On the Motion of a System with a Moving Internal Element in the Presence of External Viscous Friction

Abstract

We consider a system consisting of a platform moving translationally along a fixed straight line in the presence of the viscous friction force and a body making a given translational motion along the same straight line relative to the platform due to internal forces. In relative motion, the value of the body velocity is bounded. It is proved that in the case of linear viscous friction, unlimited displacement of the platform in any direction is impossible. In the general case, under certain conditions imposed on the viscous friction force, the value of the velocity of the platform is bounded. In this case, if the displacement of the platform in any direction, e.g., to the right, is not limited, then the value of the velocity of the platform changes its sign an infinite number of times over time, and the total time of the platform’s motion to the left and the distance traveled tend to infinity.