Department of Mathematics, University of Toledo, Toledo, OH, 43606, USA. E-mail:
Department of Mathematics, Central Michigan University, Mt. Pleasant, MI, 48859, USA. E-mail:
Let P be a principal G-bundle over M and a Hamiltonian G-space Q, we point out the relationship between the universal phase space associated with P and Q and the reduced phase space associated with T*P × Q in a general sense.