In case of a very specific rotation, even one suffices, but it must be located just right for that specific axis of rotation, and if you want to rotate the satellite, it can do so in that specific axis only, and one direction only.
So, first, assumptions:
- RCS is the only method of rotational stabilization. If there are any gyroscopes, magnetorquers etc, we don't take them into account.
- we don't care about translation.
- the thrusters are not gimballed, vectorable or anything like that - each provides thrust in one direction only.
- but the moment and power at which they are fired can be very precisely controlled. No negative thrust though, that requires a second thruster.
- we also have a good information about the attitude changes from the sensors, but the spin/tumble we have entered is arbitrary (within reason, not destructive).
- for simplicity let's assume a spherical satellite with all mass concentrated in the center, massless thrusters, they may be installed on (massless) trusses extending from the satellite, if need be.
One solution I came up while thinking about this problem requires 5 thrusters.
The cluster of three thrusters can stop any spin/tumble except one going straight through their axis of symmetry (the blue axis). This can be negated by the two thrusters on the "equator".
I have a strong suspicion this can be done with four thrusters though - for example, offsetting the three away from the "pole", that they create a "turbine" pattern, always creating a "polar" spin next to their normal activity, and remove one of the "equatorial" ones.
I wonder if it can be done with even less, or what other layouts would be beneficial.