Measuring bar pattern speeds from single simulation snapshots

We describe methods to measure simultaneously the orientation angle $\psi$ and pattern speed $\mathrm{\Omega }$ from single snapshots of simulated barred galaxies. Unlike previous attempts, our approach is unbiased, precise, and consistent in the sense that $\psi =\int \mathrm{\Omega }\mathrm{d}t$. It can be extended to obtain the rate and axis of rotation, i.e. the vector $\mathbf{\Omega }$. We provide computer code implementing our method.