Variational Principles in Classical Mechanics - Revised Second Edition
Douglas Cline, University of Rochester
Copyright Year:
Last Update: 2019
ISBN 13: 9780998837260
Publisher: University of Rochester River Campus Libraries
Language: English
Formats Available
Conditions of Use
Attribution-NonCommercial-ShareAlike
CC BY-NC-SA
Reviews
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
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 between Newton through Einstein. The Preface recommends the textbook for upper-level physics and astrophysics students, but it is a great reference for first-year graduate students in any applied physics or engineering fields as well.
The book provides a very detailed and accurate reference for physics and dynamic motion.
The textbook accurately describes Newtonian and Lagrangian frameworks. These frameworks have been in use for over 100 years. New applications will fit these frameworks easily and keep the textbook relevant.
The textbook describes each equation in detail. It could help to move proofs and derivations into their own sections if the book is meant to be accessible to non-physics majors.
The equations and definitions remain consistent throughout. Cline does a great job introducing and maintaining definitions in physics.
The chapters and examples are neatly divided. It would certainly be possible to divide the text into smaller reading sections or learning modules.
The topics are presented in a logical and clear fashion that adheres to the chronology of physics.
_Side note_: The textbook maintains the chronological development of physics, but I don't think students need to learn physics in the same progression as history created physics. Analagously, it would be like teaching students that atoms are solid spheres, then tell them they are plum pudding models, and finally revealing the latest quantum model for atoms. The author does a great job presenting physics, but I do see a need to introduce the most useful models first and then, if necessary, show students the history of physics.
As a pdf, the textbook is easy to navigate.
No grammatical errors found.
No culturally insensitive material found. __Note__: there are some examples that could be rewritten as gender-neutral, instead of assuming the sex is female. e.g. 17.3.5 simultaneaity, p. 65 the soprano singer, 12.3 pirouette,
Cline does an excellent job guiding the reader through ~300 years of physics advancements. This textbook is an excellent resource for anyone searching for reference in Newtonian and Lagrangian frameworks in physics.
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 resourceAbout 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.