Matched Approximations of a Clamped Filament

This lecture covers the derivation of equations for the equilibrium of an inextensible string, including the inextensibility condition and the principle of virtual works. It also explores the effects of perturbations on the equilibrium equations and the deflection of the string. The lecture concludes with the development of a hybrid model that bridges two different regimes by incorporating linear constitutive laws and strain approximations for moderate rotations.