Hamiltonian Formulation and Order Reduction for Nonlinear Splines in the Euclidean 3-Space

Abstract

The authors use the procedure developed in [9] to develop a Hamiltonian structure into the variational problem given by the integral of the squared curvature on the spatial curves. The solutions of that problem are the elasticae or nonlinear splines. The symmetry of the problem under rigid motions is then used to reduce the Euler–Lagrange equations to a firstorder dynamical system.