Suppose you have a regular old Stanford torus space station with a 'glass ceiling' rotating at 1.3 RPM. Put it in orbit around a star such that its axis of rotation intersects the star (in other words, the plane of the torus is tangent to its orbit).
Now add another axis of rotation along that tangent, such that it 'flips' around at 1 revolution per day (RPD I guess!), giving the station's inhabitants a regular human diurnal cycle. Obviously the regions at the nodes would be pretty much in constant shadow, but those areas could be used for storage etc. Further, there would be a "noon shadow" for the sunlit side when the night side eclipses the sun, but I guess that's ok.
Would there be any specific problems with this? Has anyone ever written about this or implemented it in fiction? I suspect it would further complicate the Coriolis and similar effects...
Edit: I'm willing to allow an arbitrary amount of continuous, active propulsion to provide the necessary torque.
Further edit: This is pretty much exactly the effect I'm looking for: a very slow tumble w.r.t. the sun so that the inhabitants are experiencing something vaguely like a day/night cycle. I can use active propulsion to create the torque analogous to the added weight in the video.