When it comes to "slender elastic bodies"—think human hairs or steel pipes—MIT researchers have done Euler one better with work that both engineers and animators will find useful.
While the equation Euler derived in 1744 to describe a slender elastic body has no explicit solutions, the model the researchers developed will, given curvature, length, weight, and stiffness, predict the shape of a hair, steel pipe, or Internet cable suspended under its own weight.
Animators will be able to use the model to give their creations bouncy curls; engineers will be better equipped to foresee the effect coiling will have on a cable.
Says researcher Pedro Reis:
The importance of the work is being able to take the intrinsic natural curvature of rods into account for this class of problems, which can dramatically affect their mechanical behavior. Curvature can delay undesirable instability that happens at higher loads or torsion, and this is an effect that engineers need to be able to understand and predict.
Read MIT's coverage.