Lagrange’s Equations for Complex Bond Graph Systems

[+] Author and Article Information
Dean Karnopp

Department of Mechanical Engineering, University of California, Davis, Calif.

J. Dyn. Sys., Meas., Control 99(4), 300-306 (Dec 01, 1977) (7 pages) doi:10.1115/1.3427123 History: Received September 26, 1977; Online July 13, 2010


The standard means of imposing causality to extract state equations for bond graph models of physical systems can be inconvenient when algebraic loops and derivative causality in combination with nonlinear constraints are present. This paper presents an alternative means of writing system differential equations using energy and coenergy state functions and Lagrange’s equations. For certain types of systems, particularly mechanical and electromechanical systems, this indirect means of finding state equations turns out to be very convenient. In this technique, causality is used in a new way to establish generalized coordinates and generalized efforts for nonconservative elements. Finally, it is shown that in some cases in which a Lagrangian can be written by inspection for a complex mechanism, a detailed bond graph for this component is unnecessary and yet the equations of the mechanism can be easily coupled to the bond graph equations for the remainder of the system.

Copyright © 1977 by ASME
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