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Angular Momentum
τ = I · α
A motor accelerates the reaction wheel (Moment of Inertia I). Newton's Third Law dictates an equal and opposite torque is applied to the spacecraft, allowing it to turn in a vacuum.
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Magnetic Torque
τ = m × B
A magnetorquer generates a magnetic dipole moment (m) that interacts with Earth's field (B). The torque is physically limited and weak, so detumbling takes time.
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PID Control
u = Kp·e + Ki·∫e - Kd·ω
Kp drives toward target, Ki removes steady-state offset, and Kd prevents overshoot. We use actual velocity (-ω) instead of error derivative to prevent "derivative kick" when targets change.