Class of Trajectories ℝ³ in Most Remote from Observers

Abstract

The set of extremal trajectories is completely described. Their construction is reduced to finding the best routes on a directed graph whose vertices are subsets (boxes) of $Y\backslash \mathop \cup \limits_S K\left( S \right)$ and whose edges are segments T(S) of the trajectory T that intersect the cones K(S) in the “best way.” The edge length is the deviation of S from T(S). The best routes are ones for which the length of the shortest edge is maximal.