On the shape and stability of a conducting fluid drop rotating in an electric field

TLDR: The equilibrium and stability of an isolated, inviscid, incompressible, neutral conducting fluid drop whose axis of uniform rotation coincides with the direction of a uniform applied electric field are examined by using an appropriate extension of the virial method developed by Chandrasekhar.

Abstract: The equilibrium and stability of an isolated, inviscid, incompressible, neutral conducting fluid drop whose axis of uniform rotation coincides with the direction of a uniform applied electric field are examined by using an appropriate extension of the virial method developed byChandrasekhar Rotating spherical, spheroidal, and ellipsoidal equilibrium shapes are shown to satisfy the first twelve moment equations A linear, one-parameter (the elongation) family of equilibrium curves relates the electrostatic energy,x, to the square of the angular momentum,y, of a given spheroidal shape Conditions for the onset of instability, obtained from a linearized normal-mode analysis associated with second-harmonic deformations, restrict stable spheroidal configurations to a closed region of thisx−y configuration plane Genuine triaxial configurations are shown to bifurcate from these axisymmetric configurations in the same manner as the classical, self-gravitating Jacobi ellipsoids bifurcate from the Maclaurin spheroids