On the Extension of the Bondgraphic Power Postulate to Some Relativistic Phenomena

Nasser M. N. Gussn
Saudi Aramco
P.O. Box 11335
Dhahran 31311
Saudi Arabia
Email: benghanm@aramco.com.sa
François E. Cellier
Institute of Computational Science
ETH Zürich
CH-8092 Zürich
Switzerland
Email: FCellier@Inf.ETHZ.CH

Keywords

Bondgraphs
Coenergy
Contravariance
Covariance
Electromagnetic Field-Strength Tensor
Energy
Energy-Momentum Tensor
Galilean Transformations
General Relativity
Lorentz Transformations
Principle of Relativity
Special Relativity
Tensors

Abstract

Since their official birth on April 24, 1959, bondgraphs evolved to become one of the most effective and most elegant tools for modeling system dynamics. The unifying attitude of bondgraphs, or BGs for short, towards systems, enables model builders to connect system components from different physical domains using the same set of bondgraphic elements. It was this unifying attitude that furnished the impetus for this work that investigates the possibility of applying BGs to Einstein's standard theories of relativity, thus extending the BG approach of modeling to relativistic dynamics. To this end, a new formulation of the bondgraphic power postulate (that is built using four-vector efforts and flows) is developed. Then special relativistic (SR) particle-mechanics and electro-dynamics (via a one particle system) are investigated, and the bondgraphic interpretation for both is also provided. Finally, we provide Einstein's gravitational field equations, a bondgraphic interpretation of them, and the energetic problems facing standard general relativity (GR).

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