Filament tension ($T$)

Filament tension is the axial force enforcing local inextensibility. Its force density is ${\partial }_s(T{\mathbf{r}}_s)$. A pre-existing constant tension contributes $T{y}_{xx}$ to small-slope transverse dynamics; in an unloaded, initially straight filament, tension induced by transverse motion begins at second order in amplitude.