void eraPn06(double date1, double date2, double dpsi, double deps,
double *epsa,
double rb[3][3], double rp[3][3], double rbp[3][3],
double rn[3][3], double rbpn[3][3])
/*
** - - - - - - - -
** e r a P n 0 6
** - - - - - - - -
**
** Precession-nutation, IAU 2006 model: a multi-purpose function,
** supporting classical (equinox-based) use directly and CIO-based use
** indirectly.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** dpsi,deps double nutation (Note 2)
**
** Returned:
** epsa double mean obliquity (Note 3)
** rb double[3][3] frame bias matrix (Note 4)
** rp double[3][3] precession matrix (Note 5)
** rbp double[3][3] bias-precession matrix (Note 6)
** rn double[3][3] nutation matrix (Note 7)
** rbpn double[3][3] GCRS-to-true matrix (Note 8)
**
** 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 caller is responsible for providing the nutation components;
** they are in longitude and obliquity, in radians and are with
** respect to the equinox and ecliptic of date. For high-accuracy
** applications, free core nutation should be included as well as
** any other relevant corrections to the position of the CIP.
**
** 3) The returned mean obliquity is consistent with the IAU 2006
** precession.
**
** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean
** equator and equinox by applying frame bias.
**
** 5) The matrix rp transforms vectors from J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 6) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 7) The matrix rn transforms vectors from mean equator and equinox
** of date to true equator and equinox of date by applying the
** nutation (luni-solar + planetary).
**
** 8) The matrix rbpn transforms vectors from GCRS to true equator and
** equinox of date. It is the product rn x rbp, applying frame
** bias, precession and nutation in that order.
**
** 9) The X,Y,Z coordinates of the Celestial Intermediate Pole are
** elements (3,1-3) of the GCRS-to-true matrix, i.e. rbpn[2][0-2].
**
** 10) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the stated order.
**
** Called:
** eraPfw06 bias-precession F-W angles, IAU 2006
** eraFw2m F-W angles to r-matrix
** eraCr copy r-matrix
** 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) 2013-2017, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double gamb, phib, psib, eps, r1[3][3], r2[3][3], rt[3][3];
/* Bias-precession Fukushima-Williams angles of J2000.0 = frame bias. */
eraPfw06(ERFA_DJM0, ERFA_DJM00, &gamb, &phib, &psib, &eps);
/* B matrix. */
eraFw2m(gamb, phib, psib, eps, r1);
eraCr(r1, rb);
/* Bias-precession Fukushima-Williams angles of date. */
eraPfw06(date1, date2, &gamb, &phib, &psib, &eps);
/* Bias-precession matrix. */
eraFw2m(gamb, phib, psib, eps, r2);
eraCr(r2, rbp);
/* Solve for precession matrix. */
eraTr(r1, rt);
eraRxr(r2, rt, rp);
/* Equinox-based bias-precession-nutation matrix. */
eraFw2m(gamb, phib, psib + dpsi, eps + deps, r1);
eraCr(r1, rbpn);
/* Solve for nutation matrix. */
eraTr(r2, rt);
eraRxr(r1, rt, rn);
/* Obliquity, mean of date. */
*epsa = eps;
return;
}
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 eraFw2xy(double gamb, double phib, double psi, double eps,
double *x, double *y)
/*
** - - - - - - - - -
** e r a F w 2 x y
** - - - - - - - - -
**
** CIP X,Y given Fukushima-Williams bias-precession-nutation 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:
** x,y double CIP unit vector X,Y
**
** 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(-epsA).R_3(-psi).R_1(phib).R_3(gamb)
**
** The returned values x,y are elements [2][0] and [2][1] of the
** matrix. Near J2000.0, they are essentially angles in radians.
**
** Called:
** eraFw2m F-W angles to r-matrix
** eraBpn2xy extract CIP X,Y coordinates from NPB matrix
**
** Reference:
**
** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double r[3][3];
/* Form NxPxB matrix. */
eraFw2m(gamb, phib, psi, eps, r);
/* Extract CIP X,Y. */
eraBpn2xy(r, x, y);
return;
}
void eraPmat06(double date1, double date2, double rbp[3][3])
/*
** - - - - - - - - - -
** e r a P m a t 0 6
** - - - - - - - - - -
**
** Precession matrix (including frame bias) from GCRS to a specified
** date, IAU 2006 model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rbp double[3][3] bias-precession matrix (Note 2)
**
** 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 operates in the sense V(date) = rbp * V(GCRS), where
** the p-vector V(GCRS) is with respect to the Geocentric Celestial
** Reference System (IAU, 2000) and the p-vector V(date) is with
** respect to the mean equatorial triad of the given date.
**
** Called:
** eraPfw06 bias-precession F-W angles, IAU 2006
** eraFw2m F-W angles to r-matrix
**
** References:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double gamb, phib, psib, epsa;
/* Bias-precession Fukushima-Williams angles. */
eraPfw06(date1, date2, &gamb, &phib, &psib, &epsa);
/* Form the matrix. */
eraFw2m(gamb, phib, psib, epsa, rbp);
return;
}