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

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