Classical Mechanics

Theory and Mathematical Modeling

  • Emmanuele DiBenedetto
Part of the Cornerstones book series (COR)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Emmanuele DiBenedetto
    Pages 1-31
  3. Emmanuele DiBenedetto
    Pages 33-53
  4. Emmanuele DiBenedetto
    Pages 55-92
  5. Emmanuele DiBenedetto
    Pages 93-110
  6. Emmanuele DiBenedetto
    Pages 111-140
  7. Emmanuele DiBenedetto
    Pages 141-172
  8. Emmanuele DiBenedetto
    Pages 173-205
  9. Emmanuele DiBenedetto
    Pages 207-229
  10. Emmanuele DiBenedetto
    Pages 231-256
  11. Emmanuele DiBenedetto
    Pages 257-282
  12. Emmanuele DiBenedetto
    Pages 299-333
  13. Back Matter
    Pages 335-351

About this book

Introduction

Classical mechanics is a chief example of the scientific method organizing a "complex" collection of information into theoretically rigorous, unifying principles; in this sense, mechanics represents one of the highest forms of mathematical modeling. This textbook covers standard topics of a mechanics course, namely, the mechanics of rigid bodies, Lagrangian and Hamiltonian formalism, stability and small oscillations, an introduction to celestial mechanics, and Hamilton–Jacobi theory, but at the same time features unique examples—such as the spinning top including friction and gyroscopic compass—seldom appearing in this context. In addition, variational principles like Lagrangian and Hamiltonian dynamics are treated in great detail.

Using a pedagogical approach, the author covers many topics that are gradually developed and motivated by classical examples. Through `Problems and Complements' sections at the end of each chapter, the work presents various questions in an extended presentation that is extremely useful for an interdisciplinary audience trying to master the subject. Beautiful illustrations, unique examples, and useful remarks are key features throughout the text.

Classical Mechanics: Theory and Mathematical Modeling may serve as a textbook for advanced graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference or self-study guide for applied mathematicians and mathematical physicists. Prerequisites include a working knowledge of linear algebra, multivariate calculus, the basic theory of ordinary differential equations, and elementary physics.

Keywords

Areolar Velocity Canonical Transformations Constrained Mechanical Systems Dynamics of a Point Mass Subject Geodesics Lagrange–Jacobi Identity Lagrangian Coordinates Material Systems and Measures Mathematical Pendulum Precessions and Gyroscopes Relative Rigid Motions Variational Principles

Authors and affiliations

  • Emmanuele DiBenedetto
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4648-6
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4526-7
  • Online ISBN 978-0-8176-4648-6
  • About this book