Dispersal Curve Properties in the Time-Optimal Control Problem for a Second-Order Nonlinear System*

We consider the time-optimal control problem for a nonlinear mechanical system with one degree of freedom. The system describes the dynamics of an inertial object under the action of a bounded control force and a given disturbance force that is periodic in the coordinate. The terminal set consists of points located on the abscissa axis of the phase plane; here, the distance between two adjacent points is equal to the period of the disturbance force in coordinate. We investigate properties of the dispersal curve on the phase cylinder when the magnitude of the control force is sufficiently large.