Inextensible elastic rods with torsional friction based on Lagrange multipliers

Elastic rods are thin flexible objects typically undergoing large non-linear deformations that cannot be modeled with linear methods. They are used in a number of research fields, e. g., to represent hair or ropes in animations, or catheters or needles in medical simulations. In this paper, we propose a deformation model for inextensible elastic rods. The method of Lagrange multipliers is employed to enforce the inextensibility of the rod, and to couple the material frames with the centerline. The resulting system is banded, allowing for an efficient linear time solution. We also propose a manifold projection method to incorporate the non-penetration constraints resulting from contact handling into our constrained Lagrangian mechanics