# Variational Principles in Classical Mechanics - Second Edition

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Douglas Cline, University of Rochester

Copyright Year: 2018

ISBN 13: 9780998837260

Publisher: University of Rochester River Campus Libraries

Language: English

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Table of Contents

- Contents
- Preface
- Prologue
- 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 Conservative two-body central forces
- 10 Non-inertial reference frames
- 11 Rigid-body rotation
- 12 Coupled linear oscillators
- 13 Hamilton's principle of least action
- 14 Advanced Hamiltonian mechanics
- 15 Analytical formulations for continuous systems
- 16 Relativistic mechanics
- 17 The transition to quantum physics
- 18 Epilogue
- Appendices

## 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:

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

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

## About the Contributors

### Author

**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.