Constrained Lagrangian Formulation for Multibody Systems using Bond Graphs

Abstract

A method for deriving the constrained form of Lagrangian equations of motion for an interconnected system of rigid bodies using bond graphs is presented. Intrinsically, this approach allows the formulation of the final form of equations for holonomic systems without recourse to the Lagrangian function. Consequently, the burdens of deriving the expressions for kinetic and potential energies, and performing the necessary differentiations have been eliminated. This method calls only for constructing the Jacobian matrix of constraints, and then employing a bond graph that accounts for the generalized constraint reaction forces.