Аннотация:In the "kinematic" formulation, two problems of speed - optimal control of the position of a single - link pendulum fixed on a movable base are considered . The base can move along the horizontal axis. In the first problem, the initial position of the pendulum is the lower, stable position of the pendulum; you need to move it to the upper, unstable position with calming either in an arbitrary or a given place along the horizontal axis. In the second problem, on the contrary, the top position is the initial one. You need to move the pendulum along the horizontal axis, while maintaining its original vertical position at the end. Both problems are considered on the basis of nonlinear equations. The numerical solution of the problems is preceded by an analysis of the optimality conditions that follow from the maximum principle in the case of kinematic control of these objects.