  We study the system of massive and mixed neutrinos interacting with
background matter moving with an acceleration. We start with the derivation of
the Dirac equation for a single neutrino in the noninertial frame where matter
is at rest. A particular case of matter rotating with a constant angular
velocity is considered. The Dirac equation is solved and the neutrino energy
levels are found for ultrarelativistic particles propagating in rotating
matter. Then we generalize our results to include several neutrino generations
and consider mixing between them. Using the relativistic quantum mechanics
approach we derive the effective Schr\"{o}dinger equation for the description
of neutrino flavor oscillations in rotating matter. We obtain the resonance
condition for neutrino oscillations and examine how it can be affected by the
matter rotation. We also compare our results with the findings of other authors
who studied analogous problem previously.
