We know that E and B transform as follows for S and S' moving with
relative speed V :

E'=E
B'=B for the components of E,B along the direction parallel with V

and

E'=gamma(V) (E+VxB)
B'=gamma(V) (B=VxE/c^2) for the components of E,B along the direction
perpendicular to V

Now, imagine that the axis x,y are rotating with the uniform angular
speed omega in the plane x-y while S' moves with uniform speed V along
the common axis x.
How can I find the transformation that ties E,B,E',B'? Any reference
that you can suggest? Thank you.