多体系统动力学方程的无违约数值计算方法

Precise numerical solution for multi-body system's equations of motion based on algorithm without constraint violation

多体系统动力学方程为3阶微分代数方程,已有的约束违约稳定法存在位移违约问题,数值仿真准确性和稳定性不足。本文将求解高阶微分代数方程的降阶理论、ε嵌入处理方式与隐式龙格库塔法相结合,提出了直接满足位移约束条件的多体系统动力学方程的无违约算法,避免了约束违约问题。该方法先将多体动力学方程转化为2阶微分代数方程,并与位移约束方程联立;再应用ε嵌入隐式龙格库塔法进行数值求解。应用两种方法分别对单摆机构进行数值仿真,结果表明本文的方法不仅能适应较大步长,且准确性和稳定性均优于约束违约稳定法。

The multi-body system＇s equations of motion belong to differential algebraic equation（DAE） of index-3.For the constraint violation,the accuracy and stabilization of the constraint violation stabilization method（CVSM）is rather inadequate.In this paper,incorporating the theory of reducing-order for DAE of high index,εembedding method and implicit Runge-Kutta method,aprecise algorithm without constraint violation is presented.Applying the method,the constraint violation could be avoided.Firstly,the equations of motion are converted into DAE with index-2 and the displacement constraint equation remains.Secondly,implicit Runge-Kutta method embeddedεis applied to solve the equation directly.Using the two methods,respectively,a single-pendulum system is simulated.The results show that our method has better computational precision and stabilization than CVSM,even using large-steps.