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: 2007 June 8 * * Copyright (C) 2008 IAU SOFA Review Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION DATE1, DATE2, BZETA, BZ, BTHETA DOUBLE PRECISION R(3,3), R31, R32 * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Precession matrix via Fukushima-Williams angles. CALL iau_PMAT06 ( DATE1, DATE2, R ) * Solve for z. BZ = ATAN2 ( R(2,3), R(1,3) ) * Remove it from the matrix. CALL iau_RZ ( BZ, R ) * Solve for the remaining two angles. BZETA = ATAN2 ( R(2,1), R(2,2) ) R31 = R(3,1) R32 = R(3,2) BTHETA = ATAN2 ( -SIGN(SQRT(R31*R31+R32*R32),R(1,3)), R(3,3) ) * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2008 * 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