When I do multiple rotations in 3D, how do I do the second rotation in relation to the original frame, how do I do the second rotation in relation to the rotated frame? I think if I multiply the rotation matrix for the Z axis, then by the rotation matrix for the X axis, I'll get the a rotation matrix rotating about the original Z, then about the original X. Then I'm trying to rotate a frame by the original Z, then by the new frame X axis. I think I'm missing something here - maybe something in the difference between rotating a vector and rotating the frame. Can anyone clarify?
2026-04-03 04:23:47.1775190227
Can anyone explain what frame multiple 3D rotations are in relation to?
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The quaternion imaginary units are a basis for 3d space; as such, if you use the same imaginary units throughout a computation, they must always refer to the same basis--whatever that basis is.
It's a known result that if you wish to rotate by intrinsic axes only, you need only take the sequence of rotations as though it were in the extrinsic frame and perform them in reverse order. This can be verified by writing all the rotations in the quaternions' exponential form.