A rotating gyroscope that is mounted in a gimbal maintains its rotational axis relative to space when it is moved – and not to the surface of the earth, as illustrated below (the figure shows only the gyroscope without the gimbal). Also see this training film for illustration.
When a gyroscope is on board of an airship, the orientation of the gyroscope’s rotational axis remains unchanged (relative to space) during flight, while the orientation of the airship constantly changes (relative to space).
The figure below shows the airship and the mounted gyroscope beneath it.
Additionally, there is a “swing” beneath the gyroscope. It is mounted, so it can move around the gyroscope and gets accelerated towards the center of the earth.
The figure below shows the gyroscope and the swing in detail. Furthermore, this figure illustrates the orientation of both the gyroscope and the swing when the airship is “north” of the earth.
The following figures show the orientation of the gyroscope and the swing when the airship is “east”…
and “west” of the earth.
The orientation of the gyroscope’s rotational axis is the same in all locations. The swing points in a changing direction, because it gets accelerated in a changing direction when it moves around the earth.
As a consequence, the orientation of the gyroscope’s rotational axis remains unchanged while the swing moves around it. Technically speaking, it is a rotor-stator assembly, where the gyroscope represents the stator and the swing represents the rotor, respectively.
This assembly can do work to a limited extent as long as the torque acting onto the gyroscope is not big enough to push it out of its orientation. Because this work is done along a closed path, gravitation shows to be not a conservative force. The reason why gravitation can do work along a closed path is because the “field lines” of gravitational force are not parallel and a mass moving around the earth at a constant height gets accelerated in a changing direction (relative to space).
Do you have objections against this conclusion? If yes, what did I miss?