SUCCESSIVE POSITIONAL PURSUIT

A linear problem of successive pursuit is considered, where the evader s are to be captured in a fixed order and the pursuer's control is pos itional. The solvability criteria for this problem in a rather general situation are derived. The result is illustrated by a model example w ith a simple motion of the players. For this example, on the basis of the equation of the pursuit curve, formulas are derived that determine the locus of the capture points both for simultaneous and non-simulta neous start of the players. Recurrent relations for the calculation of the total time of the game are derived.