Evasion from a group of rigidly coordinated objects in a third-order game

A conflict interaction of groups of controlled objects is considered. The pursuers' goal is to catch, and the evaders' goal is to avoid contact with pursuers. All players have equal dynamic capabilities. Players' motion is defined by a third order differential equation. All evaders have equal control, therefore they can be considered as rigidly coordinated inertial objects. It is proved that if the convex hull spanned by pursuers' initial acceleration vector is not intersected with the convex hull spanned by evaders' initial acceleration vector, then the evasion is possible.