On the Maximum Displacement of a System of Interacting Point Masses Along a Straight Line with Dry Friction*

The paper investigates the motion of the system, consisting of three or more identical point masses, along a straight line with dry friction. The motion occurs when the configuration changes due to the forces acting between the masses. An optimal control problem is solved to maximize the displacement of the system for a fixed time with both initial and terminal states of the system having the same configuration and being at rest. No constraints are imposed on the interaction forces. Nonuniqueness of optimal solution is proved and an optimal solution is constructed such that the distance between any two points of the system is less than a given positive constant over all time of the motion.