Power of a periodic planar filament
= Power of a periodic planar filament
{title2=$\dot W=\frac{\xi_\perp}{T}\int_0^T\int_0^\lambda y_t^2\,dx\,dt$}
The leading <viscous dissipation> due to a small planar filament stroke is $\dot W=\xi_\perp T^{-1}\int_0^T\int_0^\lambda y_t^2\,dx\,dt$. It follows from the work against the local <resistive-force theory> force. The transverse velocity controls the leading power; the quadratic longitudinal velocity contributes only at higher order.