多刚体系统动力求解的矩阵变换方法

Matrix Transform Method for Dynamic Analysis of Rigid Multibody Systems

该文提出了求解多刚体系统动力学问题的矩阵变换法，是由带不定乘子的拉格朗日方程为基础推导得到的，其中不含拉格朗日不定乘子和约束反力。利用该方法，可根据无耦合单刚体的动力学参数和系统的速度变换矩阵通过矩阵运算获得多刚体系统的动力学方程。该方法主要面向计算机实现程式化的算法，系统动力方程可由计算机自动生成。文末给出了一个多刚体系统动力求解的例子。

The Matrix transform method for dynamic analysis of rigid multibody systems is presented in the paper. This method is based on the Lagrange multiplier method, but the resulting dynamic equations do not include the Lagrange multipliers and constraint forces. With the aid of the dynamic matrixes of each rigid body in its uncoupled system and the velocity transform matrix for a rigid multibody system, the dynamic equations of the coupled system can be obtained by the matrix operations. The method is especially suitable to programming dynamic analysis by computers. A rigid multibody system is illustrated in the end of the paper.