# How Euler angles change when we reverse direction of some axes

I looked at the other questions but couldn't find an answer for this particular question: I have measured Euler angles of an object in one coordinate system and I need to use these data in another coordinate system that is slightly different from the first coordinates system. In the second coordinate system, the x- and y-axes have a direction opposite to the x- and y-axes used in the measurement coordinates. The z-axis remains identical for both cases. My question is upon the transfer from one coordinate system to the other, how Euler angles change?

• There are different conventions out there as to how the Euler angles are defined relative to the $x$-, $y$-, and $z$-axes. Can you edit your question to include the convention you're using? – Michael Seifert Jul 27 '18 at 16:19
• The measurements are done in the "proper euler angles". Is that what you meant to edit in the question? – mfaieghi Jul 27 '18 at 16:22
• I mean that the Euler angles are differently defined by various sources depending on the axes of rotation at each of the three stages. And even if the same axes are used in the same order, the angles are sometimes denoted by different symbols. See the discussion on the MathWorld page. Concerning "proper Euler angles", are you referring to the Wikipedia definition, or something else? – Michael Seifert Jul 27 '18 at 16:27