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Chases and Escapes:
The Mathematics of Pursuit and Evasion
Paul J. Nahin
With a new preface by the author

Book Description | Reviews
Introduction [in PDF format]

TABLE OF CONTENTS:

Preface to the Paperback Edition xiii

What You Need to Know to Read This Book (and How I Learned What I Needed to Know to Write It) xxvii

Introduction 1

Chapter 1. The Classic Pursuit Problem 7

  • 1.1 Pierre Bouguer's Pirate Ship Analysis 7
  • 1.2 A Modern Twist on Bouguer 17
  • 1.3 Before Bouguer: The Tractrix 23
  • 1.4 The Myth of Leonardo da Vinci 27
  • 1.5 Apollonius Pursuit and Ramchundra's Intercept Problem 29

Chapter 2. Pursuit of (Mostly) Maneuvering Targets 41

  • 2.1 Hathaway's Dog-and-Duck Circular Pursuit Problem 41
  • 2.2 Computer Solution of Hathaway's Pursuit Problem 52
  • 2.3 Velocity and Acceleration Calculations for a Moving Body 64
  • 2.4 Houghton's Problem: A Circular Pursuit That Is Solvable in Closed Form 78
  • 2.5 Pursuit of Invisible Targets 85
  • 2.6 Proportional Navigation 93

Chapter 3. Cyclic Pursuit 106

  • 3.1 A Brief History of the n-Bug Problem, and Why It Is of Practical Interest 106
  • 3.2 The Symmetrical n-Bug Problem 110
  • 3.3 Morley's Nonsymmetrical 3-Bug Problem 116

Chapter 4. Seven Classic Evasion Problems 128

  • 4.1 The Lady-in-the-Lake Problem 128
  • 4.2 Isaacs's Guarding-the-Target Problem 138
  • 4.3 The Hiding Path Problem 143
  • 4.4 The Hidden Object Problem: Pursuit and Evasion as a Simple Two-Person, Zero-Sum Game of Attack-and-Defend 156
  • 4.5 The Discrete Search Game for a Stationary Evader -- Hunting for Hiding Submarines 168
  • 4.6 A Discrete Search Game with a Mobile Evader -- Isaacs's Princess-and-Monster Problem 174
  • 4.7 Rado's Lion-and-Man Problem and Besicovitch's Astonishing Solution 181

Appendix A
Solution to the Challenge Problems of Section 1.1 187

Appendix B
Solutions to the Challenge Problems of Section 1.2 190

Appendix C
Solution to the Challenge Problem of Section 1.5 198

Appendix D
Solution to the Challenge Problem of Section 2.2 202

Appendix E
Solution to the Challenge Problem of Section 2.3 209

Appendix F
Solution to the Challenge Problem of Section 2.5 214

Appendix G
Solution to the Challenge Problem of Section 3.2 217

Appendix H
Solution to the Challenge Problem of Section 4.3 219

Appendix I
Solution to the Challenge Problem of Section 4.4 222

Appendix J
Solution to the Challenge Problem of Section 4.7 224

Appendix K
Guelman's Proof 229

Notes 235

Bibliography 245

Acknowledgments 249

Index 251

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File created: 11/11/2014

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