Note that the challenge is to find [[File:RW11.gif]] and [[File:RW12.gif]] about the center of mass of the system, rather than their own centers of mass, which can be easily done. Please refer to [https://pdfs.semanticscholar.org/d2b5/e126c3d4bd54e39ee134b1cc28227b99a2b8.pdf this]. <br \>

Now we have everything, but before moving ahead let’s state some assumptions made to during the final derivation. It’s assumed that the center of mass of satellite body and center of mass of the system are very close. Also the wheel of reaction wheel is assumed to be uniform. <br \>

Let's substitute equation 1 in equation 2. <br \>

After several manipulations, we get,

Note: [[File:RW15.gif]] and [[File:RW16.gif]] in the above expression are the derivatives in the B frame and the W frame respectively. [[File:RW19.gif]] is the unit vector along the axis of rotation of the wheel and [[File:RW21.gif]] is the inertia about the axis of rotation of the wheel. <br \>

In the above equation it is visible that we are able to relate the angular speed of the wheel and the disturbance torque acting on the satellite. And what we have control is on the speed of the reaction wheel. Therefore it can be accelerated and decelerated suitably to actuate the satellite.

== Limitations of Reaction Wheels ==

* Has moving parts