Periodic Regimes of Motion of a Chain of Interacting Bodies in a Medium with Resistance

A system of bodies moving along a straight line in a resistive medium is considered. Distances between the bodies change periodically. Periodic regimes of motion of the system in which the velocities of all bodies are also periodic are studied. It is shown that for a wide class of laws of resistance of a medium, the periodic regime of motion exists, is unique, and is exponentially stable.