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ABSTRACT
This paper will discuss the differential equations which describe curves of pure pursuit, in which the pursuer's velocity is always pointing directly toward the pursued.
Keywords: pursuit, curve
(ProQuest: ... denotes formulae omitted.)
1. INTRODUCTION
The idea of pursuit curve is that a point, which we will call the rabbit, follows a prescribed curve. The rabbit is followed by another point, which we will call the fox. Two conditions will be specified to determine a pursuit curve:
1 . The fox heads directly towards the rabbit.
2. The fox's speed is directly proportional to the rabbit's.
Pursuit curves were considered in general bay the French scientist Piene Bouguer in 1732. However, the term "pursuit curve" was first defined by George Boole in his "Treatise on differential equations" in 1859. The curved path described by a fighter plane making an attack on a moving target while holding the proper aiming allowance is a pursuit curve, so such curves are relevant to cunent military research.
2. PIRATES!
We will begin with what is generally assumed to be the original pursuit problem, posed by French mathematician and hydrographer Piene Bouguer in 1732. The problem was published in the French Academy's Mémoires de l'Academie Royale des Sciences and it deals with a pirate ship pursuing a merchant vessel. The merchant vessel is taken to be at (x^sub 0^,0) at time t =0, and travels at a constant speed V^sub m^ along the vertical line x = X0. (See Figure 2.1). The pirate ship starts at (0,0) at time t = O and travels at constant speed V^sub p^ along a curved path, such that its velocity vector is always pointing directly at the merchant vessel. This is what is defined as a pure pursuit, and is described geometrically in Figure 1.1. The problem is to determine the equation...