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A NASA ISS reference guide (PDF; 37 MB) explains the use of reaction wheels -- Control Moment Gyroscopes (CMGs) -- to control the station's attitude/orientation.

My understanding is the station is actively controlled to keep the nadir always pointing toward the Earth (belly down). This is confirmed by the post: Why does the ISS rotate exactly once per orbit?

[The ISS maintains] a constant attitude relative to Local Vertical Local Horizontal (LVLH).

Issue: Most animations show the ISS moving forward section forward, but during the course of one Shuttle flight, that does not seem to be the case, which may mean the station is yawed with respect to its zenith-nadir axis (either purposefully or due to some orbital mechanics).

For example, from the STS-115 presentation video at 4:36, the view shows the nose-up docked Shuttle moving bay forward, which means the station is moving aft section forward (Russian segment first). That's because the Shuttle was docked on PMA-2 (Destiny forward), meaning if the station is moving Destiny first, it would have been the Shuttle underside moving forward, not the bay door.

During the final fly-around days later at 12:43, the station is seen moving Destiny forward.

Q: Does (and why if yes) the ISS yaw in orbit? If not, how can that linked view (and others) be explained?

enter image description here
As seen after STS-115 to avoid configuration confusion (source: linked PDF; modified).

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tl;dr During ISS assembly the station maneuvered more than it does these days.

You are correct that the docked Shuttle / ISS stack maneuvered during the STS-115 mission.

The planned attitudes for the last several Shuttle missions are available in the Attitude Timeline sections of their flightplans, published at the JSC FDF page. The STS-115 flight plan is here.

Referencing that (pp 4-5 and 4-6), we can see that for the majority of the docked phase the stack flew in a Bias -XLV -ZVV attitude, but maneuvered to a couple of XPOP attitudes for deployment of the solar arrays installed by the mission.

ISS will maneuver to the 4A Solar Array Deploy attitude. During the first insulation [sic] period after post sleep, the crew is expected to deploy the 4A Solar Array mast to 15.5 bays (49%) then to 31.5 bays (100%). After 4A is deployed and visual verifications are complete, the SSRMS will be set up in preparation for 2A Solar Array Deploy. ISS will maneuver to the 2A Solar Array Deploy attitude and hand over attitude control to shuttle. Shuttle will maintain attitude control during the 2A deploy and for an additional insulation [sic] period. The 2A Solar Array mast is deployed to 15.5 bays (49%), held for 30 minutes for thermal conditioning and then complete deployment to 31.5 bays (100%). The timeline protects for 1 insulation [sic] period per Solar Array and an additional insulation [sic] period for a contingency deploy. After these three insolation periods, due to ISS thermal a 6 hr. recovery period in the nominal attitude is required prior to another attempt at deploying. Shuttle will maneuver back to the nominal TEA attitude prior to handing attitude control back over to ISS.

  • -XLV -ZVV means the ISS negative X axis is pointed to the local vertical and the negative Z axis is pointed into the velocity vector. This "biased -XLV -ZVV" attitude was a torque equilibrium attitude for the stack at this stage of ISS construction when the station was asymmetrical. Torque equilibrium attitudes are explained here.
  • XPOP means that the ISS X axis is perpendicular to the orbital plane.

The X-Axis Perpendicular to Orbit Plane (XPOP) reference frame is shown in Figure C-3. XPOP is a quasi-inertial reference frame that can be visualized by a 90° yaw of the LVLH frame at orbital noon. The X-axis points out of plane, while both the Y- and Z-axes lie in the orbital plane. Note that unlike LVLH, which is rotating with the Station as the Station rotates about the Earth, XPOP remains fixed with the Station X-axis pointing out of plane and the Z-axis is aligned with the orbit noon vector. XPOP is a “quasi-inertial” reference frame, because as the orbital plane slowly regresses, the XPOP reference frame also regresses to keep the X-axis pointing out of the orbital plane.

enter image description here

(XPOP description and image from here)

During the early, asymmetrical stages of ISS construction, various attitudes were used. Some other ones are discussed here. I can't find the attitude that the proto-ISS was flying in before STS-115 docking, but it was yet another attitude - the flight plan states "The shuttle will maneuver the stack into the Bias -XLV +ZVV attitude" after docking.

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    $\begingroup$ Furthermore (though I have no public documentation to point to that I've found), they have recently been introducing a yaw bias to the attitudes during high beta periods to improve power production. $\endgroup$ – Tristan Jul 31 '19 at 14:34

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