Mechanics of Kirchhoff Rods I

This lecture covers the differential geometry of curves, the Frénet-Serret frame, the Cosserat frame, the Darboux Vector, and Kirchhoff's equilibrium equations of rods. It delves into the mechanics of slender structures, introducing concepts like finite strain and finite rotation theory, simplifications, and examples like the buckling of a ring. The lecture also explores the differential geometry of curves in 3D, the choice of parameterization, and the introduction of the Cosserat frame and Darboux vector for cross-section analysis.