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A theorem is proved extending results of Cockayne on pursuit with curvature constraints. Let two points (pursuer and evader) move in Euclidean 3-space with constant speeds. Provided the pursuer has greater speed and greater normal acceleration, it is shown that pursuit is always successful. The methods used are similar to Cockayne’s. The pursuer, by some preliminary maneuvers, sets up a condition where he is leaving the line of sight in the same direction and with the same speed as the evader. It is shown that from this instant, the pursuer can, without violating constraints, keep the line of sight parallel to the original and ultimately collide with the evader.
G. Rublein (Tue,) studied this question.