= Gyrotactic circular paths in a rotating cylinder
For fluid <velocity> $\Omega(-x_3,0,x_1)$ and $B\Omega<1$, the stable deterministic orientation is $\mathbf p=(-B\Omega,0,\sqrt{1-B^2\Omega^2})$. Once this orientation has relaxed, swimming at speed $V_s$ shifts the centre of the circular material trajectories to $(-V_s\sqrt{1-B^2\Omega^2}/\Omega,-V_sB)$ in the $(x_1,x_3)$ plane. Its distance from the cylinder axis is $V_s/\Omega$. General initial orientations produce an orientation transient before these circular paths.
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