Mechanics of Kirchhoff Rods II

This lecture delves into the mechanics of Kirchhoff rods, focusing on the framework of the Kirchhoff equation, kinematics in 3D, twisted solutions, and the relationship between moment and strain. The slides cover topics such as the Darboux vector, Frenet-Serret frame, Cosserat frame, bending and twist moduli, internal and external forces, torque, and boundary conditions. The lecture also explores examples of kinematics, twisted solutions, and recent developments in rod mechanics, including fluid-structure interaction and the mechanics of growing elastic rods. The presentation emphasizes the analytical solvability of problems in Kirchhoff rods and the reliance on numerical simulations for post-buckling behavior.