Naturally Curved Hair in 2D

This lecture explores the mechanics of slender structures, focusing on naturally curved hair falling under gravity. The hair's properties, such as density, Young's modulus, and cross-section area, are considered. The lecture delves into the calculus of variation and Kirchhoff equations to analyze the hair's shape. It discusses the Darboux vector components, internal forces, and distributed external loads. The governing equations for the hair's shape and tip displacement are derived, emphasizing weak and strong gravity scenarios. Boundary conditions and solutions for the shape of the hair near the scalp are also examined.