We consider geometric variational problems for a functional defined on a
curve in three-dimensional space. The functional is assumed to be written in
a form invariant under the group of Euclidean motions. We present the
Euler-Lagrange equations as equilibrium equations for the internal force and
moment. Classical as well as new examples are discussed to illustrate our
approach. This new form of the equations particularly serves to promote the
study of bio- and nanofilaments.
keywords: one-dimensional variational problem, Euclidean invariance, Euler-Lagrange equations, elastic curves, bio- and nanofilamentsPhysical Review E 79, 066602 (2009)