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 * * SOFA release 2012-03-01 * * Copyright (C) 2012 IAU SOFA 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) 2012 * Standards Of Fundamental Astronomy Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND * CONDITIONS WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Board ("SOFA"). * * 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 distribute SOFA source code to others, * and use and adapt its code and algorithms in your own software, * on a world-wide, royalty-free basis. That portion of your * distribution that does not consist of intact and unchanged copies * of SOFA source code files is a "derived work" that must comply * 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 itself constitute software provided by and/or * endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon, contains and/or differs * from the original SOFA software. * * c) The names of all routines in your derived work shall not * include the prefix "iau" or "sofa" or trivial modifications * thereof such as changes of case. * * d) 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. * * e) 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. * * Note that, as originally distributed, the SOFA software is * intended to be a definitive implementation of the IAU standards, * and consequently third-party modifications are discouraged. All * variations, no matter how minor, must be explicitly marked as * such, as explained above. * * 4. You shall not cause the SOFA software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or * by inappropriate modification. * * 5. The SOFA software is provided "as is" and SOFA makes no warranty * as to its use or performance. SOFA does not and cannot warrant * the performance or results which the user may obtain by using the * SOFA software. SOFA 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 SOFA be * liable to the user for any consequential, incidental, or special * damages, including any lost profits or lost savings, even if a * SOFA representative has been advised of such damages, or for any * claim by any third party. * * 6. 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. * * In any published work or commercial product which uses the SOFA * software directly, acknowledgement (see www.iausofa.org) is * appreciated. * * Correspondence concerning SOFA software should be addressed as * follows: * * By email: sofa@ukho.gov.uk * By post: IAU SOFA Center * HM Nautical Almanac Office * UK Hydrographic Office * Admiralty Way, Taunton * Somerset, TA1 2DN * United Kingdom * *----------------------------------------------------------------------- END