From: https://en.smath.info/forum/yaf_postsm54527_AlgLib-3-1x.aspx#post54527

Hi Ber7. Thanks for the angles, which gives this beatifull view point!

Wrote

Your error may be caused by the use of the left coordinate system in Smath- graphs.

Using SMath convention for axis it's very difficult to me, and also add the fact that in Latin America we use this as Euler angles:

https://es.wikipedia.org/wiki/%C3%81ngulos_de_Euler



In the attached, I can invert emulating the matlab robots toolbox's rotm2eul.m function, but notice that I need to swap the product order to get the same matrix with those angles that I obtain first.



So, I don't sure now if we are doing the rotations ok taking Ω1*Ω2*Ω3 or, for SMath, the correct order is Ω3*Ω2*Ω1, and this swap is the math meaning for "left coordinate system".

rotm2eul.sm (83 KiB) downloaded 50 time(s).

Best regards.
Alvaro.

Wrote

So, I'm not sure now if we are doing the rotations ok taking Ω1*Ω2*Ω3 or, for SMath, the correct order is Ω3*Ω2*Ω1, and this swap is the math meaning for "left coordinate system".

Euler traditional [Roll, Pitch, Yaw] is not commutative once angles are defined.
Some 3D solids will show convenient in any of the possible 3! = 6 commutative.

Cheers ... Jean

Rotate Euler NOT Commutative.sm (16 KiB) downloaded 58 time(s).