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Complex contact interactions between the robot and its environment (contact between a dextrous hand and a grasped object, contact between an all-terrain vehicle and the terrain, ..) depend on physical properties such as mass, mass distribution, rigidity/elasticity factors, viscosity, and collision forces. Classical geometrical models (representing the spatial properties of an object) are obviously not helpful to study such interactions. So one needs another model which represents not only the form of the object but also its motion, its deformation and, its interaction with the environment. Such a model is called the "dynamic model". This paper describes the RobotΦ system, which enables one to physically represent robots and to study their physical behaviour. This system uses a hierarchical representation of objects in order to accelerate collision detection (linear time for rigid objects). An energy based adaptative time step approach was developed in order to detect and avoid numerical divergence and to reduce computational time.