  Greenlees established an equivalence of categories between the homotopy
category of rational SO(3)-spectra and the derived category DA(SO(3)) of a
certain abelian category. In this paper we lift this equivalence of homotopy
categories to the level of Quillen equivalences of model categories. Methods
used in this paper provide the first step towards obtaining an algebraic model
for the toral part of rational G-spectra, for any compact Lie group G.
