Nonlinear vibrations of a charged drop due to the initial excitation of neighboring modes

The asymptotic analysis of the nonlinear vibrations of a charged drop that are induced by a multi-mode initial deformation of its equilibrium shape is performed. It is shown that when two, three, or several neighboring modes are present in the initial deformation spectrum, the mode with the number one (translational mode) appears in the second-order mode spectrum. The excitation of the translational mode follows from the requirement of center-of-mass immobility and causes the dipole components (which are absent in the linear analysis) to appear in the spectra of the acoustic and electromagnetic radiation of the charged drop.