Motion of a deformed contour in a flow of an ideal incompressible liquid with a constant vorticity

The article gives a solution to the plane problem of the motion of a deformed contour in a flow of an ideal incompressible liquid with a constant vorticity. An explicit expression is obtained for the hydrodynamic force when the velocity of the external flow depends linearly on the coordinates. In the case of a contour of small dimensions, this expression is valid also for an arbitrary external flow.