# Rotation matrix of three intrinsic rotations

• dbeckam
dbeckam
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:

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?

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 )

IMU ?

##\ ##

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

##\ ##

Filip Larsen

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