Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 77 / 1 / b / Solution

In the oscillating rigid rod in resistive-force theory, $\sin \theta \cos \theta =\theta +O({ϵ}^3)$ and $\dot{x}=-ϵa\omega \sin \omega t$. Sincethe mean transverse force from a rocking rod, on the fluid in the tilt convention of part (a), isThe parallel and perpendicular drag coefficients of a slender filament are per unit length here. Their difference is essential: isotropic local drag gives zero transverse force. The hydrodynamic force on the rod is the negative of the displayed answer.