In this paper we present a model Hamiltonian to treat the dynamics of reactions of the general type X + YCZ(3)--> XY + CZ(3), where the CZ(3) group has C-3 upsilon symmetry. The main assumption of the model is that CZ(3) maintains its symmetry during the reaction. The Hamiltonian we derive can be used as the starting point for more simplified models. We present here one of these simpler models and use it to study the role of the umbrella vibrational motion in the reaction O(P-3) + CH4--> OH + CH3. Finally, we compare our results with previous theoretical and experimental results.