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- fw2m

# fw2m

erfa.fw2m(gamb, phib, psi, eps)

  Form rotation matrix given the Fukushima-Williams angles.

  Parameters:
    gamb double array
    phib double array
    psi double array
    eps double array
  Returns:
    r double array

  Notes

  Wraps ERFA function `eraFw2m`. The ERFA documentation is:

      - - - - - - - -
       e r a F w 2 m
      - - - - - - - -

      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) 2013-2023, NumFOCUS Foundation.
      Derived, with permission, from the SOFA library.  See notes at end of file.