So I have a rotating object _a_. It is rotating at non-constant speed around it's `local x` axis. It is parented to object _b_. When the object _a_ rotates, it's `local x` axis stays facing the same direction relatively to object _b_, but not the `local y` and `local z` axis. 
[![The problem in image][1]][1] 
In image the problem is explained a bit better. So I need to get a vector that is relative to the `local x` axis, but rotated by 90 degrees. And it should always match the _b_ object's `local y` arrow's rotation around it's `local x` arrow. And I need to obtain a vector in global axis. I hope that you understand my problem.
So all I need is the math behind. Of course, if there is need for a dot product or cross product or something similar down there, please, don't start typing down all the math of that function:D

 [1]: https://i.sstatic.net/knLTD.png