| Symmetry in Mechanics 2004 Edition Contributor(s): Singer, Stephanie Frank (Author) |
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ISBN: 0817641459 ISBN-13: 9780817641450 Publisher: Birkhauser OUR PRICE: $56.99 Product Type: Paperback - Other Formats Published: March 2001 Annotation: "Symmetry in Mechanics is directed to students at the undergraduate level and beyond, and offers a lovely presentation of the subject...The first chapter presents a standard derivation of the equations for two-body planetary motion. Kepler's laws are then obtained and the rule of conservation laws is emphasized. ..... Singer uses this example from classical physics throughout the book as a vehicle for explaining the concepts of differential geometry and for illustrating their use. ... These ideas and techniques will allow the reader to understand advanced texts and research literature in which considerably more difficult problems are treated and solved by identical or related methods. The book contains 122 student exercises, many of which are solved in an appendix. The solutions, especially, are valuable for showing how a mathematician approaches and solves specific problems. Using this presentation, the book removes some of the language barriers that divide the worlds of mathematics and physics..." ---- Physics Today Recent years have seen the appearance of several books bridging the gap between mathematics and physics; most are aimed at the graduate level and above. Symmetry in Mechanics: A Gentle, Modern Introduction is aimed at anyone who has observed that symmetry yields simplification and wants to know why. The monograph was written with two goals in mind: to chip away at the language barrier between physicists and mathematicians and to link the abstract constructions of symplectic mechanics to concrete, explicitly calculated examples. The context is the two-body problem, i.e., the derivation of Kepler's Laws of planetary motion from Newton's laws of gravitation. After astraightforward and elementary presentation of this derivation in the language of vector calculus, subsequent chapters slowly and carefully introduce symplectic manifolds, Hamiltonian flows, Lie group actions, Lie algebras, momentum maps and symplectic reduction, with many examples, illustrations and exercises. The work ends with the derivation it started with, but in the more sophisticated language of symplectic and differential geometry. For the student, mathematician or physicist, this gentle introduction to mechanics via symplectic reduction will be a rewarding experience. The freestanding chapter on differential geometry will be a useful supplement to any first course on manifolds. The book contains a number of exercises with solutions, and is an excellent resource for self-study or classroom use at the undergraduate level. Requires only competency in multivariable calculus, linear algebra and introductory physics. |
| Additional Information |
| BISAC Categories: - Science | Physics - Mathematical & Computational - Science | Mechanics - General - Mathematics | Group Theory |
| Dewey: 531 |
| LCCN: 00049398 |
| Physical Information: 0.49" H x 6.15" W x 9.26" (0.81 lbs) 193 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: "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 taught: 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 required: we introduce and illustrate all necessary con- structs. |
