Role of zero frequency modes in bond graph adapted dual space formulation

The technique of analysing dynamic systems making use of a bond graph adapted dual formulation was presented earlier by the authors. In that paper representation of the subsystems and their subsequent modal decomposition was based on their dynamic modes, removing altogether the nondynamic modes characterized by zero frequencies. However, sometimes in a momentum based formulation there are zero frequency modes which play a significant role in the overall dynamics of the system and when eliminated lead to anomalous results. In the present work, the role of such nondynamic modes in bond graph adapted dual formulation is discussed. An algorithm is presented for retaining these modes in the overall system models. The procedure is extended to obtain system response taking advantage of a second-stage modal decomposition. The procedure is illustrated by suitable examples.