Force-free straight-rod orientation equation
= Force-free straight-rod orientation equation
{title2=$\dot{\mathbf p}=\boldsymbol\Omega\times\mathbf p+E\mathbf p-(\mathbf p\cdot E\mathbf p)\mathbf p$}
The orientation of a <force-free>, <torque-free> infinitely slender straight rod follows background rotation plus the transverse component of strain. The last term preserves $|\mathbf p|=1$. Finite aspect ratio changes the strain coefficient and permits periodic tumbling in a <simple shear flow>.