多体系统动力学的高斯拘束分析方法

为研究高斯拘束原理下多体系统的动力学分析问题,针对一类多体开环链状结构,运用高斯拘束方法建立了动力学方程,讨论了动力学方程的符号推导过程,并给出了封闭形式的动力学方程解析表达式.以刚性和柔性结构为例,比较分析了不同分析方法、不同自由度下符号推导多体结构动力学方程的运算时间.分析结果表明,高斯拘束方法与传统的拉格朗日方法相比,更适合于多体结构动力学方程的符号推导,且结构自由度越高,其运算优势越明显.高斯拘束方法为一种较好的多体系统动力学分析方法.

DYNAMIC ANALYSIS OF MULTIBODY SYSTEM USING GAUSS CONSTRAINT

The dynamic analysis of multibody systems is carried out in this paper based on Gauss constraint principle, for a family of multibody open loop chain structures.  Gauss constraint method is used to derive the dynamic equation of multibody chain structures, in a symbolic derivation process, and the analytic expressions of the dynamic equation are obtained in closed form. By taking the rigid and flexible structures as examples, the time used for symbolic derivation of dynamic equations is analyzed for different analysis methods and degrees of freedom. It is shown that Gauss constraint method is more suitable for symbolic derivation of dynamic equations of multibody structures compared with Lagrange's method. Furthermore, the calculation advantage of Gauss constraint method increases with the increase of degrees of freedom.