Power of a rocking rod ($⟨P⟩$)

The leading mean viscous dissipation of a translating and rotating rigid rod is $c_{\perp }{ϵ}^2{\omega }^2(L{a}^2+L^3/12)/2$ for equal dimensionless translation and angle amplitudes. Both terms are quadratic in amplitude; rotational material velocity cannot be omitted simply because the angle is small.