Implicit Hamiltonian formulation of bond graphs

This paper deals with mathematical formulation of bond graphs. It is proven that the power continuous part of bond graphs, the junction structure, can be associated with a Dirac structure and that equations describing a bond graph model correspond to an implicit port-controlled Hamiltonian system with dissipation. The condition for well-posedness of the modelled system are given and representations suitable for numerical simulation are derived. The index of the representations is analysed and sufficient conditions for computational efficiency are given. The results are applied to some models arising in automotive applications.