void iauNum06a(double date1, double date2, double rmatn[3][3])
/*
** - - - - - - - - - -
** i a u N u m 0 6 a
** - - - - - - - - - -
**
** Form the matrix of nutation for a given date, IAU 2006/2000A model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rmatn double[3][3] nutation matrix
**
** 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(true) = rmatn * V(mean), where
** the p-vector V(true) is with respect to the true equatorial triad
** of date and the p-vector V(mean) is with respect to the mean
** equatorial triad of date.
**
** Called:
** iauObl06 mean obliquity, IAU 2006
** iauNut06a nutation, IAU 2006/2000A
** iauNumat form nutation matrix
**
** Reference:
**
** Explanatory Supplement to the Astronomical Almanac,
** P. Kenneth Seidelmann (ed), University Science Books (1992),
** Section 3.222-3 (p114).
**
** This revision: 2013 June 18
**
** SOFA release 2017-04-20
**
** Copyright (C) 2017 IAU SOFA Board. See notes at end.
*/
{
double eps, dp, de;
/* Mean obliquity. */
eps = iauObl06(date1, date2);
/* Nutation components. */
iauNut06a(date1, date2, &dp, &de);
/* Nutation matrix. */
iauNumat(eps, dp, de, rmatn);
return;
/*----------------------------------------------------------------------
**
** Copyright (C) 2017
** Standards Of Fundamental Astronomy Board
** of the International Astronomical Union.
**
** =====================
** SOFA Software License
** =====================
**
** NOTICE TO USER:
**
** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
** CONDITIONS WHICH APPLY TO ITS USE.
**
** 1. The Software is owned by the IAU SOFA Board ("SOFA").
**
** 2. Permission is granted to anyone to use the SOFA software for any
** purpose, including commercial applications, free of charge and
** without payment of royalties, subject to the conditions and
** restrictions listed below.
**
** 3. You (the user) may copy and distribute SOFA source code to others,
** and use and adapt its code and algorithms in your own software,
** on a world-wide, royalty-free basis. That portion of your
** distribution that does not consist of intact and unchanged copies
** of SOFA source code files is a "derived work" that must comply
** with the following requirements:
**
** a) Your work shall be marked or carry a statement that it
** (i) uses routines and computations derived by you from
** software provided by SOFA under license to you; and
** (ii) does not itself constitute software provided by and/or
** endorsed by SOFA.
**
** b) The source code of your derived work must contain descriptions
** of how the derived work is based upon, contains and/or differs
** from the original SOFA software.
**
** c) The names of all routines in your derived work shall not
** include the prefix "iau" or "sofa" or trivial modifications
** thereof such as changes of case.
**
** d) The origin of the SOFA components of your derived work must
** not be misrepresented; you must not claim that you wrote the
** original software, nor file a patent application for SOFA
** software or algorithms embedded in the SOFA software.
**
** e) These requirements must be reproduced intact in any source
** distribution and shall apply to anyone to whom you have
** granted a further right to modify the source code of your
** derived work.
**
** Note that, as originally distributed, the SOFA software is
** intended to be a definitive implementation of the IAU standards,
** and consequently third-party modifications are discouraged. All
** variations, no matter how minor, must be explicitly marked as
** such, as explained above.
**
** 4. You shall not cause the SOFA software to be brought into
** disrepute, either by misuse, or use for inappropriate tasks, or
** by inappropriate modification.
**
** 5. The SOFA software is provided "as is" and SOFA makes no warranty
** as to its use or performance. SOFA does not and cannot warrant
** the performance or results which the user may obtain by using the
** SOFA software. SOFA makes no warranties, express or implied, as
** to non-infringement of third party rights, merchantability, or
** fitness for any particular purpose. In no event will SOFA be
** liable to the user for any consequential, incidental, or special
** damages, including any lost profits or lost savings, even if a
** SOFA representative has been advised of such damages, or for any
** claim by any third party.
**
** 6. The provision of any version of the SOFA software under the terms
** and conditions specified herein does not imply that future
** versions will also be made available under the same terms and
** conditions.
*
** In any published work or commercial product which uses the SOFA
** software directly, acknowledgement (see www.iausofa.org) is
** appreciated.
**
** Correspondence concerning SOFA software should be addressed as
** follows:
**
** By email: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
void iauP06e(double date1, double date2,
double *eps0, double *psia, double *oma, double *bpa,
double *bqa, double *pia, double *bpia,
double *epsa, double *chia, double *za, double *zetaa,
double *thetaa, double *pa,
double *gam, double *phi, double *psi)
/*
** - - - - - - - -
** i a u P 0 6 e
** - - - - - - - -
**
** Precession angles, IAU 2006, equinox based.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical models.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (see Note 2):
** eps0 double epsilon_0
** psia double psi_A
** oma double omega_A
** bpa double P_A
** bqa double Q_A
** pia double pi_A
** bpia double Pi_A
** epsa double obliquity epsilon_A
** chia double chi_A
** za double z_A
** zetaa double zeta_A
** thetaa double theta_A
** pa double p_A
** gam double F-W angle gamma_J2000
** phi double F-W angle phi_J2000
** psi double F-W angle psi_J2000
**
** 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) This function returns the set of equinox based angles for the
** Capitaine et al. "P03" precession theory, adopted by the IAU in
** 2006. The angles are set out in Table 1 of Hilton et al. (2006):
**
** eps0 epsilon_0 obliquity at J2000.0
** psia psi_A luni-solar precession
** oma omega_A inclination of equator wrt J2000.0 ecliptic
** bpa P_A ecliptic pole x, J2000.0 ecliptic triad
** bqa Q_A ecliptic pole -y, J2000.0 ecliptic triad
** pia pi_A angle between moving and J2000.0 ecliptics
** bpia Pi_A longitude of ascending node of the ecliptic
** epsa epsilon_A obliquity of the ecliptic
** chia chi_A planetary precession
** za z_A equatorial precession: -3rd 323 Euler angle
** zetaa zeta_A equatorial precession: -1st 323 Euler angle
** thetaa theta_A equatorial precession: 2nd 323 Euler angle
** pa p_A general precession
** gam gamma_J2000 J2000.0 RA difference of ecliptic poles
** phi phi_J2000 J2000.0 codeclination of ecliptic pole
** psi psi_J2000 longitude difference of equator poles, J2000.0
**
** The returned values are all radians.
**
** 3) Hilton et al. (2006) Table 1 also contains angles that depend on
** models distinct from the P03 precession theory itself, namely the
** IAU 2000A frame bias and nutation. The quoted polynomials are
** used in other SOFA functions:
**
** . iauXy06 contains the polynomial parts of the X and Y series.
**
** . iauS06 contains the polynomial part of the s+XY/2 series.
**
** . iauPfw06 implements the series for the Fukushima-Williams
** angles that are with respect to the GCRS pole (i.e. the variants
** that include frame bias).
**
** 4) The IAU resolution stipulated that the choice of parameterization
** was left to the user, and so an IAU compliant precession
** implementation can be constructed using various combinations of
** the angles returned by the present function.
**
** 5) The parameterization used by SOFA is the version of the Fukushima-
** Williams angles that refers directly to the GCRS pole. These
** angles may be calculated by calling the function iauPfw06. SOFA
** also supports the direct computation of the CIP GCRS X,Y by
** series, available by calling iauXy06.
**
** 6) The agreement between the different parameterizations is at the
** 1 microarcsecond level in the present era.
**
** 7) When constructing a precession formulation that refers to the GCRS
** pole rather than the dynamical pole, it may (depending on the
** choice of angles) be necessary to introduce the frame bias
** explicitly.
**
** 8) It is permissible to re-use the same variable in the returned
** arguments. The quantities are stored in the stated order.
**
** Reference:
**
** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
**
** Called:
** iauObl06 mean obliquity, IAU 2006
**
** This revision: 2013 June 18
**
** SOFA release 2016-05-03
**
** Copyright (C) 2016 IAU SOFA Board. See notes at end.
*/
{
double t;
/* Interval between fundamental date J2000.0 and given date (JC). */
t = ((date1 - DJ00) + date2) / DJC;
/* Obliquity at J2000.0. */
*eps0 = 84381.406 * DAS2R;
/* Luni-solar precession. */
*psia = ( 5038.481507 +
( -1.0790069 +
( -0.00114045 +
( 0.000132851 +
( -0.0000000951 )
* t) * t) * t) * t) * t * DAS2R;
/* Inclination of mean equator with respect to the J2000.0 ecliptic. */
*oma = *eps0 + ( -0.025754 +
( 0.0512623 +
( -0.00772503 +
( -0.000000467 +
( 0.0000003337 )
* t) * t) * t) * t) * t * DAS2R;
/* Ecliptic pole x, J2000.0 ecliptic triad. */
*bpa = ( 4.199094 +
( 0.1939873 +
( -0.00022466 +
( -0.000000912 +
( 0.0000000120 )
* t) * t) * t) * t) * t * DAS2R;
/* Ecliptic pole -y, J2000.0 ecliptic triad. */
*bqa = ( -46.811015 +
( 0.0510283 +
( 0.00052413 +
( -0.000000646 +
( -0.0000000172 )
* t) * t) * t) * t) * t * DAS2R;
/* Angle between moving and J2000.0 ecliptics. */
*pia = ( 46.998973 +
( -0.0334926 +
( -0.00012559 +
( 0.000000113 +
( -0.0000000022 )
* t) * t) * t) * t) * t * DAS2R;
/* Longitude of ascending node of the moving ecliptic. */
*bpia = ( 629546.7936 +
( -867.95758 +
( 0.157992 +
( -0.0005371 +
( -0.00004797 +
( 0.000000072 )
* t) * t) * t) * t) * t) * DAS2R;
/* Mean obliquity of the ecliptic. */
*epsa = iauObl06(date1, date2);
/* Planetary precession. */
*chia = ( 10.556403 +
( -2.3814292 +
( -0.00121197 +
( 0.000170663 +
( -0.0000000560 )
* t) * t) * t) * t) * t * DAS2R;
/* Equatorial precession: minus the third of the 323 Euler angles. */
*za = ( -2.650545 +
( 2306.077181 +
( 1.0927348 +
( 0.01826837 +
( -0.000028596 +
( -0.0000002904 )
* t) * t) * t) * t) * t) * DAS2R;
/* Equatorial precession: minus the first of the 323 Euler angles. */
*zetaa = ( 2.650545 +
( 2306.083227 +
( 0.2988499 +
( 0.01801828 +
( -0.000005971 +
( -0.0000003173 )
* t) * t) * t) * t) * t) * DAS2R;
/* Equatorial precession: second of the 323 Euler angles. */
*thetaa = ( 2004.191903 +
( -0.4294934 +
( -0.04182264 +
( -0.000007089 +
( -0.0000001274 )
* t) * t) * t) * t) * t * DAS2R;
/* General precession. */
*pa = ( 5028.796195 +
( 1.1054348 +
( 0.00007964 +
( -0.000023857 +
( 0.0000000383 )
* t) * t) * t) * t) * t * DAS2R;
/* Fukushima-Williams angles for precession. */
*gam = ( 10.556403 +
( 0.4932044 +
( -0.00031238 +
( -0.000002788 +
( 0.0000000260 )
* t) * t) * t) * t) * t * DAS2R;
*phi = *eps0 + ( -46.811015 +
( 0.0511269 +
( 0.00053289 +
( -0.000000440 +
( -0.0000000176 )
* t) * t) * t) * t) * t * DAS2R;
*psi = ( 5038.481507 +
( 1.5584176 +
( -0.00018522 +
( -0.000026452 +
( -0.0000000148 )
* t) * t) * t) * t) * t * DAS2R;
return;
/*----------------------------------------------------------------------
**
** Copyright (C) 2016
** Standards Of Fundamental Astronomy Board
** of the International Astronomical Union.
**
** =====================
** SOFA Software License
** =====================
**
** NOTICE TO USER:
**
** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
** CONDITIONS WHICH APPLY TO ITS USE.
**
** 1. The Software is owned by the IAU SOFA Board ("SOFA").
**
** 2. Permission is granted to anyone to use the SOFA software for any
** purpose, including commercial applications, free of charge and
** without payment of royalties, subject to the conditions and
** restrictions listed below.
**
** 3. You (the user) may copy and distribute SOFA source code to others,
** and use and adapt its code and algorithms in your own software,
** on a world-wide, royalty-free basis. That portion of your
** distribution that does not consist of intact and unchanged copies
** of SOFA source code files is a "derived work" that must comply
** with the following requirements:
**
** a) Your work shall be marked or carry a statement that it
** (i) uses routines and computations derived by you from
** software provided by SOFA under license to you; and
** (ii) does not itself constitute software provided by and/or
** endorsed by SOFA.
**
** b) The source code of your derived work must contain descriptions
** of how the derived work is based upon, contains and/or differs
** from the original SOFA software.
**
** c) The names of all routines in your derived work shall not
** include the prefix "iau" or "sofa" or trivial modifications
** thereof such as changes of case.
**
** d) The origin of the SOFA components of your derived work must
** not be misrepresented; you must not claim that you wrote the
** original software, nor file a patent application for SOFA
** software or algorithms embedded in the SOFA software.
**
** e) These requirements must be reproduced intact in any source
** distribution and shall apply to anyone to whom you have
** granted a further right to modify the source code of your
** derived work.
**
** Note that, as originally distributed, the SOFA software is
** intended to be a definitive implementation of the IAU standards,
** and consequently third-party modifications are discouraged. All
** variations, no matter how minor, must be explicitly marked as
** such, as explained above.
**
** 4. You shall not cause the SOFA software to be brought into
** disrepute, either by misuse, or use for inappropriate tasks, or
** by inappropriate modification.
**
** 5. The SOFA software is provided "as is" and SOFA makes no warranty
** as to its use or performance. SOFA does not and cannot warrant
** the performance or results which the user may obtain by using the
** SOFA software. SOFA makes no warranties, express or implied, as
** to non-infringement of third party rights, merchantability, or
** fitness for any particular purpose. In no event will SOFA be
** liable to the user for any consequential, incidental, or special
** damages, including any lost profits or lost savings, even if a
** SOFA representative has been advised of such damages, or for any
** claim by any third party.
**
** 6. The provision of any version of the SOFA software under the terms
** and conditions specified herein does not imply that future
** versions will also be made available under the same terms and
** conditions.
*
** In any published work or commercial product which uses the SOFA
** software directly, acknowledgement (see www.iausofa.org) is
** appreciated.
**
** Correspondence concerning SOFA software should be addressed as
** follows:
**
** By email: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
