Hamilton equations for elasticae in the Euclidean 3-space

The variational problem on spatial curves defined by the integral of the sq uared curvature, whose solutions are the elasticae or nonlinear splines, is analyzed from the Hamiltonian point of view, using a procedure developed b y Munoz Masqueand Pozo Coronado [J. Munoz Masque, LM. Pozo Coronado, J. Phy s. 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 dynami cal system. (C) 2000 Elsevier Science B.V. All rights reserved.