Switching between frames of reference

[csocean]

hey :)

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!

 

[jimvoit]

Need Problem Clarification

I don't quite understand the problem. Here’s the difficulty:

Suppose we represent the clock in a 3D Cartesian coordinate system in which the x-axis comes out of the face towards the observer, the y-axis is at 3 , and the z axis is at 12. The first rotation you describe is about x, the second is about z for an Euler sequence of x z.

You then wish to replace this sequence by the sequence z x z. This can be accomplished by a first rotation about z of 0 degrees. I don’t think this is what you had in mind.