On the stability of trajectories in the task of pursuit

Abstract

In two-dimensional and three-dimensional statements, a generalization of the pursuit problem is considered, when the object being pursued moves in a circle (plane case) or in a helical line (three-dimensional case), and various cases of dependence of object velocities in the problem are considered. Conditions are analytically obtained for the stability of the trajectories of motion of objects in the problem. Possible realization of this problem - the pursuit of one drone by another one as flying objects.