Finite rotations in dynamics of beams and implicit time-stepping schemes

We examine theoretical and computational aspects of three-dimensional finite rotations pertinent to the dynamics of beams. The model problem chosen for consideration is the Reissner beam theory capable of modelling finite strains and finite rotations in geometrically exact manner. Special emphasis is placed on clarifying the geometry aspects, finite rotation updates and the associated linearization procedure pertaining to different choices of rotation parameters. The latter is shown to play an important role in constructing the optimal implementation of a time-stepping scheme.