THE STABILITY OF A ROTATING LIQUID DROP.
CHICAGO UNIV ILL
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The stability of a rotating drop held together by surface tension is investigated by an appropriate extension of the method of the tensor virial. Consideration is restricted to axisymmetric figures of equilibrium which enclose the origin. These figures form a one-parameter sequence. It is shown that with respect to stability, the axisymmetric sequence of rotating drops bears a remarkable similarity to the Maclaurin sequence of rotating liquid masses held together by their own gravitation. Thus, at a point along the sequence where 0.4587 a neutral mode of oscillation occurs without instability setting in at that point i.e. provided no dissipative mechanism is present and the instability actually sets in at a subsequent point where 0.8440 by overstable oscillations with a frequency F. The dependence on of the six characteristic frequencies, belonging to the second harmonics, is determined and exhibited. Author