  We devise a symbolic-numeric approach to the integration of the dynamical
part of the Cosserat equations, a system of nonlinear partial differential
equations describing the mechanical behavior of slender structures, like fibers
and rods. This is based on our previous results on the construction of a closed
form general solution to the kinematic part of the Cosserat system. Our
approach combines methods of numerical exponential integration and symbolic
integration of the intermediate system of nonlinear ordinary differential
equations describing the dynamics of one of the arbitrary vector-functions in
the general solution of the kinematic part in terms of the module of the twist
vector-function. We present an experimental comparison with the
well-established generalized alpha-method illustrating the computational
efficiency of our approach for problems in structural mechanics.
