SUBROUTINE iau_PB06 ( DATE1, DATE2, BZETA, BZ, BTHETA ) *+ * - - - - - - - - - * i a u _ P B 0 6 * - - - - - - - - - * * This routine forms three Euler angles which implement general * precession from epoch J2000.0, using the IAU 2006 model. Frame * bias (the offset between ICRS and mean J2000.0) is included. * * 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) * * Returned: * BZETA d 1st rotation: radians clockwise around z * BZ d 3rd rotation: radians clockwise around z * BTHETA d 2nd rotation: radians counterclockwise around y * * Notes: * * 1) The TT date DATE1+DATE2 is a Julian Date, apportioned in any * convenient way between the arguments DATE1 and DATE2. 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 traditional accumulated precession angles zeta_A, z_A, theta_A * cannot be obtained in the usual way, namely through polynomial * expressions, because of the frame bias. The latter means that two * of the angles undergo rapid changes near this date. They are * instead the results of decomposing the precession-bias matrix * obtained by using the Fukushima-Williams method, which does not * suffer from the problem. The decomposition returns values which * can be used in the conventional formulation and which include * frame bias. * * 3) The three angles are returned in the conventional order, which * is not the same as the order of the corresponding Euler rotations. * The precession-bias matrix is R_3(-z) x R_2(+theta) x R_3(-zeta). * * 4) Should zeta_A, z_A, theta_A angles be required that do not contain * frame bias, they are available by calling the SOFA routine * iau_P06E. * * Called: * iau_PMAT06 PB matrix, IAU 2006 * iau_RZ rotate around Z-axis * * This revision: 2020 May 27 * * SOFA release 2023-10-11 * * Copyright (C) 2023 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION DATE1, DATE2, BZETA, BZ, BTHETA DOUBLE PRECISION R(3,3), Y, X * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Precession matrix via Fukushima-Williams angles. CALL iau_PMAT06 ( DATE1, DATE2, R ) * Solve for z, choosing the +/- pi alternative. Y = R(2,3) X = -R(1,3) IF ( X .LT. 0D0 ) THEN Y = -Y X = -X END IF IF ( X.NE.0D0 .OR. Y.NE.0D0 ) THEN BZ = - ATAN2 ( Y, X ) ELSE BZ = 0D0 END IF * Derotate it out of the matrix. CALL iau_RZ ( BZ, R ) * Solve for the remaining two angles. Y = R(1,3) X = R(3,3) IF ( X.NE.0D0 .OR. Y.NE.0D0 ) THEN BTHETA = - ATAN2 ( Y, X ) ELSE BTHETA = 0D0 END IF Y = -R(2,1) X = R(2,2) IF ( X.NE.0D0 .OR. Y.NE.0D0 ) THEN BZETA = - ATAN2 ( Y, X ) ELSE BZETA = 0D0 END IF * 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. 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