Appendix D. Physical Interactions

Physical systems are governed by conservation laws. When two (or more) components of a (1) mechanical, (2) electrical, (3) thermal or (4) hydraulical system are connected with each other, their connection points share the same value of a potential variable, such as (1) position/angle, (2) voltage, (3) temperature or (4) pressure, and they exchange (1) force/torque, (2) current, (3) heat or (4) liquid mass, which can be treated as flow variables that are governed by the balance equation f₁ + f₂ + ... f_n = 0.

In many cases, the product of a potential variable and a flow variable is power, which is the derivative of energy over time:

• force * velocity
• voltage * current
• pressure * mass flow

Electricity

Current (I) is the rate of flow of electric charge (Q): I = Q / t. So current (measured in amperes) is just coulombs per second. One amp means one coulomb of charge flowing by every second.

Voltage (or electric potential difference) represents the energy per unit charge: V = W / Q where W is the work done (energy) in moving charge Q between two points. Voltage is measured in volts, which are joules per coulomb. So voltage tells you how much "push" or potential energy each unit of charge carries.

So charge is the foundational quantity — current is its flow rate, and voltage is the energy it carries per unit. Power is their product: P = IV. Both charge and energy are conserved, but in different ways. Charge is absolutely conserved — it can't be created or destroyed, only moved around. Energy is also conserved, but it can change forms, and in practical systems it often degrades into heat

A useful analogy: imagine water in a pipe. Charge is like the water itself, current is how fast it flows (liters per second), and voltage is like the pressure driving it.

Mechanics

Force is the rate of change of momentum. So if current is like force, then naturally charge is like momentum. Both are conserved quantities, and both are the time-integral of their "flow" counterparts. Like voltage is energy per charge, velocity is energy per momentum. Consequently, velocity is, like voltage, a good choice for a potential variable, preserving the mapping of electrical power (current times voltage) to mechanical power (force times velocity).

However, also position is a possible choice for a potential variable. It's, in fact, the choice made in Modelica's standard library. Force times position is energy (work), and not power. So this choice breaks the mapping of electrical power to mechanical power.

Hydraulics

Pressure driving flow is like voltage driving current. Consequently, pressure is, like voltage, a good choice for a potential variable, while mass/volume flow rate is the natural choice for a flow variable.

Thermodynamics

Heat flow rate is, like current, the natural choice for a flow variable. Temperature is, like voltage, a good choice for a potential variable. However, it breaks the mapping of power.

The power-mapping-preserving choice for the flow variable is the entropy flow rate, since power is entropy flow rate times temperature.