void eraBp06(double date1, double date2,
double rb[3][3], double rp[3][3], double rbp[3][3])
/*
** - - - - - - - -
** e r a B p 0 6
** - - - - - - - -
**
** Frame bias and precession, IAU 2006.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rb double[3][3] frame bias matrix (Note 2)
** rp double[3][3] precession matrix (Note 3)
** rbp double[3][3] bias-precession matrix (Note 4)
**
** 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) The matrix rb transforms vectors from GCRS to mean J2000.0 by
** applying frame bias.
**
** 3) The matrix rp transforms vectors from mean J2000.0 to mean of
** date by applying precession.
**
** 4) The matrix rbp transforms vectors from GCRS to mean of date by
** applying frame bias then precession. It is the product rp x rb.
**
** Called:
** eraPfw06 bias-precession F-W angles, IAU 2006
** eraFw2m F-W angles to r-matrix
** eraPmat06 PB matrix, IAU 2006
** eraTr transpose r-matrix
** eraRxr product of two r-matrices
**
** References:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
** Copyright (C) 2013, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double gamb, phib, psib, epsa, rbt[3][3];
/* B matrix. */
eraPfw06(ERFA_DJM0, ERFA_DJM00, &gamb, &phib, &psib, &epsa);
eraFw2m(gamb, phib, psib, epsa, rb);
/* PxB matrix. */
eraPmat06(date1, date2, rbp);
/* P matrix. */
eraTr(rb, rbt);
eraRxr(rbp, rbt, rp);
return;
}
void eraPb06(double date1, double date2,
double *bzeta, double *bz, double *btheta)
/*
** - - - - - - - -
** e r a P b 0 6
** - - - - - - - -
**
** 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.
**
** 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 ERFA
** function eraP06e.
**
** Called:
** eraPmat06 PB matrix, IAU 2006
** eraRz rotate around Z-axis
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double r[3][3], r31, r32;
/* Precession matrix via Fukushima-Williams angles. */
eraPmat06(date1, date2, r);
/* Solve for z. */
*bz = atan2(r[1][2], r[0][2]);
/* Remove it from the matrix. */
eraRz(*bz, r);
/* Solve for the remaining two angles. */
*bzeta = atan2 (r[1][0], r[1][1]);
r31 = r[2][0];
r32 = r[2][1];
*btheta = atan2(-ERFA_DSIGN(sqrt(r31 * r31 + r32 * r32), r[0][2]),
r[2][2]);
return;
}
