#include "sofa.h"
#include "sofam.h"
void iauPrec76(double date01, double date02, double date11, double date12,
double *zeta, double *z, double *theta)
/*
** - - - - - - - - - -
** i a u P r e c 7 6
** - - - - - - - - - -
**
** IAU 1976 precession model.
**
** This function forms the three Euler angles which implement general
** precession between two dates, using the IAU 1976 model (as for the
** FK5 catalog).
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date01,date02 double TDB starting date (Note 1)
** date11,date12 double TDB ending date (Note 1)
**
** Returned:
** zeta double 1st rotation: radians cw around z
** z double 3rd rotation: radians cw around z
** theta double 2nd rotation: radians ccw around y
**
** Notes:
**
** 1) The dates date01+date02 and date11+date12 are Julian Dates,
** apportioned in any convenient way between the arguments daten1
** and daten2. For example, JD(TDB)=2450123.7 could be expressed in
** any of these ways, among others:
**
** daten1 daten2
**
** 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
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
** The two dates may be expressed using different methods, but at
** the risk of losing some resolution.
**
** 2) The accumulated precession angles zeta, z, theta 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.
**
** 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 matrix is
** R_3(-z) x R_2(+theta) x R_3(-zeta).
**
** Reference:
**
** Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations
** (6) & (7), p283.
**
** This revision: 2021 May 11
**
** SOFA release 2021-05-12
**
** Copyright (C) 2021 IAU SOFA Board. See notes at end.
*/
{
double t0, t, tas2r, w;
/* Interval between fundamental epoch J2000.0 and start date (JC). */
t0 = ((date01 - DJ00) + date02) / DJC;
/* Interval over which precession required (JC). */
t = ((date11 - date01) + (date12 - date02)) / DJC;
/* Euler angles. */
tas2r = t * DAS2R;
w = 2306.2181 + (1.39656 - 0.000139 * t0) * t0;
*zeta = (w + ((0.30188 - 0.000344 * t0) + 0.017998 * t) * t) * tas2r;
*z = (w + ((1.09468 + 0.000066 * t0) + 0.018203 * t) * t) * tas2r;
*theta = ((2004.3109 + (-0.85330 - 0.000217 * t0) * t0)
+ ((-0.42665 - 0.000217 * t0) - 0.041833 * t) * t) * tas2r;
/* 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
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** 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
**
**--------------------------------------------------------------------*/
}