SUBROUTINE iau_FW2M ( GAMB, PHIB, PSI, EPS, R )
*+
* - - - - - - - - -
* i a u _ F W 2 M
* - - - - - - - - -
*
* Form rotation matrix given the Fukushima-Williams angles.
*
* This routine is part of the International Astronomical Union's
* SOFA (Standards of Fundamental Astronomy) software collection.
*
* Status: support routine.
*
* Given:
* GAMB d F-W angle gamma_bar (radians)
* PHIB d F-W angle phi_bar (radians)
* PSI d F-W angle psi (radians)
* EPS d F-W angle epsilon (radians)
*
* Returned:
* R d(3,3) rotation matrix
*
* Notes:
*
* 1) Naming the following points:
*
* e = J2000.0 ecliptic pole,
* p = GCRS pole,
* E = ecliptic pole of date,
* and P = CIP,
*
* the four Fukushima-Williams angles are as follows:
*
* GAMB = gamma = epE
* PHIB = phi = pE
* PSI = psi = pEP
* EPS = epsilon = EP
*
* 2) The matrix representing the combined effects of frame bias,
* precession and nutation is:
*
* NxPxB = R_1(-EPS).R_3(-PSI).R_1(PHIB).R_3(GAMB)
*
* 3) The present routine can construct three different matrices,
* depending on which angles are supplied as the arguments GAMB,
* PHIB, PSI and EPS:
*
* o To obtain the nutation x precession x frame bias matrix,
* first generate the four precession angles known conventionally
* as gamma_bar, phi_bar, psi_bar and epsilon_A, then generate
* the nutation components Dpsi and Depsilon and add them to
* psi_bar and epsilon_A, and finally call the present routine
* using those four angles as arguments.
*
* o To obtain the precession x frame bias matrix, generate the
* four precession angles and call the present routine.
*
* o To obtain the frame bias matrix, generate the four precession
* angles for date J2000.0 and call the present routine.
*
* The nutation-only and precession-only matrices can if necessary
* be obtained by combining these three appropriately.
*
* Called:
* iau_IR initialize r-matrix to identity
* iau_RZ rotate around Z-axis
* iau_RX rotate around X-axis
*
* References:
*
* Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
*
* Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
*
* This revision: 2020 November 17
*
* SOFA release 2021-05-12
*
* Copyright (C) 2021 IAU SOFA Board. See notes at end.
*
*-----------------------------------------------------------------------
IMPLICIT NONE
DOUBLE PRECISION GAMB, PHIB, PSI, EPS, R(3,3)
* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
* Construct the matrix.
CALL iau_IR ( R )
CALL iau_RZ ( GAMB, R )
CALL iau_RX ( PHIB, R )
CALL iau_RZ ( -PSI, R )
CALL iau_RX ( -EPS, R )
* Finished.
*+----------------------------------------------------------------------
*
* Copyright (C) 2021
* Standards Of Fundamental Astronomy Board
* of the International Astronomical Union.
*
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* =====================
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*-----------------------------------------------------------------------
END