On the motion of a sphere in a rotating liquid

Abstract

1. In previous papers the author has considered certain special problems dealing with small disturbances in rotating liquids. In the present paper the general small motion of a sphere in a rotating liquid is dealt with ; it is assumed that the sphere is initially at rest relative to rotating axes and that a sudden small motion is imparted to it bv means of a set of impulses. The motion is made to depend upon two special types of motion, and these special types are considered in detail. Expressions for the pressure and velocity at any time are obtained, and the variation of the resultant pressure on the sphere with time, and the initial variation of the velocity at particular points are shown by means of diagrams. The first type of motion is a uniform translation of the sphere parallel to the axis of rotation.