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Introduction to Analytical Dynamics

Revised Edition

  • Nicholas Woodhouse

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Nicholas M. J. Woodhouse
    Pages 1-33
  3. Nicholas M. J. Woodhouse
    Pages 35-66
  4. Nicholas M. J. Woodhouse
    Pages 67-98
  5. Nicholas M. J. Woodhouse
    Pages 99-113
  6. Nicholas M. J. Woodhouse
    Pages 115-145
  7. Nicholas M. J. Woodhouse
    Pages 147-160
  8. Nicholas M. J. Woodhouse
    Pages 161-182
  9. Nicholas M. J. Woodhouse
    Pages 183-224
  10. Nicholas M. J. Woodhouse
    Pages 225-228
  11. Back Matter
    Pages 229-240

About this book

Introduction

Analytical dynamics forms an important part of any undergraduate programme in applied mathematics and physics: it develops intuition about three-dimensional space and provides invaluable practice in problem solving.

First published in 1987, this text is an introduction to the core ideas. It offers concise but clear explanations and derivations to give readers a confident grasp of the chain of argument that leads from Newton’s laws through Lagrange’s equations and Hamilton’s principle, to Hamilton’s equations and canonical transformations.

This new edition has been extensively revised and updated to include:

  • A chapter on symplectic geometry and the geometric interpretation of some of the coordinate calculations. 
  • A more systematic treatment of the conections with the phase-plane analysis of ODEs; and an improved treatment of Euler angles.
  • A greater emphasis on the links to special relativity and quantum theory, e.g., linking Schrödinger’s equation to Hamilton-Jacobi theory, showing how ideas from this classical subject link into contemporary areas of mathematics and theoretical physics.

Aimed at second- and third-year undergraduates, the book assumes some familiarity with elementary linear algebra, the chain rule for partial derivatives, and vector mechanics in three dimensions, although the latter is not essential. A wealth of examples show the subject in action and a range of exercises – with solutions – are provided to help test understanding.

Keywords

Analytical Dynamics Hamiltonian mechanics Lagrangian mechanics Mechanics Theoretical physics classical mechanics linear optimization

Authors and affiliations

  • Nicholas Woodhouse
    • 1
  1. 1.Mathematical InstituteUniversity of OxfordOxfordUnited Kingdom

Bibliographic information