Muñoz Masqué, JaimePozo Coronado, Luis Miguel2023-06-202023-06-202000966-02-1401-4https://hdl.handle.net/20.500.14352/60704Proceedings of the third international conference on symmetry in nonlinear mathematical physics, Kyiv, Ukraine, July 12-18, 1999. Part 1. Transl. from the Ukrainian. Kyiv: Institute of Mathematics of NAS of UkraineThe 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.engbook parthttp://www.slac.stanford.edu/econf/C990712/papers/art23.pdfopen access517.9Variational problemNonlinear splineHamiltonian formalismGeneralized symmetryReductionEcuaciones diferenciales1202.07 Ecuaciones en Diferencias