Rotations in 2 different coordinate systems

I have a question concerning the definition of rotations in a left- or right handed coordinate system. I’m switching the index of the vector [0,1,2] to [0,2,1] when taking coordinates from one coordinate system to the other. What about rotations? I guess I can’t just exchange the index in a quaternion to [x,z,y,w], but can I change the axis part of an axis angle notation?
Thx!

Simplest way to deal with it:

1. make two paper cubes and draw your axes on those
2. inspect and compare

Most likely, you’ll have to switch two angles and you may have to invert one.

Personally, I deal with it differently, since I deal with rotations differently:
I use a special rotator class that keeps track of three unit vectors.
The unit vectors (the local X/Y/Z axes rotated into the world coordinate system) are calculated when the rotation is updated, and I can apply those and the location in one glMultMatrix.

In my case, I only need to swap the second and third components of each vector and swap the second and third unit vector.