1 | #include "erfa.h"
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2 |
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3 | void eraPb06(double date1, double date2,
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4 | double *bzeta, double *bz, double *btheta)
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5 | /*
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6 | ** - - - - - - - -
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7 | ** e r a P b 0 6
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8 | ** - - - - - - - -
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9 | **
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10 | ** This function forms three Euler angles which implement general
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11 | ** precession from epoch J2000.0, using the IAU 2006 model. Frame
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12 | ** bias (the offset between ICRS and mean J2000.0) is included.
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13 | **
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14 | ** Given:
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15 | ** date1,date2 double TT as a 2-part Julian Date (Note 1)
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16 | **
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17 | ** Returned:
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18 | ** bzeta double 1st rotation: radians cw around z
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19 | ** bz double 3rd rotation: radians cw around z
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20 | ** btheta double 2nd rotation: radians ccw around y
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21 | **
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22 | ** Notes:
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23 | **
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24 | ** 1) The TT date date1+date2 is a Julian Date, apportioned in any
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25 | ** convenient way between the two arguments. For example,
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26 | ** JD(TT)=2450123.7 could be expressed in any of these ways,
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27 | ** among others:
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28 | **
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29 | ** date1 date2
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30 | **
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31 | ** 2450123.7 0.0 (JD method)
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32 | ** 2451545.0 -1421.3 (J2000 method)
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33 | ** 2400000.5 50123.2 (MJD method)
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34 | ** 2450123.5 0.2 (date & time method)
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35 | **
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36 | ** The JD method is the most natural and convenient to use in
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37 | ** cases where the loss of several decimal digits of resolution
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38 | ** is acceptable. The J2000 method is best matched to the way
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39 | ** the argument is handled internally and will deliver the
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40 | ** optimum resolution. The MJD method and the date & time methods
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41 | ** are both good compromises between resolution and convenience.
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42 | **
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43 | ** 2) The traditional accumulated precession angles zeta_A, z_A,
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44 | ** theta_A cannot be obtained in the usual way, namely through
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45 | ** polynomial expressions, because of the frame bias. The latter
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46 | ** means that two of the angles undergo rapid changes near this
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47 | ** date. They are instead the results of decomposing the
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48 | ** precession-bias matrix obtained by using the Fukushima-Williams
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49 | ** method, which does not suffer from the problem. The
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50 | ** decomposition returns values which can be used in the
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51 | ** conventional formulation and which include frame bias.
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52 | **
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53 | ** 3) The three angles are returned in the conventional order, which
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54 | ** is not the same as the order of the corresponding Euler
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55 | ** rotations. The precession-bias matrix is
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56 | ** R_3(-z) x R_2(+theta) x R_3(-zeta).
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57 | **
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58 | ** 4) Should zeta_A, z_A, theta_A angles be required that do not
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59 | ** contain frame bias, they are available by calling the ERFA
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60 | ** function eraP06e.
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61 | **
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62 | ** Called:
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63 | ** eraPmat06 PB matrix, IAU 2006
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64 | ** eraRz rotate around Z-axis
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65 | **
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66 | ** Copyright (C) 2013-2016, NumFOCUS Foundation.
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67 | ** Derived, with permission, from the SOFA library. See notes at end of file.
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68 | */
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69 | {
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70 | double r[3][3], r31, r32;
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71 |
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72 |
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73 | /* Precession matrix via Fukushima-Williams angles. */
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74 | eraPmat06(date1, date2, r);
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75 |
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76 | /* Solve for z. */
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77 | *bz = atan2(r[1][2], r[0][2]);
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78 |
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79 | /* Remove it from the matrix. */
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80 | eraRz(*bz, r);
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81 |
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82 | /* Solve for the remaining two angles. */
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83 | *bzeta = atan2 (r[1][0], r[1][1]);
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84 | r31 = r[2][0];
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85 | r32 = r[2][1];
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86 | *btheta = atan2(-ERFA_DSIGN(sqrt(r31 * r31 + r32 * r32), r[0][2]),
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87 | r[2][2]);
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88 |
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89 | return;
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90 |
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91 | }
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92 | /*----------------------------------------------------------------------
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93 | **
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94 | **
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95 | ** Copyright (C) 2013-2016, NumFOCUS Foundation.
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96 | ** All rights reserved.
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97 | **
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98 | ** This library is derived, with permission, from the International
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99 | ** Astronomical Union's "Standards of Fundamental Astronomy" library,
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100 | ** available from http://www.iausofa.org.
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101 | **
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102 | ** The ERFA version is intended to retain identical functionality to
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103 | ** the SOFA library, but made distinct through different function and
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104 | ** file names, as set out in the SOFA license conditions. The SOFA
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105 | ** original has a role as a reference standard for the IAU and IERS,
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106 | ** and consequently redistribution is permitted only in its unaltered
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107 | ** state. The ERFA version is not subject to this restriction and
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108 | ** therefore can be included in distributions which do not support the
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109 | ** concept of "read only" software.
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110 | **
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111 | ** Although the intent is to replicate the SOFA API (other than
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112 | ** replacement of prefix names) and results (with the exception of
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113 | ** bugs; any that are discovered will be fixed), SOFA is not
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114 | ** responsible for any errors found in this version of the library.
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115 | **
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116 | ** If you wish to acknowledge the SOFA heritage, please acknowledge
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117 | ** that you are using a library derived from SOFA, rather than SOFA
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118 | ** itself.
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119 | **
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120 | **
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121 | ** TERMS AND CONDITIONS
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122 | **
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123 | ** Redistribution and use in source and binary forms, with or without
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124 | ** modification, are permitted provided that the following conditions
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125 | ** are met:
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126 | **
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127 | ** 1 Redistributions of source code must retain the above copyright
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128 | ** notice, this list of conditions and the following disclaimer.
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129 | **
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130 | ** 2 Redistributions in binary form must reproduce the above copyright
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131 | ** notice, this list of conditions and the following disclaimer in
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132 | ** the documentation and/or other materials provided with the
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133 | ** distribution.
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134 | **
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135 | ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
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136 | ** the International Astronomical Union nor the names of its
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137 | ** contributors may be used to endorse or promote products derived
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138 | ** from this software without specific prior written permission.
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139 | **
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140 | ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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141 | ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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142 | ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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143 | ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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144 | ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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145 | ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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146 | ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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147 | ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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148 | ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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149 | ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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150 | ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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151 | ** POSSIBILITY OF SUCH DAMAGE.
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152 | **
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153 | */
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