  Sagnac interferometers with massive particles promise unique advantages in
achieving high precision measurements of rotation rates over their optical
counterparts. Recent proposals and experiments are exploring non-ballistic
Sagnac interferometers where trapped atoms are transported along a closed path.
This is achieved by using superpositions of internal quantum states and their
control with state-dependent potentials. We address emergent questions
regarding the dynamical behavior of Bose-Einstein condensates in such an
interferometer and its impact on rotation sensitivity. We investigate complex
dependencies on atomic interactions as well as trap geometries, rotation rates,
and speed of operation. We find that temporal transport profiles obtained from
a simple optimization strategy for non-interacting particles remain
surprisingly robust also in the presence of interactions over a large range of
realistic parameters. High sensitivities can be achieved for short
interrogation times far from the adiabatic regime. This highlights a route to
building fast and robust guided ring Sagnac interferometers with fully trapped
atoms.
