The hamiltonian dynamics of coupled structures is discussed. There are geometric parallels in earlier work on the Newtonian (gravitational) many-body problem. In the study of relative equilibria, a theorem due to Smale has a useful role. Relative stabiliq modulo a group of symmetries can be determined using the energy~asimir (or energy - momentum) method. For nongeneric values of momenta, the Poisson structure can affect stability.