1 /*
2 * - - - - - - - - -
3 * g a l _ p n 0 6
4 * - - - - - - - - -
5 *
6 * This routine is part of the General Astrodynamics Library
7 *
8 * Description:
9 *
10 * Precession-nutation, IAU 2006 model: a multi-purpose routine,
11 * supporting classical (equinox-based) use directly and CIO-based use
12 * indirectly.
13 *
14 * This routine is an independent translation of a FORTRAN routine
15 * that is part of IAU's SOFA software collection.
16 *
17 * Status:
18 *
19 * support routine.
20 *
21 * Given:
22 *
23 * date1,date2 d TT as a 2-part Julian Date (Note 1)
24 * dpsi,deps d nutation (Note 2)
25 *
26 * Returned:
27 *
28 * *epsa d mean obliquity (Note 3)
29 * rb d[3][3] frame bias matrix (Note 4)
30 * rp d[3][3] precession matrix (Note 5)
31 * rbp d[3][3] bias-precession matrix (Note 6)
32 * rn d[3][3] nutation matrix (Note 7)
33 * rbpn d[3][3] GCRS-to-true matrix (Note 8)
34 *
35 * Notes:
36 *
37 * 1) The TT date date1+date2 is a Julian Date, apportioned in any
38 * convenient way between the two arguments. For example,
39 * JD(TT)=2450123.7 could be expressed in any of these ways,
40 * among others:
41 *
42 * date1 date2
43 *
44 * 2450123.7 0.0 (JD method)
45 * 2451545.0 -1421.3 (J2000 method)
46 * 2400000.5 50123.2 (MJD method)
47 * 2450123.5 0.2 (date & time method)
48 *
49 * The JD method is the most natural and convenient to use in
50 * cases where the loss of several decimal digits of resolution
51 * is acceptable. The J2000 method is best matched to the way
52 * the argument is handled internally and will deliver the
53 * optimum resolution. The MJD method and the date & time methods
54 * are both good compromises between resolution and convenience.
55 *
56 * 2) The caller is responsible for providing the nutation components;
57 * they are in longitude and obliquity, in radians and are with
58 * respect to the equinox and ecliptic of date. For high-accuracy
59 * applications, free core nutation should be included as well as
60 * any other relevant corrections to the position of the CIP.
61 *
62 * 3) The returned mean obliquity is consistent with the IAU 2006
63 * precession.
64 *
65 * 4) The matrix rb transforms vectors from GCRS to mean J2000 by
66 * applying frame bias.
67 *
68 * 5) The matrix rp transforms vectors from mean J2000 to mean of date
69 * by applying precession.
70 *
71 * 6) The matrix rbp transforms vectors from GCRS to mean of date by
72 * applying frame bias then precession. It is the product rp x rb.
73 *
74 * 7) The matrix rn transforms vectors from mean of date to true of date
75 * by applying the nutation (luni-solar + planetary).
76 *
77 * 8) The matrix rbpn transforms vectors from GCRS to true of date
78 * (CIP/equinox). It is the product rn x rbp, applying frame bias,
79 * precession and nutation in that order.
80 *
81 * 9) The X,Y,Z coordinates of the IAU 2006/2000A Celestial Intermediate
82 * Pole are elements [0-2][2] of the matrix rbpn.
83 *
84 * Called:
85 *
86 * gal_pfw06 bias-precession F-W angles, IAU 2006
87 * gal_fw2m F-W angles to r-matrix
88 * gal_tr transpose r-matrix
89 * gal_rxr product of two r-matrices
90 *
91 * References:
92 *
93 * Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
94 *
95 * Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
96 *
97 * This revision:
98 *
99 * 2006 December 5 ( c version 2008 February 4 )
100 *
101 *
102 * Copyright (C) 2008 Paul C. L. Willmott. See notes at end.
103 *
104 *-----------------------------------------------------------------------
105 */
106
107 #include "gal_const.h"
108 #include "gal_pn06.h"
109 #include "gal_pfw06.h"
110 #include "gal_fw2m.h"
111 #include "gal_tr.h"
112 #include "gal_rxr.h"
113
114 void
gal_pn06(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])115 gal_pn06
116 (
117 double date1,
118 double date2,
119 double dpsi,
120 double deps,
121 double *epsa,
122 double rb[3][3],
123 double rp[3][3],
124 double rbp[3][3],
125 double rn[3][3],
126 double rbpn[3][3]
127 )
128 {
129
130 double gamb, phib, psib, eps, rt[3][3] ;
131
132 /*
133 * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134 */
135
136 /*
137 * Bias-precession Fukushima-Williams angles of J2000 = frame bias.
138 */
139
140 gal_pfw06 ( GAL_MJD0, GAL_MJ2000, &gamb, &phib, &psib, &eps ) ;
141
142 /*
143 * B matrix.
144 */
145
146 gal_fw2m ( gamb, phib, psib, eps, rb ) ;
147
148 /*
149 * Bias-precession Fukushima-Williams angles of date.
150 */
151
152 gal_pfw06 ( date1, date2, &gamb, &phib, &psib, &eps ) ;
153
154 /*
155 * Bias-precession matrix.
156 */
157
158 gal_fw2m ( gamb, phib, psib, eps, rbp ) ;
159
160 /*
161 * Solve for precession matrix.
162 */
163
164 gal_tr ( rb, rt ) ;
165 gal_rxr ( rbp, rt, rp ) ;
166
167 /*
168 * Equinox-based bias-precession-nutation matrix.
169 */
170
171 gal_fw2m ( gamb, phib, psib + dpsi, eps + deps, rbpn ) ;
172
173 /*
174 * Solve for nutation matrix.
175 */
176
177 gal_tr ( rbp, rt ) ;
178 gal_rxr ( rbpn, rt, rn ) ;
179
180 /*
181 * Obliquity, mean of date.
182 */
183
184 *epsa = eps ;
185
186 /*
187 * Finished.
188 */
189
190 }
191
192 /*
193 * gal - General Astrodynamics Library
194 * Copyright (C) 2008 Paul C. L. Willmott
195 *
196 * This program is free software; you can redistribute it and/or modify
197 * it under the terms of the GNU General Public License as published by
198 * the Free Software Foundation; either version 2 of the License, or
199 * (at your option) any later version.
200 *
201 * This program is distributed in the hope that it will be useful,
202 * but WITHOUT ANY WARRANTY; without even the implied warranty of
203 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
204 * GNU General Public License for more details.
205 *
206 * You should have received a copy of the GNU General Public License along
207 * with this program; if not, write to the Free Software Foundation, Inc.,
208 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
209 *
210 * Contact:
211 *
212 * Paul Willmott
213 * vp9mu@amsat.org
214 */
215