For a given set of epoch time inputs, the Earth Orientation (EO)
Matrix Calculator will generate a corresponding set of direction
cosine matrices (or quaternions) which relate vectors whose
components are written in the terrestrial frame to the celestial frame.
Suppose one has a vector in space, r_itrf, whose components are written
in the ITRF (International Terrestrial Reference Frame). That same vector
in space can have components written in the ICRF (Internation Celestial
Reference Frame), r_icrf. The equation relating r_itrf to r_icrf
is as follows:
r_icrf = [C_itrf2icrf] * r_itrf
The quantity C_itrf2icrf is the direction cosine matrix which transforms
the components of r_itrf to r_icrf. So, the Earth Orientation Matrix
Calculator will generate the C_itrf2icrf at each requested epoch time.