Periodic Non-Reverse Rectilinear Motion of a Two-Body System on a Rough Plane

摘要

A periodic rectilinear motion of a two-body system along a rough plane is considered. The system is controlled by the force of interaction of the bodies. A periodic motion is defined as a motion in which the distance between the bodies and their velocities relative to the plane are represented by time-periodic functions with the same period. The friction that acts between the bodies and the plane is Coulomb's dry friction. Necessary and sufficient conditions for possibility of a periodic non-reverse motion of the system, in which neither of the bodies changes the direction of its motion, are proved. These conditions are expressed by inequalities that involve the masses of the system's bodies and the coefficients of friction of these bodies against the underlying plane. Non-reverse motions provide a minimum for friction-induced energy losses per unit path.