First-order free swimming of a planar filament
= First-order free swimming of a planar filament
{title2=$V_1=-4G_0+6G_1/L,\quad\Omega_1=6G_0/L-12G_1/L^2$}
For $y=\epsilon g(x,t)$ on $0\leq x\leq L$, uniform local drag and force/torque balance give $U_1=0$, $V_1=-4\langle g_t\rangle_x+6\langle xg_t\rangle_x/L$, and $\Omega_1=6\langle g_t\rangle_x/L-12\langle xg_t\rangle_x/L^2$. The tangent can be replaced by the undeformed direction at this order because the velocity is already first order.