Nonadiabatic Corrections to the Hannay-Berry Phase

The effect of the Coriolis force on a moving system can be described as a holonomy with respect to a particular connection known as the Cartan–Hannay–Berry connection. The resulting geometric phase is called the Hannay–Berry phase, and it provides direct information about the imposed motion on the system. This approach assumes that the imposed motion is adiabatic. In this paper we describe the use of Hamiltonian perturbation theory to develop nonadiabatic corrections to the Hannay–Berry phase for a moving system. The technique is illustrated by applying it to a rotating free-floating spring-jointed equal-sided four-bar mechanism.