Analysis and optimization of the motion of a body controlled by means of a movable internal mass

The controlled horizontal motion of a body in the presence of dry friction forces is investigated. Control is accomplished by means of a movable mass that can move within the body in a bounded range. Some simple modes of periodic relative motions of the movable mass, under which the entire system moves as a whole, are investigated. Constraints are imposed on the relative displacement, velocity and acceleration of the movable mass. The optimum parameters of this relative motion, under which the maximum mean velocity of the body is reached, are determined.