Topology Based Linear Solver for Exploiting Sparsity in Multibody Dynamics

Summary. In this paper, a new method to eciently compute accelerations and Lagrange multipliers in the equations of multibody dynamics is presented. These quantities are the solution of a system of linear equations whose coecient matrix has the special structure of an optimization matrix. This matrix is likely to have a large number of zero entries, according to the connectivity among bodies of the me-chanical system. Advantage is taken of both the special structure and the sparsity of the coecient matrix. Simple manipulations bring the original problem of solving a system of n+m equations in n+m unknowns, to an equivalent problem in which a positive denite system of dimension m m has to be solved for the Lagrange multipliers. Accelerations are then eciently determined. For certain mechanical system models, the bandwidth of the positive denite m m matrix can be sig-ni cantly reduced by appropriately numbering the joints connecting bodies of the model. Numerical experiments show the eectiveness of the proposed algorithm. 1