The elastica is a curve in R3 that is stationary under variations of the integral of the square of the curvature. Elastica is viewed as a dynamical system that arises from the second order calculus of variations, and its quantization is discussed.

Calculus of variations, Elastica
dx.doi.org/10.1016/j.geomphys.2016.09.001
Journal of Geometry and Physics

Bates, L. (Larry), Chhabra, R, & Śniatycki, J. (Jędrzej). (2016). Elastica as a dynamical system. Journal of Geometry and Physics, 110, 348–381. doi:10.1016/j.geomphys.2016.09.001