 
Summary: SIAM J. APPL. MATH. c 2005 Society for Industrial and Applied Mathematics
Vol. 66, No. 1, pp. 98121
NONADIABATIC CORRECTIONS TO THE HANNAYBERRY
PHASE
SEAN B. ANDERSSON
Abstract. 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 CartanHannayBerry connection. The result
ing geometric phase is called the HannayBerry 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 HannayBerry phase for a moving system. The technique is illustrated by applying it to a
rotating freefloating springjointed equalsided fourbar mechanism.
Key words. geometric phases, perturbations, systems with slow and fast motions, averaging of
perturbations
AMS subject classifications. 81Q70, 37J40, 70K70, 70K65
DOI. 10.1137/040606600
1. Introduction. When a system undergoes an imposed motion, the external
forces can alter the natural dynamics. A simple example is the Foucault pendulum,
where the rotation of the Earth causes a precession of the swing plane of the pendulum.
Classically the effect of the external forces is captured by introducing fictitious forces
