# Euler angle in two given coordinates

I have two coordinates. One is standard and the other is arbitrary.

A rotation is represented as ZYX in the standard coordinates. (yes, It is not exactly a Euler angle. I'm sorry about this) and alpha, beta, gamma are angles of each corresponding axis.

If arbitrary coordinates are given and each basis are known, Can I calculate each angle of new basis?

I'm not a good hand-writer but I added an image for explanation. Thank you for your help

• Are you familiar with rotation matrices? – Brian Apr 1 at 14:46
• @Brian I'm not a total stranger to that but I'm not sure. At least I can try, If you explain. – cliwo Apr 2 at 1:06