Change of basis - find rotation history of object in global axes

I have an object that has been rotated in the local x y z about the origin (i.e. rotations using a gimble with a local axis system that rotates with an object).

Is there a way to determine xyz rotations on the world axes to obtain the same rotation result? i.e. rotations on axes that don't move with the object giving the same final orientation.

Ideally these rotations would be in the order of z y x, but I am happy for any order that can get it to work! :)

At the moment I am not looking for code, but the set of equations that I can use.

Thanks!

[darova]

• At the moment I am not looking for code, but the set of equations that I can use.

Maybe it's not the question about MATLAB then