A Bond Graph Representation of Lagrange’s Equations

Lagrange’s equations are developed for holonomic, constrained mechanical systems starting from true energy and a Legendre transformation. Each term in the traditional Lagrange’s equations are recognized as generalized efforts which allows a bond graph to be presented summing efforts associated with each generalized flow. The resulting bond graph represents kinetic energy as an IC-field since the energy is, in general, a function of both flow and displacement variables whereas the potential energy is a simple C-field. The model is explicit, no derivative causality exists and the equations of motion are written in terms of generalized momenta and generalized displacements as state variables. Because of the generalized momenta, no time derivative is necessary as in the standard Lagrangian approach which cuts down on equation complexity. Two examples are presented that show the method in relative detail.