I have got a doubt about how to create a transformation matrix for two rotation angles in extrinsic axes. I try to explain what I want to do:
We have got x,y,z axes system that has been rotated by two angles, alpha (around x axis) and beta (around y axis), obtaining a new axes system x',y',z'. I would like to get the transformation matrix between them: [X'] = [A][X].
I learnt that when we rotate around an axis , we get [X']=[A][X]. If we rotate again around the new y' axis we get [X''] = [B][X']. The whole transformation is [X'']=[A][B][X]. But in this case, we rotate around " y " and not " y' ". How should I proceed to get the transformation matrix?
Thank you very much in advance.