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Quaternion-based dynamics of geometrically exact Cosserat rods [Elektronski vir]
Zupan, Eva ...
Rotational quaternions represent a unique four dimensional representation of rotations in three-dimensional Euclidean space. In the present paper they are used as the primary quantities to describe ...the rotational degrees of freedom in the finite-element dynamic analysis of geometrically exact beam-like structures. The classical concept of parameterization of the rotation matrix by the rotational vector is thus completely abandoned. The consistency of the governing equations of the beam in terms of the quaternion algebra is preserved by extending dʼAlembertʼs principle with the unit-norm rotational quaternion constraint. In the numerical implementation the Galerkin-type discretization is employed to obtain the finite element formulation of the problem. In contrast to standard approaches, we base the spatial discretization on the interpolated velocities and angular velocities along thelength of the beam axis.
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