On the optimal motion of a body with an internal mass in a resistive medium

摘要

The motion of a system consisting of a rigid body and an internal movable mass is considered. As a result of special periodic motions of the internal mass, the system as a whole can move in a resistive medium. These motions are analyzed for the cases of piecewise linear and quadratic resistance forces acting upon the body. Optimal parameters of the periodic motions are found that correspond to the maximal average speed of the system as a whole.