On the motion of a spinning heavy plate in an ideal fluid

We consider the problem of free fall of a heavy solid plate in an infinite volume of an ideal fluid. At the initial moment the plate is horizontal, it has a vertical rotation, and its center of mass has the horizontal velocity. Under the influence of gravity, the plate goes down and rotates around a lateral axis perpendicular to the directions of the initial velocity and initial rotation. At the same time, a gyroscopic effect motivate rotation of the plate around the velocity of the center of mass, and as a result a lateral movement of a plate.