Reaction Flywheels
Author: perry
Reaction Wheels #
\(I_s\) is the moment of inertia (MOI) of the spacecraft
\(\omega_s\) is the desired angular velocity of the spacecraft
\(\omega_m\) is the maximum angular velocity the motor can produce
\(I_f\) is the necessary flywheel MOI
We start by calculating the inertial-frame flywheel angular velocity, which slightly differs from the motor’s as the stator is mounted to a spacecraft
\[\omega_f = \omega_m - \omega_s\]We then apply this to the conservation of angular momentum
\[\omega_f I_f = \omega_s I_s\] \[(\omega_m - \omega_s) I_f = \omega_s I_s\] \[I_f = \frac{\omega_s I_s}{\omega_m - \omega_s}\]To obtain the necessary flywheel moment of inertia to achieve the desired spacecraft angular velocity.
Note that this is independent of the maximum output torque of the motor, only the maximum angular velocity, as a lower torque will only reduce the angular acceleration and not the final angular velocity.