void
palDeuler( const char *order, double phi, double theta, double psi,
double rmat[3][3] ) {
int i = 0;
double rotations[3];
/* Initialise rmat */
eraIr( rmat );
/* copy the rotations into an array */
rotations[0] = phi;
rotations[1] = theta;
rotations[2] = psi;
/* maximum three rotations */
while (i < 3 && order[i] != '\0') {
switch (order[i]) {
case 'X':
case 'x':
case '1':
eraRx( rotations[i], rmat );
break;
case 'Y':
case 'y':
case '2':
eraRy( rotations[i], rmat );
break;
case 'Z':
case 'z':
case '3':
eraRz( rotations[i], rmat );
break;
default:
/* break out the loop if we do not recognize something */
i = 3;
}
/* Go to the next position */
i++;
}
return;
}
void eraC2ixys(double x, double y, double s, double rc2i[3][3])
/*
** - - - - - - - - - -
** e r a C 2 i x y s
** - - - - - - - - - -
**
** Form the celestial to intermediate-frame-of-date matrix given the CIP
** X,Y and the CIO locator s.
**
** Given:
** x,y double Celestial Intermediate Pole (Note 1)
** s double the CIO locator s (Note 2)
**
** Returned:
** rc2i double[3][3] celestial-to-intermediate matrix (Note 3)
**
** Notes:
**
** 1) The Celestial Intermediate Pole coordinates are the x,y
** components of the unit vector in the Geocentric Celestial
** Reference System.
**
** 2) The CIO locator s (in radians) positions the Celestial
** Intermediate Origin on the equator of the CIP.
**
** 3) The matrix rc2i is the first stage in the transformation from
** celestial to terrestrial coordinates:
**
** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
**
** = RC2T * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), ERA is the Earth
** Rotation Angle and RPOM is the polar motion matrix.
**
** Called:
** eraIr initialize r-matrix to identity
** eraRz rotate around Z-axis
** eraRy rotate around Y-axis
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double r2, e, d;
/* Obtain the spherical angles E and d. */
r2 = x*x + y*y;
e = (r2 != 0.0) ? atan2(y, x) : 0.0;
d = atan(sqrt(r2 / (1.0 - r2)));
/* Form the matrix. */
eraIr(rc2i);
eraRz(e, rc2i);
eraRy(d, rc2i);
eraRz(-(e+s), rc2i);
return;
}
void eraBp00(double date1, double date2,
double rb[3][3], double rp[3][3], double rbp[3][3])
/*
** - - - - - - - -
** e r a B p 0 0
** - - - - - - - -
**
** Frame bias and precession, IAU 2000.
**
** 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 J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 4) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 5) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the order given.
**
** Called:
** eraBi00 frame bias components, IAU 2000
** eraPr00 IAU 2000 precession adjustments
** eraIr initialize r-matrix to identity
** eraRx rotate around X-axis
** eraRy rotate around Y-axis
** eraRz rotate around Z-axis
** eraCr copy r-matrix
** eraRxr product of two r-matrices
**
** Reference:
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** Copyright (C) 2013-2017, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* J2000.0 obliquity (Lieske et al. 1977) */
const double EPS0 = 84381.448 * ERFA_DAS2R;
double t, dpsibi, depsbi, dra0, psia77, oma77, chia,
dpsipr, depspr, psia, oma, rbw[3][3];
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
/* Frame bias. */
eraBi00(&dpsibi, &depsbi, &dra0);
/* Precession angles (Lieske et al. 1977) */
psia77 = (5038.7784 + (-1.07259 + (-0.001147) * t) * t) * t * ERFA_DAS2R;
oma77 = EPS0 + ((0.05127 + (-0.007726) * t) * t) * t * ERFA_DAS2R;
chia = ( 10.5526 + (-2.38064 + (-0.001125) * t) * t) * t * ERFA_DAS2R;
/* Apply IAU 2000 precession corrections. */
eraPr00(date1, date2, &dpsipr, &depspr);
psia = psia77 + dpsipr;
oma = oma77 + depspr;
/* Frame bias matrix: GCRS to J2000.0. */
eraIr(rbw);
eraRz(dra0, rbw);
eraRy(dpsibi*sin(EPS0), rbw);
eraRx(-depsbi, rbw);
eraCr(rbw, rb);
/* Precession matrix: J2000.0 to mean of date. */
eraIr(rp);
eraRx(EPS0, rp);
eraRz(-psia, rp);
eraRx(-oma, rp);
eraRz(chia, rp);
/* Bias-precession matrix: GCRS to mean of date. */
eraRxr(rp, rbw, rbp);
return;
}
