Mechanics of Kirchhoff Rods II

This lecture covers the application of Kirchhoff equations to rods, focusing on kinematics in 3D and twisted solutions. It explains the derivation of Kirchhoff equations for elastic rods, including force and moment balance, and the calculus of force balance. The lecture demonstrates examples of kinematics in 3D and twisted solutions in the Kirchhoff equations, emphasizing the determination of rod shapes based on boundary conditions. It also discusses the mechanics of twisted solutions in rods, the derivation of equations for twisted rods, and the analysis of twisted circle solutions. The lecture concludes with the exploration of the mechanics of twisted rods under pure torque and the computation of rod shapes using differential geometry.