Symmetry in Mechanics: A Gentle, Modern Introduction

by Stephanie Frank Singer

"And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu­ dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has talented but ap­ preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning. To suit this audience, the author eschews density of topics and efficiency of presentation in favor of a gentler tone, a coherent story, digressions on mathe­ maticians, physicists and their notations, simple examples worked out in detail, and reinforcement of the basics. Dense and efficient texts play a crucial role in the education of budding (and budded) mathematicians and physicists. This book does not presume to improve on the classics in that genre. Rather, it aims to provide those classics with a large new generation of appreciative readers. This text introduces some basic constructs of modern symplectic geometry in the context of an old celestial mechanics problem, the two-body problem. We present the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation, first in the style of an undergraduate physics course, and x Preface then again in the language of symplectic geometry. No previous exposure to symplectic geometry is we introduce and illustrate all necessary con­ structs.

Genres: Physics, Mathematics, Science

205 pages, Paperback

First published March 1, 2001

Reviews

[Kiselev · Rating 5 out of 5]

Beautiful book. Clear exposition of linear symplectic geometry as underlying structure in classical mechanics using simple examples and tools. For those who want a quick answer (or example) of how to/why use symplectic geometry (and groups) in Physics. It's a side reading for a serious course...although there are many experienced physicist who don't know this approach to symmetries which lays in the structure of modern theories..hope that changes.

[Erik]

Very gentle way into modern mathematics and mechanics at an advanced level. Although the author doesn't mention it (yet) these results obtained for the classical Hamiltonian and symplectic spaces are by no means confined to classical mechanics but apply to quanta too (Weyl we're on the subject). I'll have to read it one more time to do the probs.