Symmetry in Mechanics

A Gentle, Modern Introduction

  • Stephanie Frank Singer

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Stephanie Frank Singer
    Pages 1-4
  3. Stephanie Frank Singer
    Pages 5-18
  4. Stephanie Frank Singer
    Pages 47-63
  5. Stephanie Frank Singer
    Pages 65-82
  6. Stephanie Frank Singer
    Pages 83-100
  7. Stephanie Frank Singer
    Pages 101-112
  8. Stephanie Frank Singer
    Pages 113-122
  9. Stephanie Frank Singer
    Pages 123-139
  10. Back Matter
    Pages 141-193

About this book

Introduction

"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.

Keywords

Lie group Lie groups algebra classical mechanics differential geometry ksa linear algebra manifold symplectic geometry sympletic geometry

Authors and affiliations

  • Stephanie Frank Singer
    • 1
  1. 1.PhiladelphiaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0189-2
  • Copyright Information Stephanie Frank Singer 2004
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-8176-4145-0
  • Online ISBN 978-1-4612-0189-2
  • About this book