We propose a method for the description and simulation of the nonlinear dynamics of slender structures modeled as Cosserat rods. It is based on interpreting the strains and the generalized velocities of the cross sections as basic variables and elements of the special Euclidean algebra. This perspective emerges naturally from the evolution equations for strands, that are one-dimensional submanifolds, of the special Euclidean group. The discretization of the corresponding equations for the three-dimensional motion of a Cosserat rod is performed, in space, by using a staggered grid. The time evolution is then approximated with a semi-implicit method. Within this approach we can easily include dissipative effects due to both the action of external forces and the presence of internal mechanical dissipation. The comparison with results obtained with different schemes shows the effectiveness of the proposed method, which is able to provide very good predictions of nonlinear dynamical effects and shows competitive computation times also as an energy-minimizing method to treat static problems.

翻译：我们建议一种方法,用于描述和模拟以Cosserat 棒为模型的微粒结构的非线性动态,其依据是将各截段的菌株和普遍速度作为欧洲碳化物特别代数的基本变量和元素加以解释。这一视角自然地产生于欧洲碳化物特殊组的线条的进化方程,即单维子元体。Coserat 棒三维运动的相应方程在空间使用错开的网格进行分解,然后将时间演变与半隐含法相近。在这个方法中,我们可以很容易地包括由于外部力量的动作和内部机械消散的存在而产生的分解效应。与不同计划所获得的结果的比较表明拟议方法的有效性,它能够很好地预测非线性动态效应,并显示有竞争力的计算时间,作为处理静态问题的能源最小化方法。