  The "body fixed frame" with respect to local gauge transformations is
introduced. Rigid gauge "rotations" in QCD and their \Sch equation are studied
for static and dynamic quarks. Possible choices of the rigid gauge field
configuration corresponding to a nonvanishing static colormagnetic field in the
"body fixed" frame are discussed. A gauge invariant variational equation is
derived in this frame. For large number N of colors the rigid gauge field
configuration is regarded as random with maximally random probability
distribution under constraints on macroscopic--like quantities. For the uniform
magnetic field the joint probability distribution of the field components is
determined by maximizing the appropriate entropy under the area law constraint
for the Wilson loop. In the quark sector the gauge invariance requires the
rigid gauge field configuration to appear not only as a background but also as
inducing an instantaneous quark-quark interaction. Both are random in the large
N limit.
