Analysis and optimization of the rectilinear motion of a two-body system

The rectilinear motion of a system of two interacting bodies when there is a dry friction force acting on both of them is considered. It is assumed that the relative velocity of the bodies can vary practically instantaneously, while the distance between them has upper and lower limits. The periodic motion of the system as a whole is constructed, and the mean velocity of motion and the energy costs per unit of path are determined. The optimum values of the parameters for which the highest mean velocity is reached with the superimposed limitations are obtained.