BGMod Ports: p1, p2, …
Tᵢ = Tⱼ; Σ ω_local = 0
Every bond has its own junction port. Equal torque; local angular velocities sum to zero. No parameters or state.
BGMod
Rotational mechanics
Effort is torque and flow is angular velocity; their product is power. This is a separate domain: its ports cannot connect directly to translational, electrical or hydraulic ports.
Rotational mechanics → Primitives / AdvancedN·m / rad/se · f = W
The torque/angular-velocity convention uses Se for applied torque, I for inertia and C for elasticity. The dual convention with effort and flow exchanged is not supported. Each shaft has its own positive axis; external gears physically rotate in opposite directions.
Primitives
0Common torque
1Common angular velocity
Ports: p1, p2, …
directionᵢ ωᵢ = directionⱼ ωⱼ; Σ sᵢ Tᵢ = 0
Every bond has its own junction port. Equal reference-adjusted angular velocity; signed torques sum to zero. Endpoint signs remain fixed when a bond reference is reversed.
RTorsional damperN·m·s/rad
Ports: R
T = B·ω_local; P = B·ω_local²
Enter finite B > 0 in N·m·s/rad; default 1. A damper on a shaft junction acts relative to the fixed support. The coupling damper acts on relative shaft speed.
CTorsional springN·m/rad
Ports: R
T = K·Δθ = Δθ/C; dΔθ/dt = ω_local; E = K·Δθ²/2
Enter finite stiffness K > 0 in N·m/rad; default 100. The editor displays derived compliance and saves params.value = C = 1/K in rad/(N·m). The reciprocal must also be finite and positive. Initial state is twist Δθ₀ in rad, default 0.
IRotational inertiakg·m²
Ports: R
ω_local = L/J; dL/dt = T; E = L²/(2J)
Enter finite inertia J > 0 in kg·m²; default 1. Initial state is angular momentum L₀ in kg·m²/s, default 0. For an initial speed ω₀, enter L₀ = J·ω₀.
SeTorque sourceN·m
Ports: R
T = u(t)
Torque in N·m; default 1. Constant or step waveform. A step has value before time and after at or after time; time ≥ 0 s. Either torque sign is allowed. No stored state.
SfAngular velocity sourcerad/s
Ports: R
ω_local = −u(t)
Angular velocity in rad/s; default 0.1. Constant or step waveform with the same settings as Se. Positive input supplies flow out of the source, hence negative inward local flow. No stored state.
TFIdeal gear1
Ports: P, S
T₁ = n·T₂; ωS_local = −n·ωP_local; T₁·ωP_local + T₂·ωS_local = 0
P is gear 1; S is gear 2. Enter finite n = N₁/N₂ > 0, default 1. For input at P and output at S: T₁ = n·T₂ and ω₂ = n·ω₁. Local flows enter both ports. Exactly one port supplies effort. Ideal, lossless and without stored energy; no backlash or gear inertia.
Advanced
No advanced rotational components yet. Build the model from primitives.
Example and results
Geared elastic shaft · rotational_geared_system
Results include torque, angular velocity, power, angular momentum and spring twist. Default plots show the two inertia velocities. Absolute shaft angles are not integrated. JSON v3 retains shared primitive types and the rotational domain.