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

Published online by Cambridge University Press:  24 October 2008

P. H. Roberts  and
K. Stewartson
P. H. Roberts
Affiliation:
University of Newcastle upon Tyne and University of Durham
K. Stewartson
Affiliation:
University of Newcastle upon Tyne and University of Durham
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Abstract

It 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 that

where 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

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 279 - 288
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCES

(1)Bondi, H. and Lyttleton, R. A.Proc. Cambridge Philos. Soc. 49 (1953), 498–515.CrossRefGoogle Scholar
(2)ErdÉlyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher transcendental functions, vol. i (McGraw-Hill; New York, 1953).Google Scholar
(3)Greenspan, H. P. and Howard, L. N.J. Fluid Mech. 17 (1963), 385–404.CrossRefGoogle Scholar
(4)Stewartson, K. and Roberts, P. H.J. Fluid Mech. 17 (1963), 1–20.CrossRefGoogle Scholar