#include "sofa.h" #include "sofam.h" void iauPn06(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 6 ** - - - - - - - - ** ** Precession-nutation, IAU 2006 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 (Notes 8,9) ** ** 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: ** iauPfw06 bias-precession F-W angles, IAU 2006 ** iauFw2m F-W angles to r-matrix ** iauCr copy r-matrix ** iauTr transpose r-matrix ** iauRxr 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 ** ** This revision: 2021 May 11 ** ** SOFA release 2023-10-11 ** ** Copyright (C) 2023 IAU SOFA Board. See notes at end. */ { double gamb, phib, psib, eps, r1[3][3], r2[3][3], rt[3][3]; /* Bias-precession Fukushima-Williams angles of J2000.0 = frame bias. */ iauPfw06(DJM0, DJM00, &gamb, &phib, &psib, &eps); /* B matrix. */ iauFw2m(gamb, phib, psib, eps, r1); iauCr(r1, rb); /* Bias-precession Fukushima-Williams angles of date. */ iauPfw06(date1, date2, &gamb, &phib, &psib, &eps); /* Bias-precession matrix. */ iauFw2m(gamb, phib, psib, eps, r2); iauCr(r2, rbp); /* Solve for precession matrix. */ iauTr(r1, rt); iauRxr(r2, rt, rp); /* Equinox-based bias-precession-nutation matrix. */ iauFw2m(gamb, phib, psib + dpsi, eps + deps, r1); iauCr(r1, rbpn); /* Solve for nutation matrix. */ iauTr(r2, rt); iauRxr(r1, rt, rn); /* Obliquity, mean of date. */ *epsa = eps; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2023 ** 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. 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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: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }