REDUCED SPACES FOR COUPLED RIGID BODIES

The motion of two identical, axially symmetric coupled rigid bodies wi th constant linear momentum gives rise to a Hamiltonian system with a fairly large symmetry group, namely, SO(3) x S-1 x S-1, which in turn leads to Hamiltonian flows on reduced spaces. In this paper, we illust rate the use of equivariant symplectomorphisms and the reduction in st ages procedure in determining the topology of these reduced spaces. It is shown that the reduced spaces corresponding to regular momenta are either two- or four-dimensional and, in the four-dimensional case, th e reduced space gets blown up (or blown down) as the momentum value cr osses the singular boundary.