SUBROUTINE iau_PV2S ( PV, THETA, PHI, R, TD, PD, RD ) *+ * - - - - - - - - - * i a u _ P V 2 S * - - - - - - - - - * * Convert position/velocity from Cartesian to spherical coordinates. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: vector/matrix support routine. * * Given: * PV d(3,2) pv-vector * * Returned: * THETA d longitude angle (radians) * PHI d latitude angle (radians) * R d radial distance * TD d rate of change of THETA * PD d rate of change of PHI * RD d rate of change of R * * Notes: * * 1) If the position part of PV is null, THETA, PHI, TD and PD * are indeterminate. This is handled by extrapolating the * position through unit time by using the velocity part of * PV. This moves the origin without changing the direction * of the velocity component. If the position and velocity * components of PV are both null, zeroes are returned for all * six results. * * 2) If the position is a pole, THETA, TD and PD are indeterminate. * In such cases zeroes are returned for all three. * * This revision: 2008 May 10 * * Copyright (C) 2008 IAU SOFA Review Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION PV(3,2), THETA, PHI, R, TD, PD, RD DOUBLE PRECISION X, Y, Z, XD, YD, ZD, RXY2, RXY, R2, : RTRUE, RW, XYP * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Components of position/velocity vector. X = PV(1,1) Y = PV(2,1) Z = PV(3,1) XD = PV(1,2) YD = PV(2,2) ZD = PV(3,2) * Component of R in XY plane squared. RXY2 = X*X + Y*Y * Modulus squared. R2 = RXY2 + Z*Z * Modulus. RTRUE = SQRT(R2) * If null vector, move the origin along the direction of movement. RW = RTRUE IF ( RTRUE .EQ. 0D0 ) THEN X = XD Y = YD Z = ZD RXY2 = X*X + Y*Y R2 = RXY2 + Z*Z RW = SQRT(R2) END IF * Position and velocity in spherical coordinates. RXY = SQRT(RXY2) XYP = X*XD + Y*YD IF ( RXY2 .NE. 0D0 ) THEN THETA = ATAN2(Y,X) PHI = ATAN2(Z,RXY) TD = ( X*YD - Y*XD ) / RXY2 PD = ( ZD*RXY2 - Z*XYP ) / ( R2*RXY ) ELSE THETA = 0D0 IF ( Z.NE.0D0 ) THEN PHI = ATAN2(Z,RXY) ELSE PHI = 0D0 END IF TD = 0D0 PD = 0D0 END IF R = RTRUE IF ( RW.NE.0D0 ) THEN RD = ( XYP + Z*ZD ) / RW ELSE RD = 0D0 END IF * Finished. *+----------------------------------------------------------------------- * * Copyright (C) 2008 * Standards Of Fundamental Astronomy Review Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS * WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Review Board ("the Board"). * * 2. Permission is granted to anyone to use the SOFA software for any * purpose, including commercial applications, free of charge and * without payment of royalties, subject to the conditions and * restrictions listed below. * * 3. You (the user) may copy and adapt the SOFA software and its * algorithms for your own purposes and you may copy and distribute * a resulting "derived work" to others on a world-wide, royalty-free * basis, provided that the derived work complies with the following * requirements: * * a) Your work shall be marked or carry a statement that it (i) uses * routines and computations derived by you from software provided * by SOFA under license to you; and (ii) does not contain * software provided by SOFA or software that has been distributed * by or endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon and/or differs from the * original SOFA software. * * c) The name(s) of all routine(s) that you distribute shall differ * from the SOFA names, even when the SOFA content has not been * otherwise changed. * * d) The routine-naming prefix "iau" shall not be used. * * e) The origin of the SOFA components of your derived work must not * be misrepresented; you must not claim that you wrote the * original software, nor file a patent application for SOFA * software or algorithms embedded in the SOFA software. * * f) These requirements must be reproduced intact in any source * distribution and shall apply to anyone to whom you have granted * a further right to modify the source code of your derived work. * * 4. In any published work or commercial products which includes * results achieved by using the SOFA software, you shall acknowledge * that the SOFA software was used in obtaining those results. * * 5. You shall not cause the SOFA software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or by * inappropriate modification. * * 6. The SOFA software is provided "as is" and the Board makes no * warranty as to its use or performance. The Board does not and * cannot warrant the performance or results which the user may obtain * by using the SOFA software. The Board makes no warranties, express * or implied, as to non-infringement of third party rights, * merchantability, or fitness for any particular purpose. In no * event will the Board be liable to the user for any consequential, * incidental, or special damages, including any lost profits or lost * savings, even if a Board representative has been advised of such * damages, or for any claim by any third party. * * 7. The provision of any version of the SOFA software under the terms * and conditions specified herein does not imply that future * versions will also be made available under the same terms and * conditions. * * Correspondence concerning SOFA software should be addressed as * follows: * * Internet email: sofa@rl.ac.uk * Postal address: IAU SOFA Center * Rutherford Appleton Laboratory * Chilton, Didcot, Oxon OX11 0QX * United Kingdom * *----------------------------------------------------------------------- END