Classical Mechanics, Second Edition

Book Preface

This book presents a reasonably complete account of the theoretical mechanics of particles and systems for physics students at the advanced undergraduate level. It is evolved from a set of lecture notes for a course on the subject, which I have taught at California State University, Stanislaus, for many years. We presume that the student has been exposed to a calculus-based general physics course (from a textbook such as that by Halliday and Resnick) and a course in calculus (including the handling of differentiations of field functions). No prior knowledge of differential equations is required. Differential equations and new mathematical methods are developed in the text as the occasion demands. Vectors are used from the start.

The book has 17 chapters, and with appropriate omission, the essential topics can be covered in a one-semester, four-hour course. We do not make any specific suggestions for a shorter course. We usually vary the topics to suit the ability and mathematical background of the students. We would encourage the more enthusiastic and able students to attempt to master on their own the material not covered in class (for extra credit).

A major departure of this book from the conventional approach is the introduction of the Lagrangian and Hamiltonian formulatio of mechanics at an early stage. In the conventional approach to the subject, Lagrangian and Hamiltonian formulations are presented near the end of the course, and students rarely develop a reasonable familiarity with these essential methods.

The choice of topics and their treatment throughout the book are intended to emphasize the modern point of view. Applications to other branches of physics are made wherever possible. Special note is made of concepts that are important to the development of modern physics. Also, the relationship between symmetries and the laws of conservation—a subject directly relevant to the most modern developments of physics—is emphasized.

The student will find that a generous amount of detail has been given in mathematical manipulations, and that occurrences of “it may be shown that” have been kept to a minimum. However, to ensure that the student does not lose sight of the development underway, some of the more lengthy and tedious algebraic manipulations have been omitted when possible.

Each chapter contains a set of homework problems of varying degrees of difficulty. They are intended to supplement or amplify the material in the text and are arranged in the order in which the material is covered in the chapter. No effort has been made to trace the origins of the homework problems and examples in our book.

We have omitted a discussion of the historical development of the subject. This is because of the length of the book, not a lack of interest on the author’s part. Also, references to the original literature have been omitted except for recent works to which the student may be expected to have access. Many individuals have been very helpful in the preparation of this text. I wish to thank my colleagues at California State University, Stanislaus, for many helpful suggestions and discussions.

Tai L. Chow
Monterey Park, CA