The motion of a two-dimensional body, controlled by two moving internal masses, in an ideal fluid

The two-dimensional problem of the control of a rigid body in an ideal fluid with the help of two mobile point masses, is considered. The equations of motion allow of a complete set of Noether integrals, linear in the velocities. For fixed values of these integrals, the equations of motion are reduced to a non-autonomous system of first-order differential equations. The complete controllability of the system for almost all values of the physical parameters is proved. Particular solutions, which enable the control problem to be solved explicitly (transferring the body from the initial position to a position specified in advance), are indicated. The problem of the speed of response is solved numerically using a genetic algorithm.