# Hierarchical Non-Linear Bond Graphs:

A Unified Methodology for Modeling Complex Physical Systems

## Abstract

Bond graphs have been around for a quarter of a century. While originally
intended for modeling mechanical systems, they have meanwhile found widespread
applications in many areas of physical system modeling. Bond graphs are a very
appealing tool for modeling physical systems, because they represent the flow
of power through a system. Since energy and mass are the only tradable goods
in our physical universe, a bond graph model is more likely to reflect physical
reality than a model derived by use of any other modeling methodology. However,
bond graphs, like all graphical techniques, become unwieldy when applied
to complex systems. Also, bond graphs were traditionally used to model
predominantly linear systems. This paper introduces new concepts for modeling
complex physical systems through hierarchical bond graphs which can include
arbitrary non-linearities. It introduces a software tool that can be used to
implement these hierarchical non--linear bond graphs. Finally, a new
application area for bond graphs will be discussed. It will be demonstrated
how these hierarchical non-linear bond graphs can be used to model chemical
reaction kinetics and chemical thermodynamics together in very general terms
also farther away from equilibrium than traditional approaches would permit.