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(Note: highly related, but different: How to compute final aircraft attitude, if we know starting attitude and degrees of rotation around each axis? (Specific example))

I'm flying due north (000 degrees heading), with bank angle of 0 degrees and a pitch attitude of 0 degrees.

I roll the airplane 30 degrees to the right, rotating only around the aircraft's roll axis (longitudinal axis).

Then I pitch the aircraft up through 45 degrees of rotation around the aircraft's pitch axis (lateral axis), with no rotation around the airplane's yaw axis (sometimes called the "directional" axis), but rotating as needed around the aircraft's roll axis (longitudinal axis) to hold the bank angle constant.

At the instant the pitch rotation is finished, what is the airplane's heading and pitch attitude? And what are the relevant formulae?

It's obviously a problem in spherical geometry...

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  • $\begingroup$ Wait, did you not a already get an answer to this question last time? Is this not a duplicate? Or what is the difference to your last question? Is it the part in bold? $\endgroup$
    – U_flow
    yesterday
  • $\begingroup$ @U_flow -- if the answer is different, then they cannot be the same question, right? $\endgroup$
    – quiet flyer
    yesterday
  • $\begingroup$ You'd end up at the same pitch attitude as the other question, but you would need to know roll and pitch rates to calculate heading. $\endgroup$
    – Michael Hall
    15 hours ago

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