Is a well studied problem. I am a textiles engineer and am doing some work on modelling the interaction of the yarn with a brush ring (circular brush with hairs slowing the yarn down). You can easily calculate the deformation of a hair caused by a force perpendicular to the curve of the hair in 2D by dividing the hair in finite elements or finite volumes - as the deformation is rather big - and apply the classical formulas for a beam in bending to the elements. Piece of cake. A bit more difficult: the yarn moving through the brush is a dynamic phenomenon, I also want to model inertia. When you move a rigid object with mass m an acceleration a in a certain direction, you know the force F = ma. However, when applying this on a hair in bending, the base of the hair is fixed and the yarn bends in the process, which corresponds to a translation and rotation of the different elements. Anyone an idea of how to calculate the inertia force caused by an acceleration of a point on the hair perpendicular to the curve of the hair in 2D, or of the inertia force of a beam in bending or something? An idea how and where to start?