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The space shuttle had a digital readout of roll-pitch-yaw angles in a chosen frame (inertial, LVLH, or reference).

What rotation sequence did they assume in that digital readout? Was it roll-pitch-yaw? Yaw-pitch-roll? Other?

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    $\begingroup$ I believe it was yaw-pitch-roll. Pitch was definitely the middle one as singularity issues arise when the middle one is at $\pm90^{\circ}$. Per the answer by @OrganicMarble to “LVLH” on Challenger's cockpit voice recording: What was that switch for, "there was a singularity in the calculations of LVLH attitude at pitch of 90 degrees (which the Orbiter was at on the pad)." $\endgroup$ – David Hammen Jan 25 at 5:16
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    $\begingroup$ I'm not giving that as an answer though, as Organic Marble is our resident Shuttle expert. $\endgroup$ – David Hammen Jan 25 at 5:18
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    $\begingroup$ Beautiful. I've been assuming pitch in the middle, which meant a singularity at +-90 deg too, and which has had me thoroughly confused over how to display my roll-pitch-yaw angles when I do a flipover... $\endgroup$ – user36480 Jan 25 at 6:04
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    $\begingroup$ I think @DavidHammen is right but I don't have a reference that explicitly states how the computation to drive the ADI is done. $\endgroup$ – Organic Marble Jan 25 at 14:15
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Found a reliable answer in the pages of "GNC ASC 2102 Ascent Guidance, Navigation, and Flight Control Workbook" from May 15, 1979.

The order of the rotation angles depends on the frame chosen. For LVLH, it is yaw-pitch-roll, which would in fact put the shuttle's body frame in gimbal lock while on the pad, as it would then be at a pitch of 90 degrees.

The middle rotation in the sequence is always limited to +-90 degrees, with the limits being "gimbal lock" singularities.

REF seems to be a chosen reference frame which can be changed by the crew. The order of the rotation angles changes to pitch-yaw-roll if this is the chosen reference frame.

Unfortunately the rotation order isn't shown for the inertial frame. OMS 2 TIG seems to be just the orientation of the frame itself. If someone knows what OMS 2 TIG is, please add below in the comments.

enter image description here

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    $\begingroup$ OMS 2 TIG is the Time of Ignition of the ascent orbit circularization burn done using the OMS engines. in the ascent checklist, post OMS-1 pages, tne OMS 2 BURN ATTITUDE MNVR steps have them check that the ADI is in inertial. $\endgroup$ – Organic Marble Jan 27 at 3:40
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    $\begingroup$ When the switch is in inertial, it uses the real inertial frame to compute the angles. Nothing is 'locked in'. $\endgroup$ – Organic Marble Jan 27 at 3:44
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    $\begingroup$ When they pushed the REF button it snapshotted the attitude and used that as the FOR if the ADI was in REF. $\endgroup$ – Organic Marble Jan 27 at 3:49
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    $\begingroup$ It means that when the adi switch is in inertial, the adi displays the orbiter attitude relative to the "basic" inertial frame. I forget which frame that is and I'm on a phone now. Look in the SCOM and see what it says for that switch position. $\endgroup$ – Organic Marble Jan 27 at 3:52
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    $\begingroup$ Ah! Thanks so much! The bit on the REF frame came in at just the right time. Everything I've read in the space shuttle manual suggests INRTL is the M50 frame, so to me the surprise would be if it were anything else. Glad to know that doesn't seem to be the case. $\endgroup$ – user36480 Jan 27 at 4:23

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