SUBROUTINE iau_PMAT76 ( EPOCH1, EPOCH2, RMATP ) *+ * - - - - - - - - - - - * i a u _ P M A T 7 6 * - - - - - - - - - - - * * Precession matrix from J2000 to a specified date, IAU 1976 model. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * Given: * EPOCH1,EPOCH2 d ending epoch, TDB (Note 1) * * Returned: * RMATP d(3,3) precession matrix, J2000 -> EPOCH1+EPOCH2 * * Notes: * * 1) The ending epoch EPOCH1+EPOCH2 is a Julian Date, apportioned * in any convenient way between the arguments EPOCH1 and EPOCH2. * For example, JD(TDB)=2450123.7 could be expressed in any of * these ways, among others: * * EPOCH1 EPOCH2 * * 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 matrix operates in the sense V(date) = RMATP * V(J2000), * where the p-vector V(J2000) is with respect to the mean * equatorial triad of epoch J2000 and the p-vector V(date) * is with respect to the mean equatorial triad of the given * epoch. * * 3) Though the matrix method itself is rigorous, the precession * angles are expressed through canonical polynomials which are * valid only for a limited time span. In addition, the IAU 1976 * precession rate is known to be imperfect. The absolute accuracy * of the present formulation is better than 0.1 arcsec from * 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD, * and remains below 3 arcsec for the whole of the period * 500BC to 3000AD. The errors exceed 10 arcsec outside the * range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to * 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD. * * References: * Lieske,J.H., 1979. Astron.Astrophys.,73,282. * equations (6) & (7), p283. * Kaplan,G.H., 1981. USNO circular no. 163, pA2. * * Called: * iau_PREC76 accumulated precession angles, IAU 1976 * iau_IR initialize r-matrix to identity * iau_RZ rotate around Z-axis * iau_RY rotate around Y-axis * iau_CR copy r-matrix * * This revision: 2001 January 12 * * Copyright (C) 2001 IAU SOFA Review Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION EPOCH1, EPOCH2, RMATP(3,3) * Reference epoch (J2000), JD DOUBLE PRECISION DJ0 PARAMETER ( DJ0 = 2451545D0 ) DOUBLE PRECISION ZETA, Z, THETA, WMAT(3,3) * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Precession Euler angles, J2000 to specified epoch. CALL iau_PREC76 ( DJ0, 0D0, EPOCH1, EPOCH2, ZETA, Z, THETA ) * Form the rotation matrix. CALL iau_IR ( WMAT) CALL iau_RZ ( -ZETA, WMAT) CALL iau_RY ( THETA, WMAT) CALL iau_RZ ( -Z, WMAT) CALL iau_CR ( WMAT, RMATP ) * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2001 * Standards Of Fundamental Astronomy Review Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS * WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Review Board ("the Board"). * * 2. The Software is made available free of charge for use by: * * a) private individuals for non-profit research; and * * b) non-profit educational, academic and research institutions. * * 3. Commercial use of the Software is specifically excluded from the * terms and conditions of this license. Commercial use of the * Software is subject to the prior written agreement of the Board on * terms to be agreed. * * 4. The provision of any version of the 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. * * 5. The user may modify the Software for his/her own purposes. The * user may distribute the modified software provided that the Board * is informed and that a copy of the modified software is made * available to the Board on request. All modifications made by the * user shall be clearly identified to show how the modified software * differs from the original Software, and the name(s) of the * affected routine(s) shall be changed. The original SOFA Software * License text must be present. * * 6. In any published work produced by the user and which includes * results achieved by using the Software, the user shall acknowledge * that the Software was used in producing the information contained * in such publication. * * 7. The user may incorporate or embed the Software into other software * products which he/she may then give away free of charge but not * sell provided the user makes due acknowledgement of the use which * he/she has made of the Software in creating such software * products. Any redistribution of the Software in this way shall be * made under the same terms and conditions under which the user * received it from the SOFA Center. * * 8. The user shall not cause the Software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or by * inappropriate modification. * * 9. The Software is provided to the user "as is" and the Board makes * no warranty as to its use or performance. The Board does not and * cannot warrant the performance or results which the user may * obtain by using the Software. The Board 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 the Board be liable to the user for any consequential, * incidental, or special damages, including any lost profits or lost * savings, even if a Board representative has been advised of such * damages, or for any claim by any third party. * * Correspondence concerning SOFA software should be addressed as * follows: * * Internet email: sofa@rl.ac.uk * Postal address: IAU SOFA Center * Rutherford Appleton Laboratory * Chilton, Didcot, Oxon OX11 0QX * United Kingdom * * *----------------------------------------------------------------------- END