The authors consider the case of a limited rigid rotor, controlled by passive mechanical devices on a circle located at theta =0 and theta = pi . The devices have the effect of restricting the particle motion to the interval (0,3 pi ). This system, which cannot be described by a Hamiltonian on (0,2 pi ), is compared with a Hamiltonian system having delta function barriers at theta =0 and theta = pi . Many of the wavefunctions of the system having systematic reflections are the same as those of the Hamiltonian system with a reflection probability of 1/4. Finally, the effect of a whisker of flux at the origin (Aharonov-Bohm effect) is discussed in the case of the non-Hamiltonian system.