Understanding multibody dynamics using bond graph representations

The dynamics of complex interconnected mechanical systems can be described using a number of formalized procedures in the field of multibody dynamics but it is not always easy to understand the significance of the quantities introduced as part of these various procedures. Bond graphs can also be used to describe mechanical systems and often provide intuitive and physically motivated means for enforcing constraints among interacting bodies. Using the example of a multilink inverted pendulum which has been often studied, we show that a bond graph can explain the form of multibody system equations. The bond graph can also suggest practical explicit differential equation formulations closely related to the descriptor differential algebraic equations of multibody formulations. Some subtleties associated with the interpretation of Lagrange multipliers will also be discussed and related to different ways in which constraint equations can be formulated.