Studying the nonautonomous differential equations by methods of qualitative theory of control dynamical systems

For nonautonomous systems of differential equations of second order which represent the family of control dynamical systems with given constraints on the control, we propose a method for constructing the borders of controllability and attainability. For this, we introduce the notions of singular points and singular trajectories, and study the structure of punctured neighborhood of a singular point. Some concrete examples of self interest are considered.