A Topology-Based Approach to Exploiting Sparsity in Multibody Dynamics: Joint Formulation*

*Communicaled by E.J. Hung

ABSTRACT

In this paper, advantage is taken of the problem structure in multibody dynamics simulation when the mechanical system is modeled using a minimal set of generalized coordinates. It is shown that the inertia matrix associated with any open- or closed-loop mechanism is positive definite by finding a simple mathematical expression for the quadratic form expressing the kinetic energy in an associated state space. Based on this result, an algorithm that efficiently solves for second time derivatives of the generalized coordinates is presented. Significant speed-ups accrue due to both the no fill-in factorization of the composite inertia matrix technique and the degree of parallelism attainable with the new algorithm.

Notes

*Communicaled by E.J. Hung