Abstract: We consider the most general case of the restricted rigid rotor, controlled by passive mechanical devices at . The purpose of theses devices is to restrict the particle’s motion to a domain of a covering space (0,Mπ), where M is an odd integer. This system, which is not a Hamiltonian one on the physical space (0, 2π), is compared with a Hamiltonian system having delta function barriers at . The case of M is even integer is also discussed by using only one mechanical device at θ=0. This non-Hamiltonian system is compared with a Hamiltonian system having a delta function barrier at θ=0. It is shown that many of the wave functions of the non-Hamiltonian system are the same as those of the Hamiltonian ones, with an average reflection coefficient of 1/(M+1) for odd M and 2/M for even M, which are the classical values. We show, how in the case of very large M, the superposition principle leads to the de Broglie resonances.