Efficiency Assessment of the Direct Integration Method by Central Differences (DIMCD)

The direct integration method by central differences (DIMCD) is an explicit method of order two for integrating the equations governing the dynamic analysis of multibody systems. So far, development has focused only on verifying the quality of the results. In this paper, it is shown that in addition to providing optimal results, it is also competitive from the point of view of computational efficiency, at least for systems with up to six bodies. For this purpose, an appropriate implementation of the method in a compiled language is presented. In turn, it is shown that the methodology is suitable for modeling in sparse matrices, although the proposed implementation is based on dense matrices. The resulting code is applied to different benchmark examples. Results from various commercial software are also included. Keywords: Computational efficiency, multibody dynamics, central differences, null space, dense matrices, quaternions