  We study analytically the dynamics of vortices in strongly coupled
exciton--photon fields in the presence of energy detuning. We derive equations
for the vortex core velocity and mass, where they mainly depend on Rabi
coupling and the relative distance between the vortex cores in photon and
exciton fields, and as the result core positions oscillate in each field. We
use Magnus force balanced with a Rabi induced force to show that the core of
the vortex behaves as an inertial-like particle. Our analysis reveals that the
core is lighter at periphery of the beam and therefore it is faster at that
region. While detuning induces oscillations in population imbalance of
components through relative phase between coupled fields, in the presence of
topological charges detuning can control the orbital dynamics of the cores.
Namely, it brings the vortex core to move on larger or smaller orbits with
different velocities, and changes angular momentum and energy content of vortex
field.
