  We use a combination of microwave fields and free precession to drive the
spin of a nitrogen-vacancy (NV) center in diamond on different trajectories on
the Bloch sphere, and investigate the physical significance of the
frame-dependent decomposition of the total phase into geometric and dynamic
parts. The experiments are performed on a two-level subspace of the spin-1
ground state of the NV, where the Aharonov-Anandan geometric phase manifests
itself as a global phase, and we use the third level of the NV ground state
triplet to detect it. We show that while the geometric Aharonov-Anandan phase
retains its connection to the solid angle swept out by the evolving spin, it is
generally accompanied by a dynamic phase that suppresses the geometric
dependence of the system dynamics. These results offer insights into the
physical significance of frame-dependent geometric phases.
