  This contribution is concerned with the motion planning for underactuated
Euler-Bernoulli beams. The design of the feedforward control is based on a
differential parametrization of the beam, where all system variables are
expressed in terms of a free time function and its infinitely many derivatives.
In the paper, we derive an advantageous representation of the set of all formal
differential parametrizations of the beam. Based on this representation, we
identify a well-known parametrization, for the first time without the use of
operational calculus. This parametrization is a flat one, as the corresponding
series representations of the system variables converge. Furthermore, we
discuss a formal differential parametrization where the free time function
allows a physical interpretation as the bending moment at the unactuated
boundary. Even though the corresponding series do not converge, a numerical
simulation using a least term summation illustrates the usefulness of this
formal differential parametrization for the motion planning.
