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 iauPn00(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])
/*
** - - - - - - - -
** i a u P n 0 0
** - - - - - - - -
**
** Precession-nutation, IAU 2000 model: a multi-purpose function,
** supporting classical (equinox-based) use directly and CIO-based
** use indirectly.
**
** 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)
** 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 2000
** precession-nutation models.
**
** 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) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the order given.
**
** Called:
** iauPr00 IAU 2000 precession adjustments
** iauObl80 mean obliquity, IAU 1980
** iauBp00 frame bias and precession matrices, IAU 2000
** iauCr copy r-matrix
** iauNumat form nutation matrix
** iauRxr product of two r-matrices
**
** Reference:
**
** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** This revision: 2013 June 18
**
** SOFA release 2015-02-09
**
** Copyright (C) 2015 IAU SOFA Board. See notes at end.
*/
{
double dpsipr, depspr, rbpw[3][3], rnw[3][3];
/* IAU 2000 precession-rate adjustments. */
iauPr00(date1, date2, &dpsipr, &depspr);
/* Mean obliquity, consistent with IAU 2000 precession-nutation. */
*epsa = iauObl80(date1, date2) + depspr;
/* Frame bias and precession matrices and their product. */
iauBp00(date1, date2, rb, rp, rbpw);
iauCr(rbpw, rbp);
/* Nutation matrix. */
iauNumat(*epsa, dpsi, deps, rnw);
iauCr(rnw, rn);
/* Bias-precession-nutation matrix (classical). */
iauRxr(rnw, rbpw, rbpn);
return;
/*----------------------------------------------------------------------
**
** Copyright (C) 2015
** 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
**
**--------------------------------------------------------------------*/
}
