Cylindrical continuity equation for a rotating stellar system
= Cylindrical continuity equation for a rotating stellar system
{title2=$\rho_t+R^{-1}(R\rho u_R)_R+R^{-1}(\rho u_\phi)_\phi=0$}
The zeroth velocity moment gives $\partial_t\rho+R^{-1}\partial_R(R\rho\langle v_R\rangle)+R^{-1}\partial_\phi(\rho\langle v_\phi\rangle)=0$. In the <rotating-frame collisionless Boltzmann equation>, velocity integration by parts supplies the geometric $\rho\langle v_R\rangle/R$ term. This equation expresses conservation of planar mass.