1 #include "erfa.h"
2
eraPn06(double date1,double date2,double dpsi,double deps,double * epsa,double rb[3][3],double rp[3][3],double rbp[3][3],double rn[3][3],double rbpn[3][3])3 void eraPn06(double date1, double date2, double dpsi, double deps,
4 double *epsa,
5 double rb[3][3], double rp[3][3], double rbp[3][3],
6 double rn[3][3], double rbpn[3][3])
7 /*
8 ** - - - - - - - -
9 ** e r a P n 0 6
10 ** - - - - - - - -
11 **
12 ** Precession-nutation, IAU 2006 model: a multi-purpose function,
13 ** supporting classical (equinox-based) use directly and CIO-based use
14 ** indirectly.
15 **
16 ** Given:
17 ** date1,date2 double TT as a 2-part Julian Date (Note 1)
18 ** dpsi,deps double nutation (Note 2)
19 **
20 ** Returned:
21 ** epsa double mean obliquity (Note 3)
22 ** rb double[3][3] frame bias matrix (Note 4)
23 ** rp double[3][3] precession matrix (Note 5)
24 ** rbp double[3][3] bias-precession matrix (Note 6)
25 ** rn double[3][3] nutation matrix (Note 7)
26 ** rbpn double[3][3] GCRS-to-true matrix (Note 8)
27 **
28 ** Notes:
29 **
30 ** 1) The TT date date1+date2 is a Julian Date, apportioned in any
31 ** convenient way between the two arguments. For example,
32 ** JD(TT)=2450123.7 could be expressed in any of these ways,
33 ** among others:
34 **
35 ** date1 date2
36 **
37 ** 2450123.7 0.0 (JD method)
38 ** 2451545.0 -1421.3 (J2000 method)
39 ** 2400000.5 50123.2 (MJD method)
40 ** 2450123.5 0.2 (date & time method)
41 **
42 ** The JD method is the most natural and convenient to use in
43 ** cases where the loss of several decimal digits of resolution
44 ** is acceptable. The J2000 method is best matched to the way
45 ** the argument is handled internally and will deliver the
46 ** optimum resolution. The MJD method and the date & time methods
47 ** are both good compromises between resolution and convenience.
48 **
49 ** 2) The caller is responsible for providing the nutation components;
50 ** they are in longitude and obliquity, in radians and are with
51 ** respect to the equinox and ecliptic of date. For high-accuracy
52 ** applications, free core nutation should be included as well as
53 ** any other relevant corrections to the position of the CIP.
54 **
55 ** 3) The returned mean obliquity is consistent with the IAU 2006
56 ** precession.
57 **
58 ** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean
59 ** equator and equinox by applying frame bias.
60 **
61 ** 5) The matrix rp transforms vectors from J2000.0 mean equator and
62 ** equinox to mean equator and equinox of date by applying
63 ** precession.
64 **
65 ** 6) The matrix rbp transforms vectors from GCRS to mean equator and
66 ** equinox of date by applying frame bias then precession. It is
67 ** the product rp x rb.
68 **
69 ** 7) The matrix rn transforms vectors from mean equator and equinox
70 ** of date to true equator and equinox of date by applying the
71 ** nutation (luni-solar + planetary).
72 **
73 ** 8) The matrix rbpn transforms vectors from GCRS to true equator and
74 ** equinox of date. It is the product rn x rbp, applying frame
75 ** bias, precession and nutation in that order.
76 **
77 ** 9) The X,Y,Z coordinates of the Celestial Intermediate Pole are
78 ** elements (3,1-3) of the GCRS-to-true matrix, i.e. rbpn[2][0-2].
79 **
80 ** 10) It is permissible to re-use the same array in the returned
81 ** arguments. The arrays are filled in the stated order.
82 **
83 ** Called:
84 ** eraPfw06 bias-precession F-W angles, IAU 2006
85 ** eraFw2m F-W angles to r-matrix
86 ** eraCr copy r-matrix
87 ** eraTr transpose r-matrix
88 ** eraRxr product of two r-matrices
89 **
90 ** References:
91 **
92 ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
93 **
94 ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
95 **
96 ** Copyright (C) 2013-2014, NumFOCUS Foundation.
97 ** Derived, with permission, from the SOFA library. See notes at end of file.
98 */
99 {
100 double gamb, phib, psib, eps, r1[3][3], r2[3][3], rt[3][3];
101
102
103 /* Bias-precession Fukushima-Williams angles of J2000.0 = frame bias. */
104 eraPfw06(ERFA_DJM0, ERFA_DJM00, &gamb, &phib, &psib, &eps);
105
106 /* B matrix. */
107 eraFw2m(gamb, phib, psib, eps, r1);
108 eraCr(r1, rb);
109
110 /* Bias-precession Fukushima-Williams angles of date. */
111 eraPfw06(date1, date2, &gamb, &phib, &psib, &eps);
112
113 /* Bias-precession matrix. */
114 eraFw2m(gamb, phib, psib, eps, r2);
115 eraCr(r2, rbp);
116
117 /* Solve for precession matrix. */
118 eraTr(r1, rt);
119 eraRxr(r2, rt, rp);
120
121 /* Equinox-based bias-precession-nutation matrix. */
122 eraFw2m(gamb, phib, psib + dpsi, eps + deps, r1);
123 eraCr(r1, rbpn);
124
125 /* Solve for nutation matrix. */
126 eraTr(r2, rt);
127 eraRxr(r1, rt, rn);
128
129 /* Obliquity, mean of date. */
130 *epsa = eps;
131
132 return;
133
134 }
135 /*----------------------------------------------------------------------
136 **
137 **
138 ** Copyright (C) 2013-2014, NumFOCUS Foundation.
139 ** All rights reserved.
140 **
141 ** This library is derived, with permission, from the International
142 ** Astronomical Union's "Standards of Fundamental Astronomy" library,
143 ** available from http://www.iausofa.org.
144 **
145 ** The ERFA version is intended to retain identical functionality to
146 ** the SOFA library, but made distinct through different function and
147 ** file names, as set out in the SOFA license conditions. The SOFA
148 ** original has a role as a reference standard for the IAU and IERS,
149 ** and consequently redistribution is permitted only in its unaltered
150 ** state. The ERFA version is not subject to this restriction and
151 ** therefore can be included in distributions which do not support the
152 ** concept of "read only" software.
153 **
154 ** Although the intent is to replicate the SOFA API (other than
155 ** replacement of prefix names) and results (with the exception of
156 ** bugs; any that are discovered will be fixed), SOFA is not
157 ** responsible for any errors found in this version of the library.
158 **
159 ** If you wish to acknowledge the SOFA heritage, please acknowledge
160 ** that you are using a library derived from SOFA, rather than SOFA
161 ** itself.
162 **
163 **
164 ** TERMS AND CONDITIONS
165 **
166 ** Redistribution and use in source and binary forms, with or without
167 ** modification, are permitted provided that the following conditions
168 ** are met:
169 **
170 ** 1 Redistributions of source code must retain the above copyright
171 ** notice, this list of conditions and the following disclaimer.
172 **
173 ** 2 Redistributions in binary form must reproduce the above copyright
174 ** notice, this list of conditions and the following disclaimer in
175 ** the documentation and/or other materials provided with the
176 ** distribution.
177 **
178 ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
179 ** the International Astronomical Union nor the names of its
180 ** contributors may be used to endorse or promote products derived
181 ** from this software without specific prior written permission.
182 **
183 ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
184 ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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196 */
197