多体系统动力学Lie群微分⁃代数方程约束稳定方法

摘要

Constraints stabilization method on Lie group is studied for different?algebraic equations(DAEs)of multibody system dynamics. Considering the displacement constraints, the velocity constraints and the accelera?tion constraints equations,the new Lagrange multipliers are used to construct the new DAEs on Lie groups.Then, using the ward difference method and CG(Crouch?Grossman)method, high accuracy simulation results is obtained by solving the constraints stabilization DAEs. The constraints stabilization method can accurately main?tain the constraint equation at all levels, and can maintain the orthogonality of rotation matrix. Meanwhile, the total energy error of the system is smaller.%针对多体系统动力学微分?代数方程求解问题,研究基于Lie群表达的约束稳定方法.首先引入新的Lagrange乘子,结合位移约束、速度级约束和加速度级约束方程,构造了新的Lie群微分?代数方程.然后使用向后差商隐式方法和CG(Crouch?Grossman)方法,对微分–代数方程进行离散求解,得到精确度较高的动力学仿真结果.该方法在精确保持各级约束方程的同时,保持旋转矩阵的正交性,并且使系统总能量误差较小.