The undulatory motion of a chain of particles in a resistive medium in the case of a smooth excitation mode

The motion of a chain of three identical bodies along a straight line in a dry-friction medium is studied. The motion is excited and controlled by changing the distances between the bodies of the chain. An undulatory excitation mode is proposed, in which the distances between the adjacent bodies of the chain change periodically and the time histories of the distances in the pairs of adjacent bodies consecutively repeat each other with a constant time shift. It looks like a wave is running along the chain. The necessary and sufficient conditions for the system to be able to move from rest are established. For a specific excitation mode, in which the time histories of the distances between the bodies of the chain are defined as piecewise quadratic functions, a steady-state motion of the system is studied for the case where the friction force is small in comparison with the force necessary for a body of the chain to be moved from a state of rest through a distance characterizing the amplitude of oscillations of adjacent bodies during the excitation period.