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#include "erfa.h"
#include "erfam.h"
void eraLtecm(double epj, double rm[3][3])
/*
** - - - - - - - - -
** e r a L t e c m
** - - - - - - - - -
**
** ICRS equatorial to ecliptic rotation matrix, long-term.
**
** Given:
** epj double Julian epoch (TT)
**
** Returned:
** rm double[3][3] ICRS to ecliptic rotation matrix
**
** Notes:
**
** 1) The matrix is in the sense
**
** E_ep = rm x P_ICRS,
**
** where P_ICRS is a vector with respect to ICRS right ascension
** and declination axes and E_ep is the same vector with respect to
** the (inertial) ecliptic and equinox of epoch epj.
**
** 2) P_ICRS is a free vector, merely a direction, typically of unit
** magnitude, and not bound to any particular spatial origin, such
** as the Earth, Sun or SSB. No assumptions are made about whether
** it represents starlight and embodies astrometric effects such as
** parallax or aberration. The transformation is approximately that
** between mean J2000.0 right ascension and declination and ecliptic
** longitude and latitude, with only frame bias (always less than
** 25 mas) to disturb this classical picture.
**
** 3) The Vondrak et al. (2011, 2012) 400 millennia precession model
** agrees with the IAU 2006 precession at J2000.0 and stays within
** 100 microarcseconds during the 20th and 21st centuries. It is
** accurate to a few arcseconds throughout the historical period,
** worsening to a few tenths of a degree at the end of the
** +/- 200,000 year time span.
**
** Called:
** eraLtpequ equator pole, long term
** eraLtpecl ecliptic pole, long term
** eraPxp vector product
** eraPn normalize vector
**
** References:
**
** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
** expressions, valid for long time intervals, Astron.Astrophys. 534,
** A22
**
** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
** expressions, valid for long time intervals (Corrigendum),
** Astron.Astrophys. 541, C1
**
** This revision: 2021 May 11
**
** Copyright (C) 2013-2021, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* Frame bias (IERS Conventions 2010, Eqs. 5.21 and 5.33) */
const double dx = -0.016617 * ERFA_DAS2R,
de = -0.0068192 * ERFA_DAS2R,
dr = -0.0146 * ERFA_DAS2R;
double p[3], z[3], w[3], s, x[3], y[3];
/* Equator pole. */
eraLtpequ(epj, p);
/* Ecliptic pole (bottom row of equatorial to ecliptic matrix). */
eraLtpecl(epj, z);
/* Equinox (top row of matrix). */
eraPxp(p, z, w);
eraPn(w, &s, x);
/* Middle row of matrix. */
eraPxp(z, x, y);
/* Combine with frame bias. */
rm[0][0] = x[0] - x[1]*dr + x[2]*dx;
rm[0][1] = x[0]*dr + x[1] + x[2]*de;
rm[0][2] = - x[0]*dx - x[1]*de + x[2];
rm[1][0] = y[0] - y[1]*dr + y[2]*dx;
rm[1][1] = y[0]*dr + y[1] + y[2]*de;
rm[1][2] = - y[0]*dx - y[1]*de + y[2];
rm[2][0] = z[0] - z[1]*dr + z[2]*dx;
rm[2][1] = z[0]*dr + z[1] + z[2]*de;
rm[2][2] = - z[0]*dx - z[1]*de + z[2];
/* Finished. */
}
/*----------------------------------------------------------------------
**
**
** Copyright (C) 2013-2021, NumFOCUS Foundation.
** All rights reserved.
**
** This library is derived, with permission, from the International
** Astronomical Union's "Standards of Fundamental Astronomy" library,
** available from http://www.iausofa.org.
**
** The ERFA version is intended to retain identical functionality to
** the SOFA library, but made distinct through different function and
** file names, as set out in the SOFA license conditions. The SOFA
** original has a role as a reference standard for the IAU and IERS,
** and consequently redistribution is permitted only in its unaltered
** state. The ERFA version is not subject to this restriction and
** therefore can be included in distributions which do not support the
** concept of "read only" software.
**
** Although the intent is to replicate the SOFA API (other than
** replacement of prefix names) and results (with the exception of
** bugs; any that are discovered will be fixed), SOFA is not
** responsible for any errors found in this version of the library.
**
** If you wish to acknowledge the SOFA heritage, please acknowledge
** that you are using a library derived from SOFA, rather than SOFA
** itself.
**
**
** TERMS AND CONDITIONS
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
**
** 1 Redistributions of source code must retain the above copyright
** notice, this list of conditions and the following disclaimer.
**
** 2 Redistributions in binary form must reproduce the above copyright
** notice, this list of conditions and the following disclaimer in
** the documentation and/or other materials provided with the
** distribution.
**
** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
** the International Astronomical Union nor the names of its
** contributors may be used to endorse or promote products derived
** from this software without specific prior written permission.
**
** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
** POSSIBILITY OF SUCH DAMAGE.
**
*/