  We derive a necessary condition for the existence of marginally stable
circular orbits of test particles in stationary axisymmetric spacetimes which
possess a refection symmetry with respect to the equatorial plane; photon
orbits are also addressed. Energy and angular momentum are shown to decouple
from metric quantities, rendering a purely geometric characterization of
circular orbits for this general class of metrics. The subsequent system is
analyzed using resultants, providing an algorithmic approach for finding MSCO
conditions. MSCOs are explicitly calculated for concrete examples of physical
interest.
