Isotropic radiation from a steadily pulsating multidimensional distribution

Abstract

A multidimensional dynamical configuration is considered, com prising an isotropic homogeneous unbounded medium steadily oscillating in response to a real constant frequency imparted by an embedded source. A Green function to the problem is first derived, and leads to the compounding of the general exact solution for an arbitrary spatial distribution of the source function. Specializations are made to yield an asymptotic solution, a spherically symmetric solution and an axisymmetric solution. All physical results satisfy an initially imposed radiation condition, whose consequence is subsequently accommodated during the construction of the Green function. Significances are attached and interpretations provided, namely, in terms of the associated isotropic waves. A cursory application is made to examine the oscillatory motion, when reduced to the isotropic state, of a rotating magnetoelastic system. An appendix is included to deal with a certain spherical integral encountered during the investigation into the axisymmetric case.