多体系统动力学方程的反馈参数自适应约束违约稳定法

Adaptive Feedback Parameters for Baumgarte's Constraint Violation Stabilization Methods of Multibody System's Equations of Motion

约束违约稳定法的反馈参数的正确选择,是影响其计算准确性和稳定性的重要因素之一.通过计算误差、位移约束违约程度和速度约束违约程度3项指标来综合选择反馈参数,提出了一种多体系统动力学方程的反馈参数自适应的约束违约稳定法.数值分析表明:该方法适用于定步长和变步长、显式和隐式算法,有利于减小数值误差的积累和数值解的漂移,执行简单、高效、易于嵌入已有算法,且无需依赖于特定的积分方法.

The reasonable selection of the feedback parameters is one of the important factors,which affects the accuracy and stability of the implement of the Baumgarte＇s constraint violation Stabilization Methods（BSM）.For the equations of motion of multibody system,a modified BSM with adaptive feedback parameters is proposed.The feedback parameters are determined by the computational error,the degree of the position constraints violation and that of the velocity constraints violation.The numerical simulations show that the proposed method is applicable to the explicit（for example Dopri5） and implicit（for example Radau5） arithmetics,with constant or adaptive step size,and is also favorable to reduce the accumulation and magnification of the computational error during iterations.It is also easy to implement and embedded into the known arithmetics,and independent of special arithmetic.