Read more about Variational Principles in Classical Mechanics - Revised Second Edition

Variational Principles in Classical Mechanics - Revised Second Edition

(1 review)

Douglas Cline, University of Rochester

Copyright Year: 2018

Last Update: 2019

ISBN 13: 9780998837260

Publisher: University of Rochester River Campus Libraries

Language: English

Formats Available

Conditions of Use

Attribution-NonCommercial-ShareAlike Attribution-NonCommercial-ShareAlike


Learn more about reviews.

Reviewed by Ryan Cooper, Assistant Prof-in-Residence, University of Connecticut on 6/24/21

The book covers a wide range of variational methods in Physics starting with the Newtonian vector-based framework and moving into the principle of least action and variational methods. It is fully comprehensive in its treatment of physics theories... read more

Table of Contents

  • 1 A brief history of classical mechanics
  • 2 Review of Newtonian mechanics 
  • 3 Linear oscillators
  • 4 Nonlinear systems and chaos
  • 5 Calculus of variations
  • 6 Lagrangian dynamics
  • 7 Symmetries, Invariance and the Hamiltonian
  • 8 Hamiltonian mechanics
  • 9 Hamilton’s Action Principle
  • 10 Nonconservative systems
  • 11 Conservative two-body central forces
  • 12 Non-inertial reference frames
  • 13 Rigid-body rotation
  • 14 Coupled linear oscillators
  • 15 Advanced Hamiltonian mechanics
  • 16 Analytical formulations for continuous systems
  • 17 Relativistic mechanics
  • 18 The transition to quantum physics
  • 19 Epilogue

Ancillary Material

  • Submit ancillary resource
  • About the Book

    Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th – 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.

    This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.

    This second edition adds discussion of the use of variational principles applied to the following topics:

    1. Systems subject to initial boundary conditions
    2. The hierarchy of the related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries
    3. Non-conservative systems.
    4. Variable-mass systems.
    5. The General Theory of Relativity.

    The first edition of this book can be downloaded at the publisher link.

    About the Contributors


    Douglas Cline received his BSc 1st Class Honours in Physics, (1957) and his PhD in Physics (1963) both from the University of Manchester. He joined the University of Rochester in 1963 as a Research Associate, and was promoted to Assistant Professor (1965), Associate Professor(1970), and Professor (1977). At the University of Rochester Nuclear Structure Research Laboratory he served as Associate Director (1977-88) and Director (1988-1999). He has held visiting appointments at Laval University, (1965), Niels Bohr Institute in Copenhagen (1973), Lawrence Berkeley Laboratory (1975-76), Australian National University (1978), and the University of Uppsala (1981). He is a Fellow of the American Physical Society (1981), and a recipient of the Lawrence Berkeley Laboratory Gammasphere Dedication Award (1995), the Award for Excellence in Teaching from the Department of Physics and Astronomy (2007, 2009), and the 2013 Marian Smoluchowski Medal from the Polish Physical Society.

    Contribute to this Page

    Suggest an edit or add missing content