This report presents the design of an extensible animation system in which rigid and deformable multibody systems are animated from their geometric models and the specification of kinematic and dynamic constraints. Theoretical, numerical and practical aspects of the system implementation are presented. One of its main features is the automatic derivation of the symbolic form of the motion equations from a physycal system model created interactively. This process is detailed by means of a simple example. Besides achieving a motion control by the application of direct dynamics, the system provides an animation of deformable objects, an automatic motion control from a specified motion without having to determine the forces required to perform this desired effect, and an object collision detection and response. Experimental results are presented to illustrate each animation control. Finally, the ability of our animation system for scientific simulation is discussed.