Formal computation of non-rigid multibody systems dynamics

The goal of this paper is to present an algorithm for computing efficiently the dynamic model of non-rigid systems. To this end it makes use of results issued from the differentiation area. First, we briefly present our unified abstract model which integrates traditional physically based models such as rigid solids, mass-springs meshes, finite elements and particle systems. Then, we discuss of the use of the two existing differentiation modes (forward and reverse) for computing formally the motion equations by the means of Lagrange's equations. Using theoretical results coming from the research's field about differentiation, in our algorithm for computing the dynamic model, we show that we obtain minimal linear complexity of the motion equations. Finally we present numerical and practical aspects of the algorithm for computing efficiently the dynamic model.