The author studies the problem of motion of a rigid ball in an ideal liquid bounded from outside by a plane surface of a vibrating (according to some periodic law) rigid wall. The velocity of the liquid is also periodic in time at infinity. For small (as compared to unity) ratio of the radius of the ball to the distance between its center and the wall, the force interaction is determined between the liquid and the ball. A law of the ball’s motion is found. It is also found that vibration of the liquid along the surface of the wall and vibrations of the liquid directed along the normal to the wall essentially influence on the motion of the ball. The effect of different densities of the liquid and the ball is studied in detail. It is also clarified which kinds of vibration of the liquid are most effective.
{In the title, the term “ball” should be used instead of “sphere.”}.