Hmmm....this explanation seems to add another discrepancy - I think the
connection to the physical process is lost -
I cannot rotate first about something I don't have yet.
Let me try to interpret what E wrote:
"I just have to write out matrices:
CCP4 rotation matrix:
[R11 R12 R13] [x]
[R21 R22 R23] [y]
[R31 R32 R33] [z]
where x y z are orthogonal coordinates relative to fixed axes"
I suppose from following this means rotating coordinate system, i.e. Euler
convention.
"represents a rotation of ccordinates by first gamma then beta then alpha
as Phil says:"
[R11 R12 R13]
[R21 R22 R23]
[R31 R32 R33]
== [R_alpha_about Z0] {R_beta_about_Y1] [ R_gamma_about_Z2]
in br alternate notation R = RZ0(al)RY1(be)RZ2(ga)
but this means: apply the first physical rotation about z2 (I don't have z2
yet!),
then about Y1 and then alpha about zo
and this is NOT what Phil says:
Phil says:
"rotate by gamma around z (i.e. zo), then by beta around the new y (i.e.
y1) ,
then by alpha around the new z (i.e. z") again, R =
Rz(al)Ry(be)Rz(ga)"
i.e., in e/br notation R = Rz"(al)Ry(be)Rzo(ga)
So I think "phil" is correct as far as the physical rotations go - first
about
the old Z axis which I know, then Y1, then about new Z2. The sequence of
angles in R
fits the Euler convention. That is consistent.
I'll get back to the roll-pitch-yaw convention about fixed X0,Y0, and Z0,
their conversion,
and the Navaza issue once it is sorted out what the interpretation of R in
Euler convention
truly is - Eleanor R(ZYZ")or Phil R(Z"YZ).
I'll tally all in a summary
B 'tin man' R
