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Classical Mechanics with Mathematica®

  • Antonio Romano
  • Addolorata Marasco

Table of contents

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

    1. Front Matter
      Pages 1-1
    2. Antonio Romano, Addolorata Marasco
      Pages 3-16
    3. Antonio Romano, Addolorata Marasco
      Pages 17-29
    4. Antonio Romano, Addolorata Marasco
      Pages 31-42
    5. Antonio Romano, Addolorata Marasco
      Pages 43-62
    6. Antonio Romano, Addolorata Marasco
      Pages 63-67
    7. Antonio Romano, Addolorata Marasco
      Pages 69-96
    8. Antonio Romano, Addolorata Marasco
      Pages 97-106
    9. Antonio Romano, Addolorata Marasco
      Pages 107-118
    10. Antonio Romano, Addolorata Marasco
      Pages 119-135
    11. Antonio Romano, Addolorata Marasco
      Pages 137-160
  3. Mechanics

    1. Front Matter
      Pages 161-161
    2. Antonio Romano, Addolorata Marasco
      Pages 163-178
    3. Antonio Romano, Addolorata Marasco
      Pages 179-198
    4. Antonio Romano, Addolorata Marasco
      Pages 199-216
    5. Antonio Romano, Addolorata Marasco
      Pages 217-249
    6. Antonio Romano, Addolorata Marasco
      Pages 251-265
    7. Antonio Romano, Addolorata Marasco
      Pages 267-291
    8. Antonio Romano, Addolorata Marasco
      Pages 293-343
    9. Antonio Romano, Addolorata Marasco
      Pages 345-380
    10. Antonio Romano, Addolorata Marasco
      Pages 381-397
    11. Antonio Romano, Addolorata Marasco
      Pages 399-426
    12. Antonio Romano, Addolorata Marasco
      Pages 427-455
    13. Antonio Romano, Addolorata Marasco
      Pages 457-471
    14. Antonio Romano, Addolorata Marasco
      Pages 473-504
    15. Antonio Romano, Addolorata Marasco
      Pages 505-537
    16. Antonio Romano, Addolorata Marasco
      Pages 539-567
    17. Antonio Romano, Addolorata Marasco
      Pages 569-597
    18. Antonio Romano, Addolorata Marasco
      Pages 599-619
  4. Back Matter
    Pages 621-644

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 authors from over 30 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 Hamilton—while also painting a clear picture of the most modern developments.

The text 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.  This new edition has been completely revised and updated and now includes almost 200 exercises, as well as new chapters on celestial mechanics, one-dimensional continuous systems, and variational calculus with applications.  Several Mathematica® notebooks are available to download that will further aid students in their understanding of some of the more difficult material.

Unique in its scope of coverage and method of approach, Classical Mechanics with Mathematica® will be useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics. 

Reviews of the First Edition:

“The volume represents a real contribution to the field, being useful not only to students but to all readers who wish to have correct and well-written information.” – Petre P. Teodorescu, zbMATH, Vol. 1263, 2013

“By centering his presentation around the major aspects and omitting less important details, the author succeeds in providing a concise though lucid introduction into the mathematical areas.  It enjoys many qualities that render this book a promising candidate for becoming a standard text in physics classrooms.” – H. Hogreve, Mathematical Reviews, October 2013

Keywords

Classical Mechanics Analytical Mechanics Differential Geometry Point Dynamics Rigid Body Dynamics Statistical Mechanics Newtonian Gravitation Lagrangian Dynamics Hamiltonian Dynamics

Authors and affiliations

  • Antonio Romano
    • 1
  • Addolorata Marasco
    • 2
  1. 1.Università degli Studi di Napoli Federico IINaplesItaly
  2. 2.Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”Università degli Studi di Napoli Federico IINaplesItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-77595-1
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-77594-4
  • Online ISBN 978-3-319-77595-1
  • Series Print ISSN 2164-3679
  • Series Online ISSN 2164-3725
  • Buy this book on publisher's site