Rotation matrix of three intrinsic rotations

AI Thread Summary
The discussion revolves around the calculation of a rotation matrix resulting from three intrinsic rotations (Z, X, Y) and the corresponding angular velocities. The original poster seeks verification of their angular velocity calculations, which include expressions for wpx, wpy, and wpz, but faces confusion from other participants regarding the clarity and definitions of variables. Additionally, the poster inquires about converting IMU sensor measurements of yaw, pitch, and roll back into the original angles PHIZ, PHIX, and PHIY. Critics highlight the lack of clarity in the original post, suggesting that visual aids and clearer definitions are necessary for understanding. Overall, the conversation emphasizes the need for precise communication in complex mathematical discussions.
dbeckam
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TL;DR Summary
Find the rotation matrix
I have three frames. The first is the fixed global frame. the second rotates an angle PHIZ with respect to the first. And the third first rotates a PHIX angle with respect to the x axis of the second frame, and then rotates a PHIY angle with respect to the last y axis. That is, there are a total of three intrinsic rotations Z, X, Y. According to Wikipedia, the final rotation matrix results from the image. I would appreciate if you could help me verify two things:
1704500949449.png

1) The angular velocity of the rotation matrix. According to my calculations the result is:
wpx=dphix.*cos(phiz)-dphiy.*cos(phix).*sin(phiz);
wpy=dphix.*sin(phiz)+dphiy.*cos(phix).*cos(phiz);
wpz=dphiz+dphiy.*sin(phix);

2) If I put an IMU sensor in the last frame, it measures the angles in a different format: yaw, pitch, and roll rotations. How can I use these angles to get my initial PHIZ, PHIX and PHIY angles?
 
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Hello,

I find your post very confusing. None of your ##\phi_z##, ##\phi_x##, ##\phi_y## appears in the picture you picked up from wikipedia (you forgot to mention where - a simple link would have been useful! ). No axis is mentioned for ##\phi_z## -- we must guess the ##z##-axis I ass-u-me ?

dbeckam said:
The angular velocity of the rotation matrix
What is that ?

dbeckam said:
According to my calculations the result is:
wpx=dphix.*cos(phiz)-dphiy.*cos(phix).*sin(phiz);
wpy=dphix.*sin(phiz)+dphiy.*cos(phix).*cos(phiz);
wpz=dphiz+dphiy.*sin(phix);
I don't see no calculations and again have to guess what variables stand for. Left hand sides may be ##\omega##'s but then right hand sides can not be differentials.

IMO: a mess ! Back to the drawing board (yes: a few sketches might help :smile: )

IMU ?

##\ ##
 
Yes, I can google too. That's not the point of my rant.

##\ ##
 
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