Hamilton equations for elasticae in the Euclidean 3-space

The 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 Muñoz Masquéand Pozo Coronado [J. Muñoz Masqué, L.M. 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.