For uniform rotation, the Newtonian gravitational potential plus the centrifugal potential generates the non-Coriolis part of the equation of motion in a rotating frame. Stationary particles obey . The Coriolis force changes perturbation dynamics, so curvature of this potential alone is not a general rotating-frame stability criterion.
Effective gravity in a uniformly rotating frame is minus the gradient of the sum of the gravitational and centrifugal potentials. A fluid surface in rotational equilibrium is an equipotential surface and is therefore normal to this effective gravity.
After reducing conserved cyclic momenta, an equilibrium at a strict local minimum of the resulting effective potential is stable in the reduced one-degree-of-freedom dynamics.
Articles by others on the same topic
The effective potential is a concept used in classical and quantum mechanics, particularly in the context of central force problems, to simplify the analysis of motion. It combines the potential energy of a system with a term that accounts for the angular momentum of a particle moving under the influence of a central force, such as gravity or electrostatic forces.