The Pendulum: A Case Study in Physics / Edition 5 by Gregory L. Baker, James A. Blackburn | | 9780199557684 | Paperback | Barnes & Noble
The Pendulum: A Case Study in Physics / Edition 5

The Pendulum: A Case Study in Physics / Edition 5

by Gregory L. Baker, James A. Blackburn
     
 

ISBN-10: 0199557683

ISBN-13: 9780199557684

Pub. Date: 01/27/2009

Publisher: Oxford University Press

The pendulum: a case study in physics is a unique book in several ways. Firstly, it is a comprehensive quantitative study of one physical system, the pendulum, from the viewpoint of elementary and more advanced classical physics, modern chaotic dynamics, and quantum mechanics. In addition, coupled pendulums and pendulum analogs of superconducting devices are

Overview

The pendulum: a case study in physics is a unique book in several ways. Firstly, it is a comprehensive quantitative study of one physical system, the pendulum, from the viewpoint of elementary and more advanced classical physics, modern chaotic dynamics, and quantum mechanics. In addition, coupled pendulums and pendulum analogs of superconducting devices are also discussed. Secondly, this book treats the physics of the pendulum within a historical and cultural context, showing, for example, that the pendulum has been intimately connected with studies of the earth's density, the earth's motion, and timekeeping. While primarily a physics book, the work provides significant added interest through the use of relevant cultural and historical vignettes. This approach offers an alternative to the usual modern physics courses. The text is amply illustrated and augmented by exercises at the end of each chapter.

Product Details

ISBN-13:
9780199557684
Publisher:
Oxford University Press
Publication date:
01/27/2009
Pages:
350
Product dimensions:
7.40(w) x 9.60(h) x 0.80(d)

Table of Contents

1 Introduction 1

2 Pendulums somewhat simple 8

2.1 The beginning 8

2.2 The simple pendulum 9

2.3 Some analogs of the linearized pendulum 13

2.3.1 The spring 13

2.3.2 Resonant electrical circuit 15

2.3.3 The pendulum and the earth 16

2.3.4 The military pendulum 19

2.3.5 Compound pendulum 20

2.3.6 Kater's pendulum 21

2.4 Some connections 23

2.5 Exercises 24

3 Pendulums less simple 27

3.1 O Botafumeiro 27

3.2 The linearized pendulum with complications 29

3.2.1 Energy loss-friction 29

3.2.2 Energy gain-forcing 34

3.2.3 Parametric forcing 42

3.3 The nonlinearized pendulum 45

3.3.1 Amplitude dependent period 45

3.3.2 Phase space revisited 51

3.3.3 An electronic "Pendulum" 53

3.3.4 Parametric forcing revisited 56

3.4 A pendulum of horror 63

3.5 Exercises 64

4 The Foucault pendulum 67

4.1 What is a Foucault pendulum? 67

4.2 Frames of reference 71

4.3 Public physics 74

4.4 A quantitative approach 75

4.4.1 Starting the pendulum 78

4.5 A darker side 85

4.6 Toward a better Foucault pendulum 86

4.7 A final note 89

4.8 Exercises 91

5 The torsion pendulum 93

5.1 Elasticity of the fiber 93

5.2 Statics and dynamics 95

5.2.1 Free oscillations without external forces 96

5.2.2 Free oscillations with external forces 98

5.2.3 Damping 98

5.3 Two historical achievements 99

5.3.1 Coulomb and the electrostatic force 99

5.3.2 Cavendish and the gravitational force 104

5.3.3 Scaling the apparatus 108

5.4 Modern applications 108

5.4.1 Ballistic galvanometer 108

5.4.2 Universal gravitational constant 110

5.4.3 Universality of free fall: Equivalence of gravitational and inertial mass 113

5.4.4 Viscosity measurementsand granular media 117

5.5 Exercises 119

6 The chaotic pendulum 121

6.1 Introduction and history 121

6.2 The dimensionless equation of motion 125

6.3 Geometric representations 126

6.3.1 Time series, phase portraits, and Poincare sections 127

6.3.2 Spectral analysis 130

6.3.3 Bifurcation diagrams 133

6.4 Characterization of chaos 135

6.4.1 Fractals 135

6.4.2 Lyapunov exponents 138

6.4.3 Dynamics, Lyapunov exponents, and fractal dimension 142

6.4.4 Information and prediction 144

6.4.5 Inverting chaos 147

6.5 Exercises 150

7 Coupled pendulums 153

7.1 Introduction 153

7.2 Chaotic coupled pendulums 161

7.2.1 Two-state model (all or nothing) 164

7.2.2 Other models 168

7.3 Applications 170

7.3.1 Synchronization machine 170

7.3.2 Secure communication 173

7.3.3 Control of the chaotic pendulum 176

7.3.4 A final weirdness 183

7.4 Exercises 185

8 The quantum pendulum 189

8.1 A little knowledge might be better than none 189

8.2 The linearized quantum pendulum 192

8.3 Where is the pendulum?-uncertainty 196

8.4 The nonlinear quantum pendulum 200

8.5 Mathieu equation 201

8.6 Microscopic pendulums 203

8.6.1 Ethane-almost free 204

8.6.2 Potassium hexachloroplatinate-almost never free 206

8.7 The macroscopic quantum pendulum and phase space 208

8.8 Exercises 209

9 Superconductivity and the pendulum 211

9.1 Superconductivity 211

9.2 The flux quantum 214

9.3 Tunneling 215

9.4 The Josephson effect 216

9.5 Josephson junctions and pendulums 220

9.5.1 Single junction: RSJC model 220

9.5.2 Single junction in a superconducting loop 224

9.5.3 Two junctions in a superconducting loop 226

9.5.4 Coupled josephson junctions 228

9.6 Remarks 230

9.7 Exercises 230

10 The pendulum clock 233

10.1 Clocks before the pendulum 233

10.2 Development of the pendulum clock 235

10.2.1 Galileo (1564-1642) 235

10.2.2 Huygens (1629-1695) 235

10.2.3 The seconds pendulum and the meter: An historical note 244

10.2.4 Escapements 246

10.2.5 Temperature compensation 249

10.2.6 The most accurate pendulum clock ever made 252

10.3 Reflections 255

10.4 Exercises 255

A Pendulum Q 258

A.1 Free pendulum 258

A.2 Resonance 259

A.3 Some numbers from the real world 261

B The inverted pendulum 263

C The double pendulum 267

D The cradle pendulum 270

E The Longnow clock 273

F The Blackburn pendulum 275

Bibliography 276

Index 286

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