Interpolation of rotational variables in nonlinear dynamics of 3D beams

The formulation of dynamic procedures for three-dimensional (3-D) beams requires extensive use of the algebra pertaining to the non-linear character of the rotation group in space. The corresponding extraction procedure to obtain the rotations that span a time step has certain limitations, which can have a detrimental e ect on the overall stability of a time-integration scheme. The paper describes two algorithms for the dy- namics of 3-D beams, which di er in their manifestation of the above limitation. The rst has already been described in the literature and involves the interpolation of iterative rotations, while an alternative formula- tion, which eliminates the above e ect by design, requires interpolation of incremental rotations. Theoretical arguments are backed by numerical results. Similarities between the conventional and new formulation are pointed out and are shown to be big enough to enable easy transformation of the conventional formulation into the new one.