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The frame bias matrix

transforms vectors from Geocentric
Celestial Reference System to the J2000.0 mean equator and equinox by
applying frame bias. It does not depend on the date.
`rb`

The precession matrix

transforms vectors from the J2000.0
mean equator and equinox to the mean equator and equinox of the date
by applying precession.
`rp`

The bias-precession matrix

transforms vectors from
Geocentric Celestial Reference System to the mean equator and equinox
of the date by applying frame bias and then precession.
`rbp``rbp` = `rp` # `rb`

The bias-precession-nutation matrix

...
`rbpn`

The Celestial Intermediate Pole coordinates

,
`x`

are components of the Celestial Intermediate Pole unit
vector in the Geocentric Celestial Reference System.
`y`

The Celestial Intermediate Origin locator

positions the
Celestial Intermediate Origin on the equator of the Celestial
Intermediate Pole.
`s`

Given celestial coordinates

(in the Geocentric
Celestial Reference System), the
celestial-to-intermediate-frame-of-date matrix `crs`

, the
polar motion matrix `rc2i`

, and Earth Rotation Angle
`rpom`

, the terrestrial coordinates `era`

(in the
International Terrestrial Reference System) are found through
`trs`

`trs` = `rpom` # R_3(`era`) # `rc2i` # `crs`

The celestial-to-terrestrial matrix

translates
coordinate from the Geocentric Celestial Reference System to the
International Terrestrial Reference System:
`rc2t`

`trs` = `rc2t` # `crs`

`rc2t` = `rpom` # R_3(`era`) # `rc2i`

Given celestial coordinates

(in the Geocentric
Celestial Reference System), the celestial-to-true matrix
`crs`

, the polar motion matrix `rbpn`

, and
Greenwich apparent Sidereal Time `rpom`

, the terrestrial
coordinates `gst`

(in the International Terrestrial
Reference System) are found through
`trs`

`trs` = `rpom` # R_3(`gst`) # `rbpn` # `crs`

The celestial-to-terrestrial matrix

translates
coordinate from the Geocentric Celestial Reference System to the
International Terrestrial Reference System:
`rc2t`

`trs` = `rc2t` # `crs`

`rc2t` = `rpom` # R_3(`gst`) # `rbpn`