Active B-Dot Magnetorquer Detumbling Simulator
Simulate 3-axis angular velocity decay under PCB magnetorquer B-dot control from tip-off to capture.
Show the data as a table
| Time (min) | |ω| (°/s) |
|---|---|
| 0 | 25.0 |
| 60 | 0.4 |
| 120 | 0.1 |
| 180 | 0.1 |
| 240 | 0.2 |
| 300 | — |
DETERMINISTIC PHYSICS & DATA METHODOLOGY
How This Calculator Works
Source modules: lib/physics/bdot.ts
Integrates full 3-axis Euler rigid-body dynamics and unit-quaternion kinematics over three 95-minute SSO orbits via fourth-order Runge–Kutta (Δt = 0.5 s) in a rotating tilted-dipole geomagnetic field with discrete 1 Hz B-dot coil saturation.
Governing Equations & Physical Model
m_i = clip(−k · (B_b,i(t) − B_b,i(t − Δt_c)) / Δt_c, −m_max, +m_max)Updates commanded PCB magnetorquer dipole every Δt_c = 1.0 s with gain k = 450 A·m²·s/T.
I · ω̇ + ω × (I · ω) = m × B_b, q̇ = ½ · q ⊗ [0, ω]Propagates in a 9.4°-tilted rotating dipole field (B₀ = 31.2 µT equatorial surface reference) at i = 97.5°.
Inputs, Parameters & Units
| Parameter | Unit | Physical definition |
|---|---|---|
| I | ×10⁻⁴ kg·m² | Transverse principal inertia (axial I_z = 1.08·I). |
| m_max | A·m² | Per-axis PCB or air-core magnetorquer saturation dipole. |
| ω₀, h | °/s, km | Initial 3-axis tip-off rate norm |ω(0)| and circular SSO altitude. |
Assumptions & Validity Limits
- Magnetometer measurements are noise-free during quiescent coil-off windows; residual spacecraft dipole and aerodynamic torques are omitted.
- Control gain is fixed at k = 450 A·m²·s/T across the 3-orbit (285 min) simulation horizon.
Worked Default Reference Case
At 525 km SSO, PCB coils saturate early to shed tip-off rate below 1 °/s in 47.2 minutes (half an orbit) and settle to 0.16 °/s after three orbits.
- Time until |ω| < 1 °/s
- 47.2 min
- Final rate after 3 orbits
- 0.16 °/s
- Coil saturation limit m_max
- 0.012 A·m²
- RK4 step / control period
- 0.5 s / 1.0 s