  We propose a method for the description and simulation of the nonlinear
dynamics of slender structures modeled as Cosserat rods. It is based on
interpreting the strains and the generalized velocities of the cross sections
as basic variables and elements of the special Euclidean algebra. This
perspective emerges naturally from the evolution equations for strands, that
are one-dimensional submanifolds, of the special Euclidean group. The
discretization of the corresponding equations for the three-dimensional motion
of a Cosserat rod is performed, in space, by using a staggered grid. The time
evolution is then approximated with a semi-implicit method. Within this
approach we can easily include dissipative effects due to both the action of
external forces and the presence of internal mechanical dissipation. The
comparison with results obtained with different schemes shows the effectiveness
of the proposed method, which is able to provide very good predictions of
nonlinear dynamical effects and shows competitive computation times also as an
energy-minimizing method to treat static problems.
