Tool 14 · Attitude Dynamics

Reaction Wheel Simulator

Simulate how a reaction wheel applies torque to a spacecraft, builds wheel momentum, changes attitude rate, and eventually reaches speed or momentum saturation. This is a real spacecraft attitude-control problem.

What this tool computes

A reaction wheel changes spacecraft attitude by exchanging angular momentum with the spacecraft body. When the wheel accelerates in one direction, the spacecraft responds with equal and opposite torque.

Wheel angular speed history
Wheel momentum buildup
Spacecraft angular velocity response
Single-axis attitude angle response
Wheel saturation warning
Simple desaturation interpretation

Core reaction-wheel model

The wheel torque and wheel angular acceleration are connected by:

\[ \tau_w = I_w \dot{\omega}_w \]

The spacecraft receives the opposite torque:

\[ \tau_{sc} = -\tau_w \]

In this one-axis educational model, the spacecraft angular acceleration is:

\[ I_{sc}\dot{\omega}_{sc} = \tau_{sc} + \tau_{dist} \]

Momentum saturation

A wheel cannot spin forever. As external disturbances accumulate, the wheel stores angular momentum. Once the wheel approaches its speed or momentum limit, it cannot keep providing control authority.

\[ h_w = I_w \omega_w \]

When \(|h_w|\) approaches the allowed limit, a spacecraft usually needs momentum dumping using magnetorquers or thrusters.

Why this matters for spacecraft GNC

Reaction wheels are precise but momentum-limited actuators.
Small disturbances can build up wheel momentum over time.
Saturation means the spacecraft may lose attitude-control authority.
Momentum management is a real operational constraint, not just a control-theory detail.

Educational simplification

This is a one-axis model. Real spacecraft use three or four wheels, full 3D attitude dynamics, wheel alignment matrices, friction, jitter, and desaturation logic.

Interactive reaction wheel simulator

Spacecraft inertia about axis (kg·m²)

Initial attitude angle (deg)

Initial spacecraft rate (deg/s)

Constant disturbance torque (N·m)

Wheel inertia (kg·m²)

Initial wheel speed (rpm)

Wheel speed limit (rpm)

Momentum limit (N·m·s)

Command mode

Simulation duration (s)

Wheel torque command (N·m)

Kp attitude hold

Kd attitude hold

Target angle for PD hold (deg)

Time step (s)

Scenario preset

Use presets to show wheel momentum buildup and saturation behaviour.

Results

Final wheel speed

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Final wheel momentum

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Saturation status

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Final spacecraft rate

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Final attitude angle

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Peak wheel usage

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Interpretation

Run the simulator to see reaction-wheel momentum buildup and saturation risk.

Wheel speed and saturation limit

Wheel momentum buildup

Spacecraft attitude response

Assumptions and limitations

This simulator assumes:

Single-axis spacecraft rotation
One reaction wheel aligned with that axis
Ideal torque command up to saturation
No bearing friction, jitter, sensor noise, or flexible dynamics
No real momentum dumping actuator; only saturation warning

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