Steady-state simulation of pitching motion
A &quot;steady&quot; rate of pitch condition is very rare because most aircraft are designed to be stable enough to avoid stalling themselves.  In other words, the more you pitch, the greater the control input you need to continue increasing AOA.
You can reach steady state in roll easily.  Here drag resistance to rolling will stabilize roll rate, provided the aircraft rolls smoothly around its axis.  Here, rudder and elevator inputs may be required.
So, for pitch, you could get a steady state pitch (relative to the horizon) in a loop.  Here, throttle inputs are definitely required (to get a perfect circle).
But for increasing AOA at a steady rate, this will lead to a stall.
There is also the analytical consideration of acceleration before reaching steady state.  Taking the easiest, the roll, roll rate goes from 0 degrees/second when ailerons are applied to steady degrees/second when drag force = rolling force (differences in AOA of rolling wings helps too).
Many early &quot;video arcade&quot; games do not simulate the acceleration (the deer is instantaneously in full gallop). To do an accurate simulation, acceleration to steady state must also be considered, so now you have a rate of acceleration to steady state.