Reduced spaces for coupled rigid bodies

摘要

The motion of two identical, axially symmetric coupled rigid bodies with constant linear momentum gives rise to a Hamiltonian system with a fairly large symmetry group, namely,SO(3)×S1×S1, which in turn leads to Hamiltonian flows on reduced spaces. In this paper, we illustrate the use of equivariant symplectomorphisms and the reduction in stages 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, the reduced space gets blown up (or blown down) as the momentum value crosses the singular boundar