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*.

** ** |
**Displace-**
ment |
**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 |

References:

http://johncarlosbaez.wordpress.com/2012/02/02/quantizing-electrical-circuits/

http://math.ucr.edu/home/baez/week288.html

http://math.ucr.edu/home/baez/week292.html

http://ncatlab.org/johnbaez/show/Diagrams

http://magisciences.tuxfamily.org/BondGraph/co/03%20Passive%20elements.html

http://www.feedcontfinals.ewebsite.com/articles/chapter-5/chapter-5-page-2/

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

[*7.60, *7.61]

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