2. Introduction

The essential difficulty of the mechanics of beams in large displacements lies in the formulation of the rotations. The rotation of a section with respect to a reference configuration is defined by the rotation vector ([bib3], [bib4], and [bib5]). Quaternions are used to update this vector.

In [bib4] and [bib5], the rotation increment is expressed in the reference configuration (total Lagrangian diagram). The calculation of mass matrices is complicated and cannot be completely completed. But in the end, all the matrices used are symmetric.

In [bib1] to [bib3], the rotation increment is expressed in the last calculated configuration (updated Lagrangian schema). This is the pattern that we have chosen. The calculation of the matrices is completed without excessive difficulty but they are not symmetric.

Unlike [bib3], we expressed angular velocities and accelerations in general axes and not in local axes. The matrices are thus more complicated, but the ambiguity that appears at the junction of two non-collinear beams is avoided.