Appendix A: Equation Sets for Various Engineering Domains

Each domain is represented by a tetrahedral figure relating four variables (two "through" variables — an integral pair — and two "across" variables — the effort/flow pair) via R, C, and L (inductance) relationships. All five domain tetrahedra follow the same structural pattern; the variable names change per domain.

Figure 32: Mechanical (Linear) Domain

Corners: Relative Velocity v, Momentum m, Force F, Relative Displacement q. Center elements: L, R, C.

• v = 1/L × m
• F = R × v
• v = 1/R × F
• q = ∫ v dt
• m = ∫ F dt
• F = 1/C × q

Figure 33: Mechanical (Rotary) Domain

Corners: Relative angular Velocity ω, Angular Momentum σ, Torque T, Relative angular Displacement θ. Center elements: L, R, C.

• ω = 1/L × σ
• T = R × ω
• ω = 1/R × T
• θ = ∫ ω dt
• σ = ∫ T dt
• T = 1/C × θ

Figure 34: Electrical/Electronic Domain

Corners: Current i, Flux λ, Voltage V, Charge q. Center elements: L, R, C.

• i = 1/L × λ
• v = R × i
• i = 1/R × V
• q = ∫ i dt
• λ = ∫ v dt
• v = 1/C × q

Figure 35: Thermal Domain

Corners: Heat flow rate q, Temperature T, Heat θ. Center elements: R, C.

• T = R × q
• q = 1/R × T
• θ = ∫ q dt
• T = 1/C × θ

Figure 36: Hydraulic/Pneumatic Domain

Corners: Flow rate Q, Pressure Momentum Γ, Pressure p, Volume V. Center elements: L, R, C.

• v = 1/L × Γ
• p = R × Q
• Q = 1/R × p
• V = ∫ Q dt
• Γ = ∫ p dt
• F = 1/C × q (as printed; volume/pressure integral relation, analogous to F = 1/C × q for the other domains — printed as "F=1/C*q" in the source figure, likely a labeling carryover from the linear-mechanical template)