Abstract : During the last years, mechanical articulated systems have become increasingly important in the field of automation. This work makes two important contributions towards a better utilization of mathematical abstraction: - The first contribution concerns the dynamic modelisation of articulated systems like mechanical manipulators and complex open kinematic chains. The mathematical abstraction by the Lie groups and Lie algebras theory offers an excellent means for simplifying the syntactical form of expressions of models. New methods for describing (by fundamental families) configurations of mechanical systems and an original efficient recursive computational scheme of Newton-Euler dynamics are developed. With this formulation, it should be possible to compute a near-optimal Newton-Euler dynamics in real time. - The second contribution concerns algebraic typing, term rewriting theory and automatic generation of codes. These problems lead to new computer algebra system architectures based on artificial intelligence methods and representations in multi-equational specifications. In this order of ideas, a prototype of computer algebra system (SURVEYOR) and an extension (MEDUSA MF77) of Maple system, based on object oriented programming and artificial intelligence control, are realized. A software tool for generating Fortran and Maple iterative symbolic optimized codes of our dynamic formulation is developed with MEDUSA MF77 system.