@Joshua's answer to What is the minimum number of RCS thrusters capable of stabilizing a satellite against an arbitrary rotation? begins:

I know this question is old, but I randomly discovered a solution requiring only three thrusters on one thruster block that works if we don't mind introducing small transverse velocities.

The question is quite interesting and as yet I don't think there's a proof that two thrusters could not do it.

@Joshua's representation is shown below.

Question: Assuming a spherical cow spacecraft has a block of three thrusters at a point on its surface, all pointing tangent to the surface spaced at 90 degrees, the object is "at rest" in some frame, and assuming plenty of delta-v available, could they:

  1. indeed de-tumble any arbitrary initial spin state (as long as it's not spinning too fast)
  2. achieve both zero spin and zero velocity in the frame in which it was initially at rest? If so, how?

three-thruster spherical spacecraft from @Joshua's answer https://space.stackexchange.com/a/49369



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