Kane’s equations for nonholonomic systems in bond-graph-compatible velocity and momentum forms

The authors’ previously published results on a bond-graph-compatible and nonholonomic momentum form of Kane’s equations are extended, from scleronomic to rheonomic systems. The momentum form is found to be partially Hamiltonian, and bond-graph-compatible velocity forms are also found, of which one is partially Lagrangian. The results are derived for general particle systems and then specialized to rigid-body systems. Direct dependence of kinetic energy upon time is avoided, making the results power-conserving and suitable for use with bond graphs. A new nonholonomic IC (NIC) bond-graph element is defined, and bond graphs for the partially Hamiltonian and partially Lagrangian forms are exhibited using this element.