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The Quarterly Journal of Mechanics and Applied Mathematics 1954 7(2):231-246; doi:10.1093/qjmam/7.2.231
© 1954 by Oxford University Press
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ON THE FREE MOTION OF AN ELLIPSOID IN A ROTATING FLUID

K. STEWARTSON

( Department of Mathematics, The University Bristol )

It is shown theoretically that, if a spheroid of density {rho}{sigma} is placed symmetrically on the axis of a rotating fluid of density {rho}, it will be in stable equilibrium for translational disturbances if {sigma} ≤ 1, and for rotational disturbances if {sigma} ≥ 1 in the case when it is oblate, or if {sigma} ≤ 1 in the case when it is prolate. Further, if 1 > {sigma} > 1/2, it will have a single period of translational oscillation, while if {sigma} < 1/2 it will have two such free rotational periods; and if stable, it may have also a free period of rotational oscillation. Some experiments on the free motion of bodies in rotating fluids are also described. These are in substantial agreement with the theoretical predictions. It was also observed that there are asymmetric positions of equilibrium, stable with respect to angular displacements, having the axes of the bodies horizontal.


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