Rotating-frame relative effective potential (${\psi }_{\mathrm{eff}}=\psi +\frac{1}{2}{\Omega }_b^2{R}^2$)

For a bar rotating with constant pattern speed ${\Omega }_b$, use ${\psi }_{\mathrm{eff}}=\psi +{\Omega }_b^2{R}^2/2$ in the force convention $+\nabla \psi$. The centrifugal acceleration is its added gradient. This is the negative of the usual physical effective potential ${\Phi }_{\mathrm{eff}}$; Coriolis acceleration is separate.