Classical Mechanics with Mathematica®

  • Romano Antonio

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introduction to Linear Algebra and Differential Geometry

    1. Front Matter
      Pages 1-1
    2. Antonio Romano
      Pages 3-15
    3. Antonio Romano
      Pages 17-28
    4. Antonio Romano
      Pages 29-40
    5. Antonio Romano
      Pages 41-59
    6. Antonio Romano
      Pages 61-65
    7. Antonio Romano
      Pages 67-93
    8. Antonio Romano
      Pages 95-103
    9. Antonio Romano
      Pages 105-115
    10. Antonio Romano
      Pages 117-133
    11. Antonio Romano
      Pages 135-158
  3. Mechanics

    1. Front Matter
      Pages 159-159
    2. Antonio Romano
      Pages 161-176
    3. Antonio Romano
      Pages 177-196
    4. Antonio Romano
      Pages 197-213
    5. Antonio Romano
      Pages 215-246
    6. Antonio Romano
      Pages 247-260
    7. Antonio Romano
      Pages 261-286
    8. Antonio Romano
      Pages 287-335

About this book

Introduction

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject.  Developed by the author from 35 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Lagrange—while also painting a clear picture of the most modern developments.  Throughout, it makes heavy use of the powerful tools offered by Mathematica®​.

The volume is organized into two parts.  The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book.  Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus.  The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others.

With a unique selection of topics and a large array of exercises to reinforce concepts, Classical Mechanics with Mathematica is an excellent resource for graduate students in physics.  It can also serve as a reference for researchers wishing to gain a deeper understanding of both classical and modern mechanics.

Keywords

Lagrangian and Hamiltonian dynamics classical mechanics, Mathematica differential geometry kinematics linear algebra rigid body dynamics

Authors and affiliations

  • Romano Antonio
    • 1
  1. 1.“Federico II”, Dipartimento di Matematica e App.Università degli Studi di NapoliNapoliItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8352-8
  • Copyright Information Springer Science+Business Media New York 2012
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8351-1
  • Online ISBN 978-0-8176-8352-8
  • Series Print ISSN 2164-3679
  • Series Online ISSN 2164-3725
  • About this book