era.fw2m.md

eraFw2m

r = ERFA.fw2m(gamb, phib, psi, eps)

Form rotation matrix given the Fukushima-Williams angles.

Given:

   gamb     double         F-W angle gamma_bar (radians)
   phib     double         F-W angle phi_bar (radians)
   psi      double         F-W angle psi (radians)
   eps      double         F-W angle epsilon (radians)

Returned:

   r        double[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 function 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 function
      using those four angles as arguments.

o To obtain the precession x frame bias matrix, generate the four precession angles and call the present function.

o To obtain the frame bias matrix, generate the four precession angles for date J2000.0 and call the present function.

The nutation-only and precession-only matrices can if necessary be obtained by combining these three appropriately.

Called:

   eraIr        initialize r-matrix to identity
   eraRz        rotate around Z-axis
   eraRx        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: 2021 May 11

Copyright (C) 2013-2021, NumFOCUS Foundation. Derived, with permission, from the SOFA library.