Pozo Coronado, Luis Miguel2023-06-202023-06-2020000167-278910.1016/S0167-2789(00)00040-3https://hdl.handle.net/20.500.14352/57769The variational problem on spatial curves defined by the integral of the squared curvature, whose solutions are the elasticae or nonlinear splines, is analyzed from the Hamiltonian point of view, using a procedure developed by Munoz Masqueand Pozo Coronado [J. Munoz Masque, LM. Pozo Coronado, J. Phys. A 31 (1998) 6225-6242]. The symmetry of the problem under rigid motions is then used to reduce the Euler-Lagrange equations to a first-order dynamical system.engjournal articlehttp://www.sciencedirect.com/science/journal/01672789http://www.sciencedirect.comrestricted access517.9Hamilton equationsElasticaeGeneralized symmetriesvariational problemSpatial curvessquared curvatureRigid body motionsEuler-Lagrange equationsFirstorder dynamical systemEcuaciones diferenciales1202.07 Ecuaciones en Diferencias