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The space shuttle used quaternions for navigation, guidance, and control which don't suffer from the singularities that affect euler angle sequences.

Yet, the attitude indicator had a digital readout with roll-pitch-yaw numbers relative to a chosen frame---LVLH, Inertial, or Reference, being the choices available to the crew.

And that roll-pitch-yaw is an Euler angle sequence which would have suffered from mathematical gimbal lock (singularities when two axes became aligned).

And two of those angles would have been limited to +-180 degrees while one of those angles would have been limited to +-90 degrees (relative whatever frame the crew had selected at the time).

So I'm curious: what would the digital roll-pitch-yaw readouts have shown when the space shuttle did a flipover of 180 degrees about the axis limited to +-90 degrees (pitch for a roll-pitch-yaw sequence)?

Or did they simply avoid flipovers about that most restricted of axes?

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    $\begingroup$ Oh wow, super cool! @OrganicMarble: is that a 180-degree pitcharound? Are you pitching up or down? I think I see the pitch angle go down while the pitch rate is positive at first? And then the pitch angle creeps up while the pitch rate goes negative? Is the pitch angle going opposite the pitch rate because you've flipped over? $\endgroup$ – user36480 Jan 25 at 1:34
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    $\begingroup$ Note that one of the few nominal switch throws during ascent was because the ADI would have been in a singularity if selected to LVLH while the shuttle was on the pad. space.stackexchange.com/q/36028/6944 $\endgroup$ – Organic Marble Jan 25 at 1:35
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    $\begingroup$ Yes! LVLH would have been in singularity! OK, I got one thing right, then. Thanks for mentioning it, @OrganicMarble! So then that means you wouldn't use LVLH until you'd pitched over at least some? Would you ever have used LVLH during launch (before orbital insertion)? If so, what is the earliest you would have used it? $\endgroup$ – user36480 Jan 25 at 1:40
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    $\begingroup$ They went to LVLH right at the famous "roll program" since the orbiter was pitching and rolling then. $\endgroup$ – Organic Marble Jan 25 at 1:42
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    $\begingroup$ This all answers so many things. This is great. I've been wondering about this and figuring I'd just have to make blind guesses and get half of them dead wrong. Thanks again for sharing. $\endgroup$ – user36480 Jan 25 at 1:58

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