PB06 Subroutine

  1. astro_module.f90
  2. astro_module
  3. PB06

public subroutine PB06(date1, date2, bzeta, bz, btheta)

This routine 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.

Status: support routine.

Notes

  1. The TT date DATE1+DATE2 is a Julian Date, apportioned in any convenient way between the arguments DATE1 and DATE2. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

        DATE1          DATE2

 2450123.7D0        0D0        (JD method)
  2451545D0      -1421.3D0     (J2000 method)
 2400000.5D0     50123.2D0     (MJD method)
 2450123.5D0       0.2D0       (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. 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.

  3. 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).

  4. Should zeta_A, z_A, theta_A angles be required that do not contain frame bias, they are available by calling the SOFA routine P06E.

History

  • IAU SOFA revision: 2007 June 8

Arguments

TypeIntentOptionalAttributesName
real(kind=wp), intent(in) :: date1

TT as a 2-part Julian Date (Note 1)
real(kind=wp), intent(in) :: date2

TT as a 2-part Julian Date (Note 1)
real(kind=wp), intent(out) :: bzeta

1st rotation: radians clockwise around z
real(kind=wp), intent(out) :: bz

3rd rotation: radians clockwise around z
real(kind=wp), intent(out) :: btheta

2nd rotation: radians counterclockwise around y

Calls

proc~~pb06~~CallsGraph proc~pb06 PB06 proc~pmat06 PMAT06 proc~pb06->proc~pmat06 proc~rz RZ proc~pb06->proc~rz proc~pfw06 PFW06 proc~pmat06->proc~pfw06 proc~fw2m FW2M proc~pmat06->proc~fw2m proc~obl06 OBL06 proc~pfw06->proc~obl06 proc~fw2m->proc~rz proc~ir IR proc~fw2m->proc~ir proc~rx RX proc~fw2m->proc~rx

Contents

Source Code

PB06

Source Code

    subroutine PB06 ( date1, date2, bzeta, bz, btheta )

    implicit none

    real(wp),intent(in) :: date1 !! TT as a 2-part Julian Date (Note 1)
    real(wp),intent(in) :: date2 !! TT as a 2-part Julian Date (Note 1)
    real(wp),intent(out) :: bzeta !! 1st rotation: radians clockwise around z
    real(wp),intent(out) :: bz !! 3rd rotation: radians clockwise around z
    real(wp),intent(out) :: btheta !! 2nd rotation: radians counterclockwise around y

    real(wp) :: r(3,3), r31, r32

    !  Precession matrix via Fukushima-Williams angles.
    call PMAT06 ( date1, date2, r )

    !  Solve for z.
    bz = atan2 ( r(2,3), r(1,3) )

    !  Remove it from the matrix.
    call RZ ( bz, r )

    !  Solve for the remaining two angles.
    bzeta = atan2 ( r(2,1), r(2,2) )
    r31 = r(3,1)
    r32 = r(3,2)
    btheta = atan2 ( -sign(sqrt(r31*r31+r32*r32),r(1,3)), r(3,3) )

    end subroutine PB06