Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid

Abstract

We consider the controlled motion in an ideal incompressible fluid of a rigid body with moving internal masses and an internal rotor in the presence of circulation of the fluid velocity around the body. The controllability of motion (according to the Rashevskii–Chow theorem) is proved for various combinations of control elements. In the case of zero circulation, we construct explicit controls (gaits) that ensure rotation and rectilinear (on average) motion. In the case of nonzero circulation, we examine the problem of stabilizing the body (compensating the drift) at the end point of the trajectory. We show that the drift can be compensated for if the body is inside a circular domain whose size is defined by the geometry of the body and the value of circulation.