ИСТИНА

The report considers a system of several interacting bodies moving along a horizontal line in a resisting medium. It is assumed that the laws of change of distances between bodies are given and periodically depend on time. The velocity-periodic modes of motion of the system are investigated, in which the velocities of all bodies are also periodic with the same period. It is shown that for a wide class of laws of resistance of the medium (for example, monotonic and infinitely increasing resistance) and laws of relative motion of bodies, the periodic velocity mode of motion of the system exists, is unique, and any other motion exponentially converges to it.