Jim's announcement that there can be up to 1.5mrad mututal rotation of chambers within a ring is welcome.
I cannot let both rings float for this exercise, so I am fixing the inner ring (which presumably has better statistics). The outer ring will be allowed to have an overall phiz rotation and a X/Y shift. Both rings will allow chambers to have an additional phiZ rotation, which must be the same within each ring. In the real world this is constrained somewhat by photogrammetry, but I don't know what role that plays in Jim's fits.
X_C and R_C are position and rotation from Jim.
R_Z is rotation about CMS Z for the outer ring
[x;y;0] is the shift of the outer ring from the center
Real outer X_C' = (1/R_Z)*(X_C-[x;y;0])
Real outer R_C' = (1/R_Zo)*(1/R_Z)*R_C
Real inner X_C' = X_C
Real inner R_C' = (1/R_Zi)*R_C
In an SLM frame we have
X_Chslm = (1/R_slm)*(X_C' - X_slm)
R_Chslm = (1/R_slm)*(R_C')
The DCOPS centers will be at
X_Chslm + R_Chslm *(X_Dcops + R_Dcops*DoweltoCenter)
The object is for all these to line up in the U/D coordinate system, which is Z_slm
So I want, for the outer chambers, the Z component of
X_Dij= (1/Rslm)*((1/R_Zo)*(1/R_Z)*(X_Ci -[x;y;0]) - X_slm) + (1/Rslm)*(1/R_Zo)*(1/R_Z)*R_Ci*(X_Dj + R_Dj * DtC)
where j represents the inner or outer DCOPS on the chamber and for the inner ring
X_Dij = (1/Rslm)*((1/R_Zi)*X_Ci - X_slm)) + (1/Rslm)(1/R_Zi)*R_Ci*(X_Dj+R_Dj*DtC)
where of course X_Ci is the X_C for the i'th chamber.
Why is X_DCOPS_outer_MEm2_1_04_IN rather than _OUT? And _DCOPS_inner_MEm2_1_14_OUT rather than _IN?
Modified 08-November-2010 at 14:47
http://hep.physics.wisc.edu/~jnb/cms/08Nov2010
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