AN APPROACH TO DERIVATIVE CAUSALITY IN BOND GRAPH MODELS OF MECHANICAL SYSTEMS

Dynamic system models involving rigidly coupled inertia elements often result in derivative causality problems when represented in bond graph form. This means that explicit state equations can only be obtained after algebraic manipulation. The problem is particularly severe when geometric nonlinearities are involved as represented by displacement modulated transformers. A practical solution is to eliminate the derivative causality by defining an I-field or an IC-field using generalized momenta and (if necessary) generalized coordinates as is done when applying Lagrange's or Hamilton's equations. The inversion of a mass matrix is required. In the worst case, the inversion may have to be done repeatedly during a computer simulation.