Pseudouptriangular decomposition method for constrained multibody systems using Kane's equations

A pseudouptriang ular decomposition method used to obtain an orthogonal complement array to automatically reduce the equations of motion is presented. The method is based on a successive multiplication of Householder transformations to develop an uptriangular matrix whose column vectors are orthogonal to the rows of the corresponding constraint matrix. The columns of the transformation matrix represent the directions for which the system is unrestrained in ^-dimensional space. The automatic generation of the transformation matrix makes the analysis of constrained multibody systems more tractable. The method developed is found to be useful when the equations of motion are developed using Kane's equations with undetermined multipliers. A discussion of the advantages of the method presented vs previous methods is presented together with illustrative examples.