# Classical Mechanics

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."

### Summary

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.

### Table of Contents

**Part I: THE ESSENTIALS**

**Newton’s Laws of Motion**1.1 Classical Mechanics

1.2 Space and Time

1.3 Mass and Force

1.4 Newton’s First and Second Laws; Inertial Frames

1.5 The Third Law and Conservation of the Momentum

1.6 Newton’s Second Law in Cartesian Coordinates

1.7 Two-Dimensional Polar Coordinates

1.8 Problems for Chapter 1**Projectiles and Charged Particles**2.1 Air Resistance

2.2 Linear Air Resistance

2.3 Trajectory and Range in a Linear Motion

2.4 Quadratic Air Resistance

2.5 Motion of a Charge in a Uniform Magnetic Field

2.6 Complex Exponentials

2.7 Solution for the Charge in a B Field

2.8 Problems for Chapter 2**Momentum and Angular Momentum**3.1 Conservation of Momentum

3.2 Rockets

3.3 The Center of Mass

3.4 Angular Momentum for a Single Particle

3.5 Angular Momentum for Several Particles

3.6 Problems for Chapter 3**Energy**4.1 Kinetic Energy and Work

4.2 Potential Energy and Conservative Forces

4.3 Force as the Gradient of Potential Energy

4.4 The Second Condition that**F**be Conservative

4.5 Time-Dependent Potential Energy

4.6 Energy for Linear One-Dimensional Systems

4.7 Curvilinear One-Dimensional Systems

4.8 Central Forces

4.9 Energy of Interaction of Two Particles

4.10 The Energy of a Multiparticle System

4.11 Problems for Chapter 4**Oscillations**5.1 Hooke’s Law

5.2 Simple Harmonic Motion

5.3 Two-Dimensional Oscillators

5.4 Damped Oscillators

5.5 Driven Damped Oscillations

5.6 Resonance

5.7 Fourier Series

5.8 Fourier Series Solution for the Driven Oscillator

5.9 The RMS Displacement; Parseval’s Theorem

5.10 Problems for Chapter 5**Calculus of Variations**6.1 Two Examples

6.2 The Euler-Lagrange Equation6.3 Applications of the Euler-Lagrange Equation

6.4 More than Two Variables

6.5 Problems for Chapter 6**Lagrange’s Equations**

7.1 Lagrange’s Equations for Unconstrained Motion

7.2 Constrained Systems; an Example

7.3 Constrained Systems in General

7.4 Proof of Lagrange’s Equations with Constraints

7.5 Examples of Lagrange’s Equations

7.6 Conclusion

7.7 Conservation Laws in Lagrangian Mechanics

7.8 Lagrange’s Equations for Magnetic Forces

7.9 Lagrange Multipliers and Constraint Forces

7.10 Problems for Chapter 7**Two-Body Central Force Problems**8.1 The Problem

8.2 CM and Relative Coordinates; Reduced Mass

8.3 The Equations of Motion

8.4 The Equivalent One-Dimensional Problems

8.5 The Equation of the Orbit

8.6 The Kepler Orbits

8.7 The Unbonded Kepler Orbits

8.8 Changes of Orbit

8.9 Problems for Chapter 8**Mechanics in Noninertial Frames**

9.1 Acceleration without Rotation

9.2 The Tides

9.3 The Angular Velocity Vector

9.4 Time Derivatives in a Rotating Frame

9.5 Newton’s Second Law in a Rotating Frame

9.6 The Centrifugal Force

9.7 The Coriolis Force

9.8 Free Fall and The Coriolis Force

9.9 The Foucault Pendulum

9.10 Coriolis Force and Coriolis Acceleration

9.11 Problems for Chapter 9**Motion of Rigid Bodies**10.1 Properties of the Center of Mass

10.2 Rotation about a Fixed Axis

10.3 Rotation about Any Axis; the Inertia Tensor

10.4 Principal Axes of Inertia

10.5 Finding the Principal Axes; Eigenvalue Equations

10.6 Precession of a Top Due to a Weak Torque

10.7 Euler’s Equations

10.8 Euler’s Equations with Zero Torque

10.9 Euler Angles

10.10 Motion of a Spinning Top

10.11 Problems for Chapter 10**Coupled Oscillators and Normal Modes**11.1 Two Masses and Three Springs

11.2 Identical Springs and Equal Masses

11.3 Two Weakly Coupled Oscillators

11.4 Lagrangian Approach; the Double Pendulum

11.5 The General Case

11.6 Three Coupled Pendulums

11.7 Normal Coordinates

11.8 Problems for Chapter 11**Part II: FURTHER TOPICS****Nonlinear Mechanics and Chaos**12.1 Linearity and Nonlinearity

12.2 The Driven Damped Pendulum or DDP

12.3 Some Expected Features of the DDP

12.4 The DDP; Approach to Chaos

12.5 Chaos and Sensitivity to Initial Conditions

12.6 Bifurcation Diagrams

12.7 State-Space Orbits

12.8 Poincare Sections

12.9 The Logistic Map

12.10 Problems for Chapter 12**Hamiltonian Mechanics**13.1 The Basic Variables

13.2 Hamilton’s Equations for One-Dimensional Systems

13.3 Hamilton’s Equations in Several Dimensions

13.4 Ignorable Coordinates

13.5 Lagrange’s Equations vs. Hamilton’s Equations

13.6 Phase-Space Orbits

13.7 Liouville’s Theorem

13.8 Problems for Chapter 13**Collision Theory**14.1 The Scattering Angle and Impact Parameter

14.2 The Collision Cross Section

14.3 Generalizations of the Cross Section

14.4 The Differential Scattering Cross Section

14.5 Calculating the Differential Cross Section

14.6 Rutherford Scattering

14.7 Cross Sections in Various Frames

14.8 Relation of the CM and Lab Scattering Angles

14.9 Problems for Chapter 14**Special Relativity**15.1 Relativity

15.2 Galilean Relativity

15.3 The Postulates of Special Relativity

15.4 The Relativity of Time; Time Dilation

15.5 Length Contraction

15.6 The Lorentz Transformation

15.7 The Relativistic Velocity-Addition Formula

15.8 Four-Dimensional Space-Time; Four-Vectors

15.9 The Invariant Scalar Product

15.10 The Light Cone

15.11 The Quotient Rule and Doppler Effect

15.12 Mass, Four-Velocity, and Four-Momentum

15.13 Energy, the Fourth Component of Momentum

15.14 Collisions

15.15 Force in Relativity

15.16 Massless Particles; the Photon

15.17 Tensors

15.18 Electrodynamics and Relativity

15.19 Problems for Chapters 15**Continuum Mechanics**16.1 Transverse Motion of a Taut String

16.2 The Wave Equation

16.3 Boundary Conditions; Waves on a Finite String

16.4 The Three-Dimensional Wave Equation

16.5 Volume and Surface Forces

16.6 Stress and Strain: the Elastic Moduli

16.7 The Stress Tensor

16.8 The Strain Tensor for a Solid

16.9 Relation between Stress and Strain: Hooke’s Law

16.10 The Equation of Motion for an Elastic Solid

16.11 Longitudinal and Transverse Waves in a Solid

16.12 Fluids: Description of the Motion

16.13 Waves in a Fluid

16.14 Problems for Chapter 16

**Appendix: Diagonalizing Real Symmetric Matrices**

Errata for the 3^{rd} printing

*Page 91, line 4 of second paragraph: (1571□630) should read (1571-1630).

*Page 166, Figure 5.3(b): The label τ on the horizontal axis needs to move about 3 mm to the right to its tick mark. (This was correct in the first printing.)

*Page 362, Problem 9.13: “is well approximated by tan α = ” should read

“is given by sin α = ”

*Page 550, line 2 of the text: Put a dot over the *q* in ∂*q _{i}*.

### Reviews

*“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, University of Kentucky

*“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, University of New Brunswick

*“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, State University of New York, Binghamton

*“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, Amherst College

*“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, Pomona College

*“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.” *

-Dmitry, Student of Mathematics and Physics at University of Waterloo