  Motion sensing in a spherical GW detector requires a multiple set of
transducers attached to its surface at suitable locations. If transducers are
of the resonant type then their motion couples to that of the sphere and the
joint dynamics of the system has to be properly understood before reliable
conclusions can be drawn from its readout. In this paper we address the problem
of the coupled motion of a sphere and a set of resonators attached to it at
arbitrary points. A remarkably elegant and powerful scheme emerges from the
general equations which shows how coupling takes place as a power series in the
small coupling constant ratio m(resonator)/M(sphere). We reasses in the new
light the response of the highly symmetric TIGA and also present a new proposal
(called PHC) which has less symmetry but which is based on 5 rather than 6
transducers per quadrupole mode sensed. We finally assess how the system
charac- teristics are affected by slight departures from ideality, and find it
to be quite robust to them. In particular we recover with full accuracy the
reportedly measured frequencies of the LSU prototype TIGA.
