Classical Mechanics is a textbook about that subject written by Herbert Goldstein, a professor at Columbia University. Intended for advanced undergraduate and beginning graduate students, it has been one of the standard references in its subject around the world since its first publication in 1950.
Overview
In the second edition, Goldstein corrected all the errors that had been pointed out, added a new chapter on perturbation theory, a new section on Bertrand's theorem, and another on Noether's theorem. Other arguments and proofs were simplified and supplemented.
Before the death of its primary author in 2005, a new (third) edition of the book was released, with the collaboration of Charles P. Poole and John L. Safko from the University of South Carolina. In the third edition, the book discusses at length various mathematically sophisticated reformations of Newtonian mechanics, namely analytical mechanics, as applied to particles, rigid bodies and continua. In addition, it covers in some detail classical electromagnetism, special relativity, and field theory, both classical and relativistic. There is an appendix on group theory. New to the third edition include a chapter on nonlinear dynamics and chaos, a section on the exact solutions to the three-body problem obtained by Euler and Lagrange, a discussion of the damped driven pendulum that explains the Josephson junctions. This is counterbalanced by the reduction of several existing chapters motivated by the desire to prevent this edition from exceeding the previous one in length. For example, the discussions of Hermitian and unitary matrices were omitted because they are more relevant to quantum mechanics rather than classical mechanics, while those of Routh's procedure and time-independent perturbation theory were reduced.
Table of Contents (3rd Edition)
Preface
Chapter 1: Survey of Elementary Principles
Chapter 2: Variational Principles and Lagrange's Equations
Chapter 3: The Central Force Problem
Chapter 4: The Kinematics of Rigid Body Motion
Chapter 5: The Rigid Body Equations of Motion
Chapter 6: Oscillations
Chapter 7: The Classical Mechanics of the Special Theory of Relativity
Chapter 8: The Hamilton Equations of Motion
Chapter 9: Canonical Transformations
Chapter 10: Hamilton–Jacobi Theory and Action-Angle Coordinates
Chapter 11: Classical Chaos
Chapter 12: Canonical Perturbation Theory
Chapter 13: Introduction to the Lagrangian and Hamiltonian Formulations for Continuous Systems and Fields Appendix A: Euler Angles in Alternate Conventions and Cayley–Klein Parameters Appendix B: Groups and Algebras Appendix C: Solutions to Select Exercises Select Bibliography Author Index Subject Index
Editions
Reception
First edition
S.L. Quimby of Columbia University noted that the first half of the first edition of the book is dedicated to the development of Lagrangian mechanics with the treatment of velocity-dependent potentials, which are important in electromagnetism, and the use of the Cayley-Klein parameters and matrix algebra for rigid-body dynamics. This is followed by a comprehensive and clear discussion of Hamiltonian mechanics. End-of-chapter references improve the value of the book. Quimby pointed out that although this book is suitable for students preparing for quantum mechanics, it is not helpful for those interested in analytical mechanics because its treatment omits too much. Quimby praised the quality of printing and binding which make the book attractive.
In the Journal of the Franklin Institute, Rupen Eskergian noted that the first edition of Classical Mechanics offers a mature take on the subject using vector and tensor notations and with a welcome emphasis on variational methods. This book begins with a review of elementary concepts, then introduces the principle of virtual work, constraints, generalized coordinates, and Lagrangian mechanics. Scattering is treated in the same chapter as central forces and the two-body problem. Unlike most other books on mechanics, this one elaborates upon the virial theorem. The discussion of canonical and contact transformations, the Hamilton-Jacobi theory, and action-angle coordinates is followed by a presentation of geometric optics and wave mechanics. Eskergian believed this book serves as a bridge to modern physics.