On the motion of a liquid in a spheroidal cavity of a precessing rigid body. II

Abstract

AbstractIt is supposed that a viscous incompressible fluid is contained in an oblate spheroidal cavity (major axes a, eccentricity e) in a rigid body, and that, up to time t = 0, both fluid and container rotate together with angular velocity ω about the minor axis LB of the spheroid, which is fixed in space. At t = 0, the axis of rotation is moved impulsively, and is given a motion of precession (angular velocity Ω) about an axis LS fixed in space, which makes an angle α with LB. It is required to find the ultimate state of motion of the fluid relative to the container. In a previous paper (Stewartson and Roberts (4)), this problem was solved for arbitrary α under the assumptions thatwhere v is the kinematic viscosity. In the present paper, it is shown how the problem may be solved for arbitrary e (including zero) under the assumptions that