  We study the dynamics of the rigid rotator on the group manifold of SU(2) as
an instance of dynamics on Lie groups together with a dual model whose carrier
space is the Borel group SB(2,C), the Lie Poisson dual of SU(2). We thus
introduce a parent action on the Drinfeldd double of the above mentioned
groups, which describes the dynamics of a system with twice as many degrees of
freedom as the two starting partners. Through a gauging procedure of its global
symmetries both the rigid rotor and the dual model are recovered.
