Classical Mechanics

Gregory’s Classical Mechanics is a major new textbook for undergraduates in mathematics and physics. It is a thorough, self-contained and highly readable account of a subject many students find difficult. The author’s clear and systematic style promotes a good understanding of the subject; each concept is motivated and illustrated by worked examples, while problem sets provide plenty of practice for understanding and technique. Computer assisted problems, some suitable for projects, are also included. The book is structured to make learning the subject easy; there is a natural progression from core topics to more advanced ones and hard topics are treated with particular care. A theme of the book is the importance of conservation principles. These appear first in vectorial mechanics where they are proved and applied to problem solving. They reappear in analytical mechanics, where they are shown to be related to symmetries of the Lagrangian, culminating in Noether’s theorem.

Table of Contents

Part One NEWTONIAN MECHANICS OF A SINGLE PARTICLE

Chapter One The algebra and calculus of vectors

Chapter Two Velocity, acceleration and scalar angular velocity

Chapter Three Newton’s laws of motion and the law of gravitation

Chapter Four Problems in particle dynamics

Chapter Five Linear oscillations and normal modes

Chapter Six Energy conservation

Chapter Seven Orbits in a cent ral field including Rutherford scattering

Chapter Eight Non-linear oscillations and phase space

Part Two MULTI-PARTICLE SYSTEMS AND CONSERVATION PRINCIPLES

Chapter Nine The energy principle and energy conservation

Chapter Ten The linear momentum principle and linear momentum conservation

Chapter Eleven The angular momentum principle and angular momentum conservation

Part Three ANALYTICAL MECHANICS

Chapter Twelve Lagrange’s equations and conservation principles

Chapter Thirteen The calculus of variations and Hamilton’s principle

Chapter Fourteen Hamilton’s equations and phase space

Part Four FURTHER TOPICS

Appendix Centers of mass and moments of inertia

A.1 CENTRE OF MASS

A.2 MOMENT OF INERTIA

A.3 PARALLEL AND PERPENDICULAR AXES

About the Author

Douglas Gregory is Professor of Mathematics at the University of Manchester. He is a researcher of international standing in the field of elasticity, and has held visiting positions at New York University, the University of British Columbia, and the University of Washington. He is highly regarded as a teacher of applied mathematics: this, his first book, is the product of many years ‘ teaching experience.