FACT++  1.0
pb06.c
Go to the documentation of this file.
1 #include "erfa.h"
2 
3 void eraPb06(double date1, double date2,
4  double *bzeta, double *bz, double *btheta)
5 /*
6 ** - - - - - - - -
7 ** e r a P b 0 6
8 ** - - - - - - - -
9 **
10 ** This function forms three Euler angles which implement general
11 ** precession from epoch J2000.0, using the IAU 2006 model. Frame
12 ** bias (the offset between ICRS and mean J2000.0) is included.
13 **
14 ** Given:
15 ** date1,date2 double TT as a 2-part Julian Date (Note 1)
16 **
17 ** Returned:
18 ** bzeta double 1st rotation: radians cw around z
19 ** bz double 3rd rotation: radians cw around z
20 ** btheta double 2nd rotation: radians ccw around y
21 **
22 ** Notes:
23 **
24 ** 1) The TT date date1+date2 is a Julian Date, apportioned in any
25 ** convenient way between the two arguments. For example,
26 ** JD(TT)=2450123.7 could be expressed in any of these ways,
27 ** among others:
28 **
29 ** date1 date2
30 **
31 ** 2450123.7 0.0 (JD method)
32 ** 2451545.0 -1421.3 (J2000 method)
33 ** 2400000.5 50123.2 (MJD method)
34 ** 2450123.5 0.2 (date & time method)
35 **
36 ** The JD method is the most natural and convenient to use in
37 ** cases where the loss of several decimal digits of resolution
38 ** is acceptable. The J2000 method is best matched to the way
39 ** the argument is handled internally and will deliver the
40 ** optimum resolution. The MJD method and the date & time methods
41 ** are both good compromises between resolution and convenience.
42 **
43 ** 2) The traditional accumulated precession angles zeta_A, z_A,
44 ** theta_A cannot be obtained in the usual way, namely through
45 ** polynomial expressions, because of the frame bias. The latter
46 ** means that two of the angles undergo rapid changes near this
47 ** date. They are instead the results of decomposing the
48 ** precession-bias matrix obtained by using the Fukushima-Williams
49 ** method, which does not suffer from the problem. The
50 ** decomposition returns values which can be used in the
51 ** conventional formulation and which include frame bias.
52 **
53 ** 3) The three angles are returned in the conventional order, which
54 ** is not the same as the order of the corresponding Euler
55 ** rotations. The precession-bias matrix is
56 ** R_3(-z) x R_2(+theta) x R_3(-zeta).
57 **
58 ** 4) Should zeta_A, z_A, theta_A angles be required that do not
59 ** contain frame bias, they are available by calling the ERFA
60 ** function eraP06e.
61 **
62 ** Called:
63 ** eraPmat06 PB matrix, IAU 2006
64 ** eraRz rotate around Z-axis
65 **
66 ** Copyright (C) 2013-2015, NumFOCUS Foundation.
67 ** Derived, with permission, from the SOFA library. See notes at end of file.
68 */
69 {
70  double r[3][3], r31, r32;
71 
72 /* Precession matrix via Fukushima-Williams angles. */
73  eraPmat06(date1, date2, r);
74 
75 /* Solve for z. */
76  *bz = atan2(r[1][2], r[0][2]);
77 
78 /* Remove it from the matrix. */
79  eraRz(*bz, r);
80 
81 /* Solve for the remaining two angles. */
82  *bzeta = atan2 (r[1][0], r[1][1]);
83  r31 = r[2][0];
84  r32 = r[2][1];
85  *btheta = atan2(-ERFA_DSIGN(sqrt(r31 * r31 + r32 * r32), r[0][2]),
86  r[2][2]);
87 
88  return;
89 
90 }
91 /*----------------------------------------------------------------------
92 **
93 **
94 ** Copyright (C) 2013-2015, NumFOCUS Foundation.
95 ** All rights reserved.
96 **
97 ** This library is derived, with permission, from the International
98 ** Astronomical Union's "Standards of Fundamental Astronomy" library,
99 ** available from http://www.iausofa.org.
100 **
101 ** The ERFA version is intended to retain identical functionality to
102 ** the SOFA library, but made distinct through different function and
103 ** file names, as set out in the SOFA license conditions. The SOFA
104 ** original has a role as a reference standard for the IAU and IERS,
105 ** and consequently redistribution is permitted only in its unaltered
106 ** state. The ERFA version is not subject to this restriction and
107 ** therefore can be included in distributions which do not support the
108 ** concept of "read only" software.
109 **
110 ** Although the intent is to replicate the SOFA API (other than
111 ** replacement of prefix names) and results (with the exception of
112 ** bugs; any that are discovered will be fixed), SOFA is not
113 ** responsible for any errors found in this version of the library.
114 **
115 ** If you wish to acknowledge the SOFA heritage, please acknowledge
116 ** that you are using a library derived from SOFA, rather than SOFA
117 ** itself.
118 **
119 **
120 ** TERMS AND CONDITIONS
121 **
122 ** Redistribution and use in source and binary forms, with or without
123 ** modification, are permitted provided that the following conditions
124 ** are met:
125 **
126 ** 1 Redistributions of source code must retain the above copyright
127 ** notice, this list of conditions and the following disclaimer.
128 **
129 ** 2 Redistributions in binary form must reproduce the above copyright
130 ** notice, this list of conditions and the following disclaimer in
131 ** the documentation and/or other materials provided with the
132 ** distribution.
133 **
134 ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
135 ** the International Astronomical Union nor the names of its
136 ** contributors may be used to endorse or promote products derived
137 ** from this software without specific prior written permission.
138 **
139 ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
140 ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
141 ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
142 ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
143 ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
144 ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
145 ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
146 ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
147 ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
148 ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
149 ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
150 ** POSSIBILITY OF SUCH DAMAGE.
151 **
152 */
eraPmat06
void eraPmat06(double date1, double date2, double rbp[3][3])
Definition: pmat06.c:3
eraRz
void eraRz(double psi, double r[3][3])
Definition: rz.c:3
eraPb06
void eraPb06(double date1, double date2, double *bzeta, double *bz, double *btheta)
Definition: pb06.c:3
ERFA_DSIGN
#define ERFA_DSIGN(A, B)
Definition: erfam.h:131