void eraBp06(double date1, double date2, double rb[3][3], double rp[3][3], double rbp[3][3]) /* ** - - - - - - - - ** e r a B p 0 6 ** - - - - - - - - ** ** Frame bias and precession, IAU 2006. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rb double[3][3] frame bias matrix (Note 2) ** rp double[3][3] precession matrix (Note 3) ** rbp double[3][3] bias-precession matrix (Note 4) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rb transforms vectors from GCRS to mean J2000.0 by ** applying frame bias. ** ** 3) The matrix rp transforms vectors from mean J2000.0 to mean of ** date by applying precession. ** ** 4) The matrix rbp transforms vectors from GCRS to mean of date by ** applying frame bias then precession. It is the product rp x rb. ** ** Called: ** eraPfw06 bias-precession F-W angles, IAU 2006 ** eraFw2m F-W angles to r-matrix ** eraPmat06 PB matrix, IAU 2006 ** eraTr transpose r-matrix ** eraRxr product of two r-matrices ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** ** Copyright (C) 2013, NumFOCUS Foundation. ** Derived, with permission, from the SOFA library. See notes at end of file. */ { double gamb, phib, psib, epsa, rbt[3][3]; /* B matrix. */ eraPfw06(ERFA_DJM0, ERFA_DJM00, &gamb, &phib, &psib, &epsa); eraFw2m(gamb, phib, psib, epsa, rb); /* PxB matrix. */ eraPmat06(date1, date2, rbp); /* P matrix. */ eraTr(rb, rbt); eraRxr(rbp, rbt, rp); return; }
void eraPb06(double date1, double date2, double *bzeta, double *bz, double *btheta) /* ** - - - - - - - - ** e r a P b 0 6 ** - - - - - - - - ** ** This function forms three Euler angles which implement general ** precession from epoch J2000.0, using the IAU 2006 model. Frame ** bias (the offset between ICRS and mean J2000.0) is included. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** bzeta double 1st rotation: radians cw around z ** bz double 3rd rotation: radians cw around z ** btheta double 2nd rotation: radians ccw around y ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The traditional accumulated precession angles zeta_A, z_A, ** theta_A cannot be obtained in the usual way, namely through ** polynomial expressions, because of the frame bias. The latter ** means that two of the angles undergo rapid changes near this ** date. They are instead the results of decomposing the ** precession-bias matrix obtained by using the Fukushima-Williams ** method, which does not suffer from the problem. The ** decomposition returns values which can be used in the ** conventional formulation and which include frame bias. ** ** 3) The three angles are returned in the conventional order, which ** is not the same as the order of the corresponding Euler ** rotations. The precession-bias matrix is ** R_3(-z) x R_2(+theta) x R_3(-zeta). ** ** 4) Should zeta_A, z_A, theta_A angles be required that do not ** contain frame bias, they are available by calling the ERFA ** function eraP06e. ** ** Called: ** eraPmat06 PB matrix, IAU 2006 ** eraRz rotate around Z-axis ** ** Copyright (C) 2013-2014, NumFOCUS Foundation. ** Derived, with permission, from the SOFA library. See notes at end of file. */ { double r[3][3], r31, r32; /* Precession matrix via Fukushima-Williams angles. */ eraPmat06(date1, date2, r); /* Solve for z. */ *bz = atan2(r[1][2], r[0][2]); /* Remove it from the matrix. */ eraRz(*bz, r); /* Solve for the remaining two angles. */ *bzeta = atan2 (r[1][0], r[1][1]); r31 = r[2][0]; r32 = r[2][1]; *btheta = atan2(-ERFA_DSIGN(sqrt(r31 * r31 + r32 * r32), r[0][2]), r[2][2]); return; }