Two-field formulation of the inertial forces of a geometrically-exact beam element

An independent velocity field is introduced via Legendre transformation of the kinetic energy of a geometrically-exact beam, leading to a first-order system of twice as many governing equations as a one-field formulation. Nevertheless, the new field does not have to be assembled across elements and can be eliminated at the element level, so that the assembled system has the same size as a one-field formulation. Furthermore, because the new field does not have to satisfy the compatibility equations that the original velocity field is subjected to, its finite-element discretization is simpler and leads to simplified inertial forces.