3D Rotation of a rigid body in Fixed Axes (Not Axes Rotation)

Dear All,

I have come across with a seemingly very simple problem but could not solve it by searching on internet and books. May be I am confused.

I want to rotate a 3D body around an arbitrary axis with fixed principal axes. The solutions I found is with Euler angles (Euler rotational matrices). But in Euler case, we are not rotating the body but rotating the principal axes, which I don't want.

In short:
In Euler case we map axes XYZ to X'Y'Z' with rotation matrices using any angle theta.
I my case I want my body position xyz to be mapped to new position x'y'z' after rotation about an arbitrary axis of angle theta. (XYZ = XYZ before and after applying rotation).

I hope I am clear to explain my question here.
Desperately waiting for help.

Thanks in advance.

Mushi