Critical study of Newmark-scheme on manifold of finite rotations Original Research Article

In this paper, we show that the usual material form of the Newmark-time-stepping scheme of finite rotations is only a simplified version of the correct formula. This is because spin material rotation vectors, angular velocity vectors and angular accelerations vectors belong to different tangential vector spaces of a manifold at separate time moments. We give corrected Newmark-time-stepping schemes for material description and for spatial description.