Rotating-frame effective potential (${\Phi }_{\mathrm{eff}}=\Phi -\frac{1}{2}|\mathbf{\omega }\times \mathbf{r}{|}^2$)

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 $\nabla {\Phi }_{\mathrm{eff}}=0$. The Coriolis force changes perturbation dynamics, so curvature of this potential alone is not a general rotating-frame stability criterion.