# Confusion with Apollo CSM attitude maneuvers (roll, pitch and yaw) during coasting to/from the Moon

Some time after Transposition, Docking, and Extraction maneuver (when coasting to the Moon) or after Trans Earth Injection (when coasting back from the Moon), the spacecraft's (CSM) guidance platform is aligned to PTC (Passive Thermal Control) REFSMMAT (Reference to Stable Member Matrix).

Apollo 15 Flight Journal Day1/part4 explains the positioning of the guidance platform axes for the PTC REFSMMAT:

[When aligned per the PTC REFSMMAT, the platform's X-axis is aligned along the ecliptic plane, perpendicular to the line between Earth and Moon at the time of Trans-Earth Injection (TEI). Its Z-axis is aligned perpendicular to the ecliptic plane, directed southward. The Y-axis is therefore directed towards Earth. This alignment is used for all translunar and trans-Earth coast maneuvers and is used as the reference for easy alignment of the PTC (Passive Thermal Control) maneuver. Note that the axes shown do not represent the orientation of the spacecraft during PTC, only that of the platform.]

And describes the location of the x-axis of the CSM itself:

The X-axis of the CSM is an imaginary line which runs from the centre of the SPS engine bell, through the centre of the SM and out through the apex of the CM's cone

So, the x(roll), y(pitch) and z(yaw) axes of the spacecraft look pretty much the same as they are for a plane:

Picture is borrowed from here.

After aligning the platform to PTC REFSMMAT, in order to get the spacecraft into PTC attitude, the Flight Plan specifies Pitch 90°, Yaw 0° maneuver:

[The last P52 aligned the X-axis of the IMU platform with the ecliptic and at right angles to the Earth-Moon line; its Z-axis was aligned southward, perpendicular to the ecliptic. If the spacecraft were aligned to match the platform, it would have its longitudinal axis aligned with the ecliptic with the Earth and Moon to either side. By pitching 90°, as called for in the Flight Plan, the longitudinal axis of the spacecraft is brought perpendicular to the ecliptic which guarantees that the Sun (which is always in the plane of the ecliptic) will strike the spacecraft side on as it rotates.

It was all perfectly clear till this point.

Now the confusion starts:

After Al has maneuvered the spacecraft to the PTC attitude, he must ensure that all discernible motions have died down before he initiates the roll maneuver, otherwise the roll will have an element of unwanted wobble, or coning, which will have to be taken out by starting over.]

So, the question is: With relation to what coordinate system the "Roll" (the actual "barbeque roll") is performed?

The CSM x-axis is now collinear with IMU z-axis (perpendicular to ecliptic plane), therefore (assuming they are still in PTC REFSMMAT) revolving around CSM x-axis would technically be a Yaw according to the PTC REFSMMAT coordinate system.

It seems that like if they introduced a new (temporary) coordinate system, which coincided with CSM coordinate system after pitching 90° to get into the PTC attitude, and before starting the actual "barbeque roll".

Another example from Apollo-11 Flight Journal Day2/part2, describing stopping the PTC "barbeque roll":

031:15:02 Collins: Okay. Well, for this TV program coming up in a couple of hours, you might give some thought to how you want us to stop PTC...

032:25:48 Duke: Roger, 11. Your TV attitude will be roll 261, pitch 090, yaw 000...

032:27:01 Collins: Charlie, Apollo 11. I have a couple of questions on stopping the PTC. It seems to me the easiest way to stop it would be - we're essentially, of course, at 0 degrees yaw and close enough to 90 degrees pitch, so it's just a question of stopping at 260 roll, roughly...

Again, assuming same positioning of PTC REFSMMAT axes as was described for Apollo-15 above, with relation to the PTC REFSMMAT, this attitude doesn't make much sense. It makes sense only if the "roll" is meant to be around CSM x-axis (located perpendicular to ecliptic), and not around the PTC REFSMMAT x -axis.

I cannot make sense of how the Roll seems to be defined around local CSM x-axis, whilst at the same time the Pitch seems to be defined around PTC REFSMMAT y-axis (Yaw just happens to be trivially 0 in this case).

• “Roll” refers to around the CSM long X axis, no? – Bob Jacobsen Jan 31 '20 at 17:48

The order in which rotations are applied matters.

260 roll around REFSMMAT x followed by 90 pitch around REFSMMAT y is the same orientation as 90 pitch around REFSMMAT y followed by 260 yaw around REFSMMAT z.

• This is exactly where I got confused. So, is it then the case, when R260, P90, Y0 specified, it is always with regards to REFSMMAT, just need to always follow the specific order? – Sergiy Lenzion Jan 31 '20 at 13:32
• The order in which rotations are applied matters because $\mathrm{SO(3)}$, the group of rotations in 3 dimensions, is non-abelian. – tfb Jan 31 '20 at 18:08
• @LeoS To clarify, it's not the order of the physical maneuvers I'm talking about, but the conversion of the actual attitude of the spacecraft into a set of roll, pitch, and yaw figures relative to the REFSMMAT axial basis. – Russell Borogove Jan 31 '20 at 21:28
• @RussellBorogove Finally I can make sense out of it. Your answer is spot on: it is indeed about the order. So, when Roll applies first, and then Pitch/Yaw (not clear though which one is 2nd, which 3rd), and with this special case of P90,Y0 (seemingly happened to be intentional, by design), if an astronaut called up their current attitude during PTC (at, say, 33deg roll, which I initially took as apparent yaw around REFSMMAT z-axis), they would indeed see R33, P90,Y0 on display, because of this special case of P90,Y0. So the barbeque roll is indeed roll by definition, just "offset" by P90. – Sergiy Lenzion Feb 1 '20 at 0:26
• Just because it reminds me of it, in Shuttle Robotics Euler sequences were always performed in the order Pitch, Yaw, Roll. – Organic Marble Feb 1 '20 at 0:32

The reference frame for roll, pitch, and yaw is itself transformed with each successive rotation.

Roll is given relative to the original x axis. Pitch is given relative to the once-transformed y axis (the transformation being roll). Yaw is given relative to the twice-transformed z axis (the transformations being roll followed by pitch).

This means the roll, pitch, and yaw axes always point in the same directions relative to the spacecraft. If you roll a little, the pitch and yaw axes roll too. If you pitch a little. The yaw axis pitches too.