SYMBOLIC GENERATION OF A MULTIBODY FORMALISM OF ORDERN—EXTENSION TO CLOSED-LOOP SYSTEMS USING THE COORDINATE PARTITIONING METHOD

Abstract

The efficient computation of multibody systems dynamic equations certainly remains of a great importance in so far as both the increasing size and refinement of the mathematical models lead to a high complexity of the equations to be solved. Among the various multibody formalisms developed and implemented into computer programs, one generally admits that the so-called O(N) formulations have an intrinsic appeal: they require, in case of 'tree' multibody structures, a number of arithmetical operations which is only proportional to the number of degrees of freedom of the mechanical system under consideration. Obviously, this feature becomes really attractive in case of large multibody models, i.e. in which the number of degrees of freedom exceeds 20,...,30. In this contribution, we shall first present a pure symbolic generation of such a formalism in order to make it even more efficient. Secondly, we shall propose an original extension of the O(N) formulation to closed-loop systems by taking advantage, in terms of reliability, of the well-known 'Co-ordinate Partitioning method'. Using the symbolic approach, this seems to exhibit a good equilibrium between reliability and efficiency to get the generalized accelerations required by explicit integrator schemes. The method is illustrated through a numerical example.