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So, I'm trying to switch between from one frame of reference to another, for a rotation of a 3d object. First of all, the object is rotated, through 2 perpendicular axis. Now, I need to model that rotation in another set of predefined Euler rotations.

In other words, imagine a clock - the hands rotate to a particular time, then the clock itself is rotated through and axis that passes through 12 and 6 o'clock. I need to then express that orientation in predefined rotations, that pass through 12 and 6, followed by an axis through the face of the clock, then through the 12 and 6 again (bearing in mind that the clock face has moved, thus the 12 and 6 axis has been moved from it's previous position.)

I'm really struggling to grasp the geometry here! Any discussion that might give me a grasp of how to think about it (physically or mathematically!) would be most helpful!