Hamilton equations for elasticae in the Euclidean 3-space
The variational problem of the spatial curves defined by the squared curvature is analyzed by using Hamiltonian formalism. The symmetry of the problem under the rigid body motions is used to reduce the Euler-Lagrange equations to a first-order dynamical system. This allows a qualitative treatment of the problem by using standard dynamical system tools.
scientific article; zbMATH DE number 1496074