Berry’s phase, locally inertial frames, and classical analogues

Berry's phase that appears in adiabatically changed quantum systems can be derived, in many cases, by considering locally inertial coordinate frames in classical mechanics, without having to appeal to quantum mechanics. This derivation is applicable to light propagation in twisted optical fibers and to other systems where the perturbation can be reduced to a coordinate transformation. The classical nature of this derivation clarifies some nonquantum analogues of Berry's phase.