Possible resonator configurations for the spherical gravitational wave antenna

Nadja S. Magalhães, Instituto Nacional de Pesquisas Espaciais
Odylio D. Aguiar, Instituto Nacional de Pesquisas Espaciais
Warren W. Johnson, Louisiana State University
Carlos Frajuca, Esc. Tec. Federal de São Paulo


We solve algebraically the equations of motion for a spherical antenna coupled to an arbitrary number of small resonators, free to move radially, and investigate the conditions under which damping forces can be neglected in the system. We show that in order that the antenna's modes be decoupled a preferred distribution of the resonators on its surface should be used. We find that either 5, 6, 10 or 16 resonators can be used as long as they are conveniently positioned on the antenna's surface. We calculate and analyse the frequency shift and the signal-to-noise ratio of the coupled system for the various distributions studied.