Cylindrical Jeans equations in a rotating frame

The first moments of the rotating-frame collisionless Boltzmann equation express radial and azimuthal momentum balance. Coriolis terms enter as $-2{\Omega }_b\rho ⟨v_{\varphi }⟩$ and $+2{\Omega }_b\rho ⟨v_R⟩$ on the left. Geometric stress terms are $\rho (⟨v_R^2⟩-⟨v_{\varphi }^2⟩)/R$ and $2\rho ⟨v_R{v}_{\varphi }⟩/R$. Second moments include random stress and streaming flux.