Improved Differential Nullspace Matrix Method for the Dynamic Analysis of Multibody Systems

This paper presents a novel method for motion analysis of rigid multibody systems. In general, dynamics of multibody systems is described by differential algebraic equations with Lagrange multipliers. For efficient and accurate analysis, it is desirable to eliminate the Lagrange multipliers and dependent variables. Methods called nullspace method and Maggi’s method eliminate the Lagrange multipliers by using the nullspace matrix for the constraint Jacobian. In a previous report, the author presented a method in which the nullspace matrix is obtained by solving a differential equation together with the equation of motion of the system. In that method QR decomposition is used. In this report, reduction in computational time with the LU decomposition is attempted. In addition, treatment of singular configurations for accurate analysis is presented. Validity of the presented method is confirmed via numerical examples.