Chases and Escapes: The Mathematics of Pursuit and Evasion

By Paul J. Nahin | Go to book overview

Chapter 1
The Classic
Pursuit Problem

1.1 Pierre Bouguer’s Pirate Ship Analysis

Modern mathematical pursuit analysis is generally assumed to begin with a problem posed and solved by the French mathematician and hydrographer Pierre Bouguer (1698–1758) in 1732. This general assumption is not quite correct, as I’ll soon elaborate, but Bouguer’s problem is today nevertheless taken as the starting point of pursuit analysis in all modern textbooks, and I’ll do the same here. In his paper, read before the French Academy on January 16, 1732, and published in the Academy’s Mémoires de l’Académie Royale des Sciences in 1735, Bouguer treated the case of a pirate ship pursuing a fleeing merchant vessel, as illustrated in figure 1.1.1. The pirate ship and the merchant vessel are taken to be at (0,0) and (x0, 0) at time t = 0, respectively, the instant the pursuit begins, with the merchant vessel traveling at constant speed Vm along the vertical line x = x0. The pirate ship travels at constant speed Vp along a curved path such that it is always moving directly toward the merchant, that is, the velocity vector of the pirate ship points directly at the merchant vessel at every instant of time. Bouguer’s problem was to determine the equation y = y(x) of the curved path which he called the courbe (or ligne) de poursuite, the curve

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