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Chases and Escapes:
The Mathematics of Pursuit and Evasion
Paul J. Nahin

Book Description | Reviews
Introduction [HTML] or [PDF format]

TABLE OF CONTENTS:

What You Need to Know to Read This Book (and How I Learned What I Needed to Know to Write It) xiii
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: 4/17/2014

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