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# pfw06

erfa.pfw06(date1, date2)

  Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation).

  Parameters
    date1 double array
    date2 double array
  Returns
    gamb double array
    phib double array
    psib double array
    epsa double array

  Notes

  Wraps ERFA function `eraPfw06`. The ERFA documentation is:

      - - - - - - - - -
       e r a P f w 0 6
      - - - - - - - - -

      Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation).

      Given:
         date1,date2  double   TT as a 2-part Julian Date (Note 1)

      Returned:
         gamb         double   F-W angle gamma_bar (radians)
         phib         double   F-W angle phi_bar (radians)
         psib         double   F-W angle psi_bar (radians)
         epsa         double   F-W angle epsilon_A (radians)

      Notes:

      1) The TT date date1+date2 is a Julian Date, apportioned in any
         convenient way between the two arguments.  For example,
         JD(TT)=2450123.7 could be expressed in any of these ways,
         among others:

                date1          date2

             2450123.7           0.0       (JD method)
             2451545.0       -1421.3       (J2000 method)
             2400000.5       50123.2       (MJD method)
             2450123.5           0.2       (date & time method)

         The JD method is the most natural and convenient to use in
         cases where the loss of several decimal digits of resolution
         is acceptable.  The J2000 method is best matched to the way
         the argument is handled internally and will deliver the
         optimum resolution.  The MJD method and the date & time methods
         are both good compromises between resolution and convenience.

      2) Naming the following points:

               e = J2000.0 ecliptic pole,
               p = GCRS pole,
               E = mean ecliptic pole of date,
         and   P = mean pole of date,

         the four Fukushima-Williams angles are as follows:

            gamb = gamma_bar = epE
            phib = phi_bar = pE
            psib = psi_bar = pEP
            epsa = epsilon_A = EP

      3) The matrix representing the combined effects of frame bias and
         precession is:

            PxB = R_1(-epsa).R_3(-psib).R_1(phib).R_3(gamb)

      4) The matrix representing the combined effects of frame bias,
         precession and nutation is simply:

            NxPxB = R_1(-epsa-dE).R_3(-psib-dP).R_1(phib).R_3(gamb)

         where dP and dE are the nutation components with respect to the
         ecliptic of date.

      Reference:

         Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351

      Called:
         eraObl06     mean obliquity, IAU 2006

      This revision:  2021 May 11

      Copyright (C) 2013-2021, NumFOCUS Foundation.
      Derived, with permission, from the SOFA library.  See notes at end of file.