树形多体系统动力学的隐式数值算法

IMPLICIT NUMERICAL ALGORITHM FOR MULTIBODY DYNAMICS WITH OPEN LOOP SYSTEMS

研究了树形多体系统动力学的隐式算法．用矩阵形式给出了多体系统的正则方程及其右端函数的Ｊａｃｏｂｉ矩阵，并给出该矩阵的分块算法和对角隐式Ｒｕｎｇｅ－Ｋｕｔａ法（ＤＩＲＫＭ）以及隐式辛Ｒｕｎｇｅ－Ｋｕｔａ法（ＩＳＲＫＭ）．该算法便于编程计算，能提高计算效率，保持长期计算的稳定性．

The implicit algorithm of multibody systems with topological tree configuration is studied. The canonical equations of the system and the general form of Jacobian matrix of the equations are obtained in the form of matrix. The paper presents the algorithm of Jacobian matrix divided into several submatrices and the diagonal implicit Runge-Kutta method( DIRKM) and implicit symplectic Runge-Kutta method (ISRKM) of canonical equations of the multibody system. The methods are suitable for programing calculation, raise calculating efficiency and keep calculation stable for long time simulation. The numerical results support the conclusion.