Will the rotational axis of a cylindrical space habitat precess? I am curious if you have a rotating cylinder in space -- let's say it's a space habitat a la Arthur C. Clarke's Rama novels. As far as I am aware once the rotation starts (we are assuming it rotates along the longer, central axis of the cylinder) it should keep on going. So far so good.
But there are tiny forces acting on it as well, especially if it is in a solar system with larger objects around it giving really tiny gravitational nudges. So I was curious if that rotation might change -- if eventually the axis of rotation would move, creating a "wobble" and ending up with a cylinder rotating on an axis 90 degrees offset from its original rotational motion, so it ends up rotating end over end. I was reading some answers on another stackexchange and someone mentioned this as an issue with a cylindrical space hab, so I was curious if it was the case or if it is one of those things that is on a relatively longish time scale so that it doesn't affect anything as a practical matter.
Planets do wobble, of course, and their axes precess, so I was thinking the same should apply to a cylindrical space habitat. On the other hand it takes 26,000 years or so for the Earth's precession to complete a full cycle, so for a space habitat it might not matter.
 A: There's a lot to untangle here.
Gyroscopic precession of a spinning body arises when an external force is acting on that spinning body in such a way that the spinning body experiences a torque. I will get back to gyroscopic precession later, first I will discuss another form of change of state of rotation.

Explorer 1 was the first satellite launched by the United States.
Explorer 1 had a diameter of 0.15 meter, and the length was 2.03 meter. Upon insertion into orbit the satellite was given a spin around its long axis.
But then something unanticipated happened. Explorer 1 had four antenna rods, and these rods turned out to be flexible enough to facilitate dissipation of kinetic energy.
In any physics taking place: if there is opportunity for energy dissipation then that energy dissipation will happen. The final state of the moving system is a state where there is no longer opportunity for energy dissipation. (In most cases the final state is one with energy left, it's just that no opportunity to dissipate that energy remains.)
The motion of the Explorer 1 satellite shifted to a form where it was tumbling end over end. The final state of motion was a state with the same angular momentum as the initial state (a single body cannot shed angular momentum), but with lower kinetic energy.

Space habitat
A space habitat will presumably also have features such as pools for swimming. It is likely to the point of certainty that there will be a rate of dissipation of kinetic energy of the space habitat. And most importantly: this effect is cumulative. Mitigating the dissipation is not enough; all you buy is a delay.
So: the designers of the space habitat will have to anticipate that. If they don't then the axis of rotation will migrate relative to the solid structure.
The state of rotating around the long axis will require active maintenance. Thrusters must be place, with algorithms in place to execute precisely timed firing of the thrusters, so that migration of the spin axis is corrected.

The above was discussion of migration of the spin axis (relative to the solid structure) due to internal processes.
Then there is being affected by external forces.
Take the case of a rod floating in space (either in orbit or not actually bound to any celestial body.)
When that rod is subject to gravity then there is a resultant torque that tends to align the rod with the gradient of the potential.
That torque arises as follows: the inertia of the rod as a whole can be thought of as inertia of the center of inertial mass.
Gravity is an inverse square force, so if the rod is already somewhat aligned with the gravitational field then the end of the rod that is furthest from the source of the gravitational field experiences a smaller gravitational force than the end that is closest to the source of the gravitational field. So: over the length of the rod there is a gradient of amount of gravitational force. As a consequence: the center of gravitational attraction does not coincide with the center of inertial mass. The difference is small, but in space motion is frictionless, so even the smallest cause has an effect; it's just a matter of time.
The situation of the center of gravitational attraction not coinciding with the center of inertial mass is what gives rise to a torque. If the effect of that torque is not counteracted then it will give rise to gyroscopic precession. Gyroscopic precession is a cyclic process. In that sence it is not cumulative. The orientation of the space habitat changes, but it is a process that repeats in a cycle, so the designers of the space habitat may opt to not suppress gyroscopic precession.
