Abstract
The authors obtain general formulae to calculate exactly the orbital Aharonov-Anandan phase for a bounded system interacting with a precessing magnetic field in the case where the binding potential is rotationally invariant around the axis of rotation of the magnetic field. The particular case of a quadratic potential is considered in full detail, and the connection with the stability problem is established. The adiabatic limit of the Aharonov-Anandan phase to obtain the corresponding Berry phase is also considered.