Symbolic differentiation library for simulation of multibody rigid systems

This article presents a symbolic kernel dedicated to differentiation which is used in a system for both animation and simulation. Theoretical aspects about complexity of motion equations using a Lagrangian formalism are discussed using research previously carried out in differentiation area. From this study we derive a method that generate motion equations whose cost is linear with the number of degrees of freedom and whose implementation is realized using this kernel. Experimental results are presented using this method and a complex physical mechanism is described in order to prove the ability of our system to deal with such mechanisms.