Progressive Locomotion of a Chain of Bodies in a Resistant Medium

Progressive motion of a multibody system consisting of equal rigid bodies in a resistive medium is considered. The bodies are connected consecutively, and between each pair of bodies the actuators are installed. The actuators can exert forces upon the two neighboring bodies so that the distance between them can change within prescribed limits. It is shown that, under the influence of these internal forces produced by the actuators and external resistance of the medium, the system can move progressively with a velocity changing periodically. The algorithm of locomotion is proposed and justified. The necessary and sufficient condition is obtained that ensures the possibility of this motion. The cases of linear and quadratic isotropic/anisotropic resistance forces depending on the velocity of moving bodies and directed against this velocity, are analyzed. The locomotion described in the paper resembles the motion of worms and other biological objects.