A contribution on the modular modelling of multibody systems

Abstract

Over the past half-century, the increasing use of computational tools for mathematical modelling and simulation was responsible for significant advances in the area of Multibody System Dynamics. However, there is still a high dependence on the use of proprietary software in this area. Noticing that most of the complex multibody systems share many components and subsystems, this paper aims to propose a modular modelling methodology in which the starting points are some already known mathematical models of subsystems and the corresponding descriptions of the constraints existing among them. The proposed algorithm is based on the computation of some orthogonal complements of Jacobian matrices, derived from the constraint equations among the subsystems, leading to a minimal system of equations without requiring the use of undetermined multipliers or generalized constraint forces. Such an algorithm can be implemented using general-purpose (eventually open source) software packages or programming languages. Another remarkable advantage of this methodology stems from the fact that even when different (Classical or Analytical Mechanics) formalisms have been used in the modelling of subsystems, it is still possible to use the proposed algorithm. Well-known examples and a rederivation of the Whipple bicycle model are used to illustrate applications of this novel methodology.