Overview

Reaction Wheels (Torque Rods) are ways of controlling a vehicle in a microgravity environment by storing angular momentum in spinning disks and discharging it as necessary to apply control forces. The team attempted to implement this in the 2018 Reaction Wheel Payload System.

Theory of Operation

The relevant starting equations are:

$//<![CDATA[ \begin{array}{l}\tau = I\alpha\end{array} //]]>$ and  $//<![CDATA[ \begin{array}{l}H = I \Omega\end{array} //]]>$ 

Where  $//<![CDATA[ \begin{array}{l}\tau\end{array} //]]>$is the torque on a vehicle,  $//<![CDATA[ \begin{array}{l}H\end{array} //]]>$ is the angular momentum of the vehicle, and  $//<![CDATA[ \begin{array}{l}I\end{array} //]]>$is the inertia tensor of the vehicle.

From conservation of angular momentum we know that  $//<![CDATA[ \begin{array}{l}H\end{array} //]]>$ must be constant. Supposing we define the system to include the vehicle, and a reaction wheel, then we could find that we can change the satellite's angular velocity  $//<![CDATA[ \begin{array}{l}\omega\end{array} //]]>$arbitrarily as long as  $//<![CDATA[ \begin{array}{l}I_{RW} \times \omega_{RW} = I_{vehicle} \times \omega_{vehicle}\end{array} //]]>$. Practically, since motors only operate around one axis, this equations can become scalar equations for a single principal axis of the vehicle.

If a perturbation acts on the vehicle, imparting angular velocity  $//<![CDATA[ \begin{array}{l}\Omega\end{array} //]]>$, you can impart  $//<![CDATA[ \begin{array}{l}H_{disturbance}\end{array} //]]>$ to the reaction wheels and nullify the disturbance velocity.

Useful Literature

https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-83x-space-systems-engineering-spring-2002-spring-2003/projects/design_final_e.pdf

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19940008667.pdf

https://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?referer=https://www.google.com/&httpsredir=1&article=2965&context=theses

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