Symmetry in Mechanics

Rating:
Summary: A welcome book
Review: There are a number of books available on the "geometric" view of physics (Classical Mathematical Physics, by Thirring, The Geometry of Physics, by Frankel, and Foundations of Mechanics, by Abraham & Marsden). The size, level of sophistication and extensive background assumed by these books can be very intimidating. On the other hand, the subject "looks" beautiful, and the benefits of using geometric intuition are desirable to many people.

Singer's book stands class of its own in these respects. All the basics of the geometrical "machinery" are there, in a book that is only 224 pages in length. Chapter one starts with a standard derivation of the equations of the "two-body planetary motion" problem; subsequent chapters proceed to introduce the necessary modern geometrical and mathematical concepts (differential geometry). The final chapter then revisits the "planetary motion" problem using the modern concepts previously introduced. Excellent!

There are some misprints, but the author has a Web page of errata. The book has numerous exercises, with many solutions included. I find myself rereading parts of this book over and over.

Reader be warned; the concepts are new, and it does take work to internalize them. However, this is the most accessible book on the subject available, and also one of the most affordable. The author references many other books, for the reader who wants to go further in the mastery of this subject (one excellent book which is not mentioned, however, is "Differential Forms: A Complement to Vector Calculus", by Weintraub). Enjoy!

Rating:
Summary: Poorly written
Review: This is one of the very few books which I returned for refund.
The subject is intrinsicly interesting, and there is a need for a serious introductory text addressing the subject of geometry and physics. This one badly falls short, - carelessly written, with numerous irrelevant asides. She seems even to fail to realize that there exist three distinct geometric solutions to the Kepler problem. The bound, elliptic case is only one.
This book has supposedly been written for high-undergraduate students or early-year graduate students. It serves neither adequately.