带约束多体系统动力学方程的隐式算法

Implicit numerical algorithm for multibody dynamics with constraint equations

研究了带约束多体系统动力学方程的隐式算法，用子矩阵的形式推导出了多体系统正则方程的Ｊａｃｏｂｉ矩阵，它适用于多种隐式算法并给出了隐式Ｒｕｎｇｅ－Ｋｕｔｔａ 算法，最后用一算例表明了隐式算法的计算效率和精度明显优于显式算法．

The implicit numerical algorithm for dynamics of multibody systems with constraint equations of motion was studied. The canonical equations for dynamics of multibody systems were used in the numerical algorithm. The Jacobian matrix used in implicit methods was obtained in the submatrix forms, that was very good in computational efficiency and suitable for many implicit numerical methods. The paper presented the diagonal implicit Runge Kutta method for multibody dynamics. The numerical results show that the computational efficiency and precision of implicit algorithms are better than that of explicit algorithms.