Abstract
Analytically, on the basis of asymptotic methods, the problem of the nonlinear oscillations of a charged ideal incompressible electroconductive fluid drop levitated at rest in gravity and homogeneous electrostatic fields is solved in the quadratic approximation in two small parameters: the initial drop shape deformation amplitude and the stationary eccentricity of the equilibrium drop shape in the electrostatic field. The calculations are performed in fractional powers of the nonlinear oscillation amplitude. The nonlinear corrections to the oscillation frequencies are always negative and already present in the second-order approximation due to the stationary deformation of the drop in the external fields rather than nonlinear interaction between the modes. In the case considered, in contrast to the nonlinear oscillations of a free charged drop, the expression for the generator of the nonlinearly oscillating drop shape contains terms proportional to the oscillation amplitude to the power 3/2.
Published Version
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