Systems Dynamics

Another interesting fourfold that I discovered while reading mathematical physicist John C. Baez’s blogs Azimuth and This Week’s Finds in Mathematical Physics concerns the notions of system dynamics and bond graphs. These concepts generalize the fourfold of the basic electronic components into other types of physical systems, such as mechanics, hydraulics, and to some extent even thermodynamics and chemistry.

The types of systems that can be modeled by system dynamics are described by two variables that vary functionally over time and their corresponding integrals. These four functions can be thought of as flow and effort and their respective integrals displacement and momentum.

Flow Momentum Effort
Mechanics of translation Position Velocity Momentum Force
Mechanics of rotation Angle Angular velocity Angular momentum Torque
Electronics Charge Current Flux Voltage
Hydraulics Volume Flow Pressure momentum Pressure
Thermo-dynamics Entropy Entropy flow Temperature momentum Temperature
Chemistry Moles Molar flow Chemical momentum Chemical potential


Dean C. Karnopp, Donald L. Margolis, Ronald C. Rosenberg / System Dynamics: modeling and simulation of mechatronic systems

[*7.60, *7.61]




One Response to “Systems Dynamics”

  1. Ohm’s Law | Equivalent eXchange Says:

    […] voltage and current have been in two fourfolds previously (Four Basic Electrical Components and System Dynamics) but not power and resistance. Well, resistance did make an appearance as a relation between […]

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