Motion analysis of multibody systems by null space matrix method of differential equation type

Abstract

This paper presents a method for analysis of motion of multibody systems. In the presented method, the null space matrix for the constraint Jacobian is determined by solving differential equations, not by solving algebraic equations which is common in other methods such as the coordinate partitioning method and the null space method. In the algorithm, the QR decomposition for the constraint Jacobian is utilized. Use of the differential equations for the null space matrix and the QR decomposition as well as the introduction of stabilization terms allow us to analyze without any problems motion of multibody systems which have redundant constraint and/or singular configuration. In addition, the presented method solves the Maggi's equation which is the equation obtained by eliminating the Lagrange multipliers from the equation of motion and by expressing the unknown variables only with the independent components. Thus the computational cost is not so high. The validity of the presented method is verified by numerical examples.