No 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.

No abstract

This paper proposes a novel approach to the modelling of lumped-parameter dynamic systems, based on representing them by hierarchies of mathematical models of increasing complexity instead of a single (complex) model. Exploring the multilevel modularity that these systems typically exhibit, a general recursive modelling methodology is proposed, in order to conciliate the use of the already existing modelling techniques. The general algorithm is based on a fundamental theorem that states the conditions for computing projection operators recursively. Three procedures for these computations are discussed: orthonormalization, use of orthogonal complements and use of generalized inverses. The novel methodology is also applied for the development of a recursive algorithm based on the Udwadia-Kalaba equation, which proves to be identical to the one of a Kalman filter for estimating the state of a static process, given a sequence of noiseless measurements representing the constraints that must be satisfied by the system.