  Recently the phase space structures governing reaction dynamics in
Hamiltonian systems have been identified and algorithms for their explicit
construction have been developed. These phase space structures are induced by
saddle type equilibrium points which are characteristic for reaction type
dynamics. Their construction is based on a Poincar{\'e}-Birkhoff normal form.
Using tools from the geometric theory of Hamiltonian systems and their
reduction we show in this paper how the construction of these phase space
structures can be generalized to the case of the relative equilibria of a
rotational symmetry reduced $N$-body system. As rotations almost always play an
important role in the reaction dynamics of molecules the approach presented in
this paper is of great relevance for applications.
