Evasion trajectories on a plane (Q5960227)

The paper deals with the following problem. Two point objects \(A\) (pursuit) and \(B\) (evasion) move on the plane. It is assumed that the object \(A\) moves in the straight line with a constant velocity \(\alpha\) and the object \(B\) performs simple motion with the velocity \(\beta\) \((\beta<\alpha)\). The object \(B\) is considered found, if the distance between it and the object \(A\) is less than \(l\) (\(l\) is a prescribed positive number). The author establishes conditions under which the object \(B\) is at distance \(l\) from the object \(A\) during the maximal time.