Bond-graph representation of ideal constraints via the principle of virtual power

In this paper we develop bond-graph representations for ideal mechanical constraints, both embedded and adjoined, by stating and applying the principle of virtual power, at the particle level, to both types of constraints. The resulting system-level bond graph provides a bond-graphic derivation of Kane’s equations for a general nonlinear nonholonomic system. Four examples are then shown to illustrate the application of the method to specific systems. In the final example, we show how to apply the method to an existing bond graph having causal conflicts that force inertial elements into derivative causality, thereby resolving the causal conflicts. This is a new and evidently powerful procedure for resolving causal conflicts with inertial elements in bond graphs, which we call the junction augmentation method, and that we recommend for integration with existing procedures for sequential causality assignment in bond graphs.