose first edition preceded "Classical Dynamics" by some 12 years.

"Classical Dynamics" is a somewhat more readable text, but just like its companion book, it fails to address issues like how one can use Lagrange's equations (or Hamilton's, for that matter) to correctly account for the effects of nonlinear dissipative forces. Also, its treatment of velocity-dependent potentials could be substantially extended, as could the chapter on Relativity.

On the other hand, the chapters on variational principles, the Pprinciple of Least Action, Hamilton's mechanics, and, above all, canonical transformations are an absolute "must-read"!

An updated, extended second edition would be most welcome now.

This book is an excellent read, and it explains concepts with unusual clarity. I wouldn't suggest it as a main text, but it is an excellent supplement to others, such as Goldstein or Jose and Saletan. I found this little book explained many concepts far better than these "standards" that are used in most graduate mechanics courses. It includes many nice examples. It also includes the answers to the problems in the back. How often do you see that in a graduate level book? I also think it is an excellent read for physics graduate students, who are just trying to get through the comprehensive exam rather than master the details of classical mechanics.

This is the first book review on the books I listed here that are good for students. The first subject is classical dynamics, in which I listed two books. The book I am gonna review in this post is "Classical Dynamics" by Donald T. Greenwood, Dover Publication.

This is a concise book, whose main text contains 324 pages. Such a small size gives students confidence to read it cover to cover. regarding the mathematical prerequisite, although it claims to be a graduate textbook, it assumes only familiarity with basic calculus and some knowledge in differential equations.

The book is very well organized into seven chapters. The first chapter introduces basic concepts such as generalized coordinates, constraints, virtual work, and so on that are essential and enough for the following chapters. Chapter two derives Lagrange's equations, discusses integrals of motion, and applies the theory to small oscillations. Many interesting examples are worked out in this chapter. Chapter 3 then analyzes four special applications of Lagrange's equations, namely Rayleigh's Dissipation Functions, Impulsive Motion, Gyroscopic Systems, Velocity-Dependent Potentials.

Chapter 4 turns to the other pillar of the theory of classical dynamics: Hamilton's equations. It first elaborates the Hamilton's principle with logical clarity, then derives Hamilton's equations with examples. Finally, it discusses other variational principles and Liouville's theorem.

Chapters 5 and 6 should be considered as a whole. Chapter 5 tells one how to obtain principal functions and characteristic functions by using the Hamilton-Jacobi method. Chapter 6 explores the theory of canonical transformations and its application to dyanamics in more details and in a generalized way, in vewing that a principle function is a generating function for a canonical transformation between two points in phase space. These two chapters contain lots of details that are worth reading carefully.

The last one, Chapter 7 discusses special relativity by applying previously introduced methods. However, I found that such a chapter is actually not very necessary, at least for me. If one did not know much special relativity, he/she would not expect to learn much from this chapter. If one knew special relativity very well, then he/she should simply skip the chapter. But anyway, if you like, it is still fun to read it.

Now, pros and cons. Compared to other polular or standard books on this subject, this book is very well balanced between volume, conciseness, and the amount of details, it is easy to read. The book works every example in a detailed and heuristic way, which are good for the readers to develop their own problem-solving skills. The pictorial illustrations in the book are also very nice. At the end of each chapter, there are a bunch of excercise problems carefully chosen by the author. Final resutls of these problems are given at the end of the book so that readers can check their own answers after working through the solutions by themselves. I found that these problems are extremely usefull and interesting; hence, I solved each of them step by step.

Frankly speaking, I did not find any nonnegligible disadvantage of this book. Someone has a review, saying that "it fails to address issues like how one can use Lagrange's equations (or Hamilton's, for that matter) to correctly account for the effects of nonlinear dissipative forces". But I disagree, because I think topics like nonlinear system should be better treated in a more contemporary method, e.g. in the book: Classical Dynamics: a contemporary approach.

You may feel that the book is a bit too old, since it is first published in 1977. But come on, the subject is <strong>Classical</strong> dynamics, on which a book can never be too old to read. Another overwhelming reason to own it is that it is priced at only 10.37USD. Can anybody convince me to give up this one and buy the 100USD Goldstein's book instead? No way, of course not.

A slightly different version of this review can be found on <a href="http://www.wanyidun.com/blog_r2u/?p=74">my web blog</a>.

I have always enjoyed Greenwood's book and it is much more original than most of the other engineering mechanics books out there. The only real deficiency here is a complete lack of any discussion of motion in a central force or vibrations. This is undoubtably due to the curriculum the book was designed for, but as a book these subjects should have been included for completeness. The absence of these subjects really mars an otherwise outstanding text.