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era.pb06.md

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eraPb06

[bzeta, bz, btheta] = ERFA.pb06(date1, date2)

This function forms three Euler angles which implement general precession from epoch J2000.0, using the IAU 2006 model. Frame bias (the offset between ICRS and mean J2000.0) is included.

Given:

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

Returned:

   bzeta        double   1st rotation: radians cw around z
   bz           double   3rd rotation: radians cw around z
   btheta       double   2nd rotation: radians ccw around y

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.

  1. The traditional accumulated precession angles zeta_A, z_A, theta_A cannot be obtained in the usual way, namely through polynomial expressions, because of the frame bias. The latter means that two of the angles undergo rapid changes near this date. They are instead the results of decomposing the precession-bias matrix obtained by using the Fukushima-Williams method, which does not suffer from the problem. The decomposition returns values which can be used in the conventional formulation and which include frame bias.

  2. The three angles are returned in the conventional order, which is not the same as the order of the corresponding Euler rotations. The precession-bias matrix is R_3(-z) x R_2(+theta) x R_3(-zeta).

  3. Should zeta_A, z_A, theta_A angles be required that do not contain frame bias, they are available by calling the ERFA function eraP06e.

Called:

   eraPmat06    PB matrix, IAU 2006
   eraRz        rotate around Z-axis

This revision: 2021 May 11

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