SUBROUTINE iau_PN06 ( DATE1, DATE2, DPSI, DEPS, : EPSA, RB, RP, RBP, RN, RBPN ) *+ * - - - - - - - - - * i a u _ P N 0 6 * - - - - - - - - - * * Precession-nutation, IAU 2006 model: a multi-purpose routine, * supporting classical (equinox-based) use directly and CIO-based use * indirectly. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * Given: * DATE1,DATE2 d TT as a 2-part Julian Date (Note 1) * DPSI,DEPS d nutation (Note 2) * * Returned: * EPSA d mean obliquity (Note 3) * RB d(3,3) frame bias matrix (Note 4) * RP d(3,3) precession matrix (Note 5) * RBP d(3,3) bias-precession matrix (Note 6) * RN d(3,3) nutation matrix (Note 7) * RBPN d(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 * * 2450123.7D0 0D0 (JD method) * 2451545D0 -1421.3D0 (J2000 method) * 2400000.5D0 50123.2D0 (MJD method) * 2450123.5D0 0.2D0 (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 mean J2000.0 by * applying frame bias. * * 5) The matrix RP transforms vectors from mean J2000.0 to mean of date * by applying precession. * * 6) The matrix RBP transforms vectors from GCRS to mean of date by * applying frame bias then precession. It is the product RP x RB. * * 7) The matrix RN transforms vectors from mean of date to true of date * by applying the nutation (luni-solar + planetary). * * 8) The matrix RBPN transforms vectors from GCRS to true of date * (CIP/equinox). 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 matrix RBPN. * * Called: * iau_PFW06 bias-precession F-W angles, IAU 2006 * iau_FW2M F-W angles to r-matrix * iau_TR transpose r-matrix * iau_RXR 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: 2013 November 14 * * SOFA release 2021-05-12 * * Copyright (C) 2021 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION DATE1, DATE2, DPSI, DEPS, : EPSA, RB(3,3), RP(3,3), RBP(3,3), : RN(3,3), RBPN(3,3) * JD for MJD 0 DOUBLE PRECISION DJM0 PARAMETER (DJM0 = 2400000.5D0 ) * Reference epoch (J2000.0), MJD DOUBLE PRECISION DJM00 PARAMETER ( DJM00 = 51544.5D0 ) DOUBLE PRECISION GAMB, PHIB, PSIB, EPS, RT(3,3) * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Bias-precession Fukushima-Williams angles of J2000.0 = frame bias. CALL iau_PFW06 ( DJM0, DJM00, GAMB, PHIB, PSIB, EPS ) * B matrix. CALL iau_FW2M ( GAMB, PHIB, PSIB, EPS, RB ) * Bias-precession Fukushima-Williams angles of date. CALL iau_PFW06 ( DATE1, DATE2, GAMB, PHIB, PSIB, EPS ) * Bias-precession matrix. CALL iau_FW2M ( GAMB, PHIB, PSIB, EPS, RBP ) * Solve for precession matrix. CALL iau_TR ( RB, RT ) CALL iau_RXR ( RBP, RT, RP ) * Equinox-based bias-precession-nutation matrix. CALL iau_FW2M ( GAMB, PHIB, PSIB+DPSI, EPS+DEPS, RBPN ) * Solve for nutation matrix. CALL iau_TR ( RBP, RT ) CALL iau_RXR ( RBPN, RT, RN ) * Obliquity, mean of date. EPSA = EPS * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2021 * 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: sofa@ukho.gov.uk * By post: IAU SOFA Center * HM Nautical Almanac Office * UK Hydrographic Office * Admiralty Way, Taunton * Somerset, TA1 2DN * United Kingdom * *----------------------------------------------------------------------- END