Application areas
Bond graphs as a modeling language are applicable to any system where energy like quantities are exchanged. Non-energetic systems like market economics can be quantized and modeled in form of pseudo bond graphs, where effort and flow equivalences can be drawn, e.g. unit price is the driving force and order flow rate is the flow equivalence leading to rate of change of wealth (unit price*order flow rate) as the equivalent quantized power variable.
Since any factor of power in a bond can be activated (i.e., a bond can be characterized to carry only information of one of the factors of power), non-energetic signal oriented system models can be drawn using bond graphs. Examples of such system modeling techniques are Block diagrams,Linear graphs and Signal flow graphs.
A bond graph model finally leads to automatic derivation of system equations. Any non-linearities in the system can thus be embedded directly in to the modeling paradigm in terms of non-linear sources, parameters and moduli of two-port elements, etc. The solution algorithm of the sorting and integrating routine is responsible to properly solve these equations.
The fastest integration schemes are mostly based on ODE's (ordinary differential equations). Bond graphs
by its shear algorithmic power and structure always lead to a set of ODE's. This is a great boon in
today's object oriented modeling world since ODE's from different sub-models can be linked to create
a larger set of ODE's representing an entire plant.
ODE's represent states of a system. These are unlike the traditional equation writing using Newton's law or Lagrangians.
For example, let us consider a single degree of freedom system represented by the equation
m d2x/dt2 + r * dx/dt + k*x = F(t).
The two state equations derived from a bond graph model would, however, be
dP/dt= -r/m * P - k*Q + SE,
dQ/dt= 1/m*P,
where, P is momentum of m*dx/dt, Q is displacement or x and SE is F(t)).
From the second equation, P=m*dQ/dt, which when replaced in the first leads to
m*d2Q/dt2=-r*dQ/dt - k*Q + F(t).