Abstract

Controlled junctions with dynamic causality can be used to generate mixed-Boolean mathematical models. Several variations on the Switched or Hybrid Bond Graph have already been proposed, with none reaching common usage. The motivation for suggesting this approach was to develop a general method for adoption by practicing engineers, which is intuitive, adheres to the principles of idealized physical modelling and facilitates both structural analysis and efficient simulation. This paper revisits the classical example of a bouncing ball in order to discuss the advantages and disadvantages of such an approach with reference to the body of literature on hybrid models and nonsmooth dynamics. A switching model (as opposed to an impulse model) is generated which is both stiff and contains kinematic constraints, making it problematic to simulate. However, the method facilitates model simplification and the derivation of a coefficient of restitution, allowing Newton’s collision law to be applied. The resulting model simulates efficiently and well, without the need for parasitic elements or state reinitialization algorithms.