Dynamics of spatial beams in quaternion description based on the Newmark integration scheme

The rotational quaternions represent a unique four dimensional parametrization of rotations in the three dimensional Euclidean space. In the present paper they are used as the basic rotational parameters in formulating the finite-element approach of geometrically exact beam-like structures. The classical concept of parameterizing the rotation matrix by the rotational vector is completely abandoned so that the only rotational parameters are the rotational quaternions representing both rotations and rotational strains in the beam. The space discretization based on the collocation method is used and the adjustment of the Newmark time-integration algorithm to the quaternion parameterizations of rotation is presented.