基于四元数表示的多体动力学系统及其保辛积分算法

Symplectic Integration for Multibody Dynamics Based on Quaternion Parameters

将四元数引入多体动力学系统,用以描述刚体转动分量,继而据此将问题转入约束动力学领域,建立相关的Lagrange体系.然后引入作用量并进行有限元近似,并保证格点上严格满足约束条件,则根据分析结构力学基本理论,可导出逐步积分的递推格式,并且积分保辛.该法具有未知数少、计算量小等优点,数值结果令人满意.

The quaternion representation was introduced into multibody dynamics for the de- scription of rigid body rotation, based on which the constrained dynamics was derived and the relevant Lagrange system was established. Then, the segmental action for discrete systems was introduced and approximated with the finite element method. According to the theory of analyti- cal structural mechanics, the symplectic numerical integration was derived with the constraints strictly satisfied at the integration points and the integration process was symplectic conserva- tive in the sense of variation principle. The proposed method has the characteristics of less cal- culation and less unknown numbers, which is confirmed with the numerical results of an exem- plary multibody hinged system.