= Axisymmetric adiabatic displacement operator
{title2=$\mathcal F\xi=(\delta\rho/\rho^2)\nabla p-\nabla\delta p/\rho-\kappa^2\xi_R\mathbf e_R$}
In the <Cowling approximation>, an axisymmetric meridional <fluid displacement> in a cylindrically rotating barotropic star obeys $-\omega^2\xi=\mathcal F\xi$, with $\delta\rho=-\nabla\cdot(\rho\xi)$ and $\delta p=-\xi\cdot\nabla p-\gamma p\nabla\cdot\xi$. Conservation of <specific angular momentum> supplies the epicyclic term, with $\kappa^2=R^{-3}d(R^4\Omega^2)/dR$. The <Cowling energy principle for a rotating barotropic star> gives its symmetric quadratic form.
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