Different Dynamic Formulations for a Mechanism using Bond Graph

Abstract

For modeling dynamics of mechanisms, various classical formulations are available in literature. The equations of dynamics given by the various classical formulations can also be derived from bond graph. Bond graph is a convenient graphical representation for modeling dynamics of physical systems in multiple energy domains. In this paper, various alternative causality assignment procedures in bond graph are used to derive different classical formulations such as Lagrange of the first kind (with multipliers), Lagrange formulation of the second kind and Hamiltonian formulations. An example of a mechanism has been modeled using bond graph technique and various alternative causality assignment procedures are applied to derive the various formulations. Simulation coding has been done using MATLAB and plots of various properties have been drawn, analyzed and discussed. The purpose of this paper is to show, how the various formulations can be obtained from bond graph using various alternative causality assignment procedures.