Classical Mechanics / Edition 1

by John R. Taylor

Overview

John Taylor has brought to his most recent book, Classical Mechanics, all of the clarity and insight that made his Introduction to Error Analysis a best-selling text. Classical Mechanics is intended for students who have studied some mechanics in an introductory physics course, such as “freshman physics.” With unusual clarity, the book covers most of the topics normally found in books at this level, including conservation laws, oscillations, Lagrangian mechanics, two-body problems, non-inertial frames, rigid bodies, normal modes, chaos theory, Hamiltonian mechanics, and continuum mechanics. A particular highlight is the chapter on chaos, which focuses on a few simple systems, to give a truly comprehensible introduction to the concepts that we hear so much about. At the end of each chapter is a large selection of interesting problems for the student, 744 in all, classified by topic and approximate difficulty, and ranging for simple exercises to challenging computer projects. A Student Solutions Manual is also available.Adopted by more than 450 colleges and universities in the US and Canada and translated into six languages, Taylor’s Classical Mechanics is a thorough and very readable introduction to a subject that is four hundred years old but as exciting today as ever. The author manages to convey that excitement as well as deep understanding and insight.

Product Details

ISBN-13:	9781891389221
Publisher:	University Science Books
Publication date:	09/15/2004
Edition description:	2005
Pages:	786
Sales rank:	262,616
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

John Taylor received his B.A. in math from Cambridge University in 1960 and his Ph.D. in theoretical physics from Berkeley in 1963. He is professor emeritus of physics and Presidential Teaching Scholar at the University of Colorado, Boulder. He is the author of some 40 articles in research journals; a book, Classical Mechanics; and three other textbooks, one of which, An Introduction to Error Analysis, has been translated into eleven foreign languages. He received a Distinguished Service Citation from the American Association of Physics Teachers and was named Colorado Professor of the Year in 1989. His television series Physics for Fun won an Emmy Award in 1990. He retired in 2005 and now lives in Washington, D.C.

Table of Contents

Part I: THE ESSENTIALS1. Newton’s Laws of Motion1.1 Classical Mechanics1.2 Space and Time1.3 Mass and Force1.4 Newton’s First and Second Laws; Inertial Frames1.5 The Third Law and Conservation of the Momentum1.6 Newton’s Second Law in Cartesian Coordinates1.7 Two-Dimensional Polar Coordinates1.8 Problems for Chapter 12. Projectiles and Charged Particles2.1 Air Resistance2.2 Linear Air Resistance2.3 Trajectory and Range in a Linear Motion2.4 Quadratic Air Resistance2.5 Motion of a Charge in a Uniform Magnetic Field2.6 Complex Exponentials2.7 Solution for the Charge in a B Field2.8 Problems for Chapter 23. Momentum and Angular Momentum3.1 Conservation of Momentum3.2 Rockets3.3 The Center of Mass3.4 Angular Momentum for a Single Particle3.5 Angular Momentum for Several Particles3.6 Problems for Chapter 34. Energy4.1 Kinetic Energy and Work4.2 Potential Energy and Conservative Forces4.3 Force as the Gradient of Potential Energy4.4 The Second Condition that F be Conservative4.5 Time-Dependent Potential Energy4.6 Energy for Linear One-Dimensional Systems4.7 Curvilinear One-Dimensional Systems4.8 Central Forces4.9 Energy of Interaction of Two Particles4.10 The Energy of a Multiparticle System4.11 Problems for Chapter 45. Oscillations5.1 Hooke’s Law5.2 Simple Harmonic Motion5.3 Two-Dimensional Oscillators5.4 Damped Oscillators5.5 Driven Damped Oscillations5.6 Resonance5.7 Fourier Series5.8 Fourier Series Solution for the Driven Oscillator5.9 The RMS Displacement; Parseval’s Theorem5.10 Problems for Chapter 56. Calculus of Variations6.1 Two Examples6.2 The Euler-Lagrange Equation6.3 Applications of the Euler-Lagrange Equation6.4 More than Two Variables6.5 Problems for Chapter 67. Lagrange’s Equations7.1 Lagrange’s Equations for Unconstrained Motion7.2 Constrained Systems; an Example7.3 Constrained Systems in General7.4 Proof of Lagrange’s Equations with Constraints7.5 Examples of Lagrange’s Equations7.6 Conclusion7.7 Conservation Laws in Lagrangian Mechanics7.8 Lagrange’s Equations for Magnetic Forces7.9 Lagrange Multipliers and Constraint Forces7.10 Problems for Chapter 78. Two-Body Central Force Problems8.1 The Problem8.2 CM and Relative Coordinates; Reduced Mass8.3 The Equations of Motion8.4 The Equivalent One-Dimensional Problems8.5 The Equation of the Orbit8.6 The Kepler Orbits8.7 The Unbonded Kepler Orbits8.8 Changes of Orbit8.9 Problems for Chapter 89. Mechanics in Noninertial Frames9.1 Acceleration without Rotation9.2 The Tides9.3 The Angular Velocity Vector9.4 Time Derivatives in a Rotating Frame9.5 Newton’s Second Law in a Rotating Frame9.6 The Centrifugal Force9.7 The Coriolis Force9.8 Free Fall and The Coriolis Force9.9 The Foucault Pendulum9.10 Coriolis Force and Coriolis Acceleration9.11 Problems for Chapter 910. Motion of Rigid Bodies10.1 Properties of the Center of Mass10.2 Rotation about a Fixed Axis10.3 Rotation about Any Axis; the Inertia Tensor10.4 Principal Axes of Inertia10.5 Finding the Principal Axes; Eigenvalue Equations10.6 Precession of a Top Due to a Weak Torque10.7 Euler’s Equations10.8 Euler’s Equations with Zero Torque10.9 Euler Angles10.10 Motion of a Spinning Top10.11 Problems for Chapter 1011. Coupled Oscillators and Normal Modes11.1 Two Masses and Three Springs11.2 Identical Springs and Equal Masses11.3 Two Weakly Coupled Oscillators11.4 Lagrangian Approach; the Double Pendulum11.5 The General Case11.6 Three Coupled Pendulums11.7 Normal Coordinates11.8 Problems for Chapter 11Part II: FURTHER TOPICS12. Nonlinear Mechanics and Chaos12.1 Linearity and Nonlinearity12.2 The Driven Damped Pendulum or DDP12.3 Some Expected Features of the DDP12.4 The DDP; Approach to Chaos12.5 Chaos and Sensitivity to Initial Conditions12.6 Bifurcation Diagrams12.7 State-Space Orbits12.8 Poincare Sections12.9 The Logistic Map12.10 Problems for Chapter 1213. Hamiltonian Mechanics13.1 The Basic Variables13.2 Hamilton’s Equations for One-Dimensional Systems13.3 Hamilton’s Equations in Several Dimensions13.4 Ignorable Coordinates13.5 Lagrange’s Equations vs. Hamilton’s Equations13.6 Phase-Space Orbits13.7 Liouville’s Theorem13.8 Problems for Chapter 1314. Collision Theory14.1 The Scattering Angle and Impact Parameter14.2 The Collision Cross Section14.3 Generalizations of the Cross Section14.4 The Differential Scattering Cross Section14.5 Calculating the Differential Cross Section14.6 Rutherford Scattering14.7 Cross Sections in Various Frames14.8 Relation of the CM and Lab Scattering Angles14.9 Problems for Chapter 1415. Special Relativity15.1 Relativity15.2 Galilean Relativity15.3 The Postulates of Special Relativity15.4 The Relativity of Time; Time Dilation15.5 Length Contraction15.6 The Lorentz Transformation15.7 The Relativistic Velocity-Addition Formula15.8 Four-Dimensional Space-Time; Four-Vectors15.9 The Invariant Scalar Product15.10 The Light Cone15.11 The Quotient Rule and Doppler Effect15.12 Mass, Four-Velocity, and Four-Momentum15.13 Energy, the Fourth Component of Momentum15.14 Collisions15.15 Force in Relativity15.16 Massless Particles; the Photon15.17 Tensors15.18 Electrodynamics and Relativity15.19 Problems for Chapters 1516. Continuum Mechanics16.1 Transverse Motion of a Taut String16.2 The Wave Equation16.3 Boundary Conditions; Waves on a Finite String16.4 The Three-Dimensional Wave Equation16.5 Volume and Surface Forces16.6 Stress and Strain: the Elastic Moduli16.7 The Stress Tensor16.8 The Strain Tensor for a Solid16.9 Relation between Stress and Strain: Hooke’s Law16.10 The Equation of Motion for an Elastic Solid16.11 Longitudinal and Transverse Waves in a Solid16.12 Fluids: Description of the Motion16.13 Waves in a Fluid16.14 Problems for Chapter 16Appendix: Diagonalizing Real Symmetric Matrices

Editorial Reviews

Taylor’s Classical Mechanics is an excellent compromise between Marion, which contains too much material explained in too much detail for my tastes, and Fowles, which is much too terse. It is accessible for strong second-semester sophomores and is probably about right for first-semester juniors. The computer exercises in the end-of-chapter problems are particularly welcome.

Alma C. Zook

I expect to use Professor Taylor’s book at every opportunity. It is a fabulous example of clarity and precision – one of my very favorite physics texts.

Ben Newling

Taylor’s book is unique among classical mechanics texts. It comprehensively covers the field at the Sophomore/Junior level. At the same time, it is immensely readable, a quality that comparable texts lack.

Jonathan Friedman

The book is excellent. The core of a truly superb mechanics course is covered in Taylor’s text. I, personally, want this book now.

Robert Pompi

I will never sell this book. When I’m a strict, bitter old professor, it will be Classical Mechanics by John R. Taylor that I will remember as the book that renewed my love for such a beautiful subject.

Student of Mathematics and Physics at University o Dmitry

A superb text. The clarity and readability of the book is so much better than anything else on the market, that I confidently predict this book will soon be the most widely used book on the subject in all American universities, and probably Canadian and European universities also. I judge it to be at least ten times better, maybe more, than the other two popular classical mechanics books on the market right now, the book by Fowles, which students say is too terse to understand, and the book by Marion and Thornton, which students say is so wordy and lengthy that they feel quickly lost.

American Journal of Physics

I taught this same course several times using a different, but well known, textbook. In my estimation, Taylor’s book is far superior. It is very sensibly organized, and can be read without hopping back and forth between sections or chapters. The introduction of variational principles and Lagrangian mechanics is seamless, and conducted fairly early on. The students grasped it much more quickly than I anticipated…Kudos to Taylor.

Michael Cavagnero