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 THETA, TD and PD. * * This revision: 2001 January 4 * * Copyright (C) 2007 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) 2007 * 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. The Software is made available free of charge for use by: * * a) private individuals for non-profit research; and * * b) non-profit educational, academic and research institutions. * * 3. Commercial use of the Software is specifically excluded from the * terms and conditions of this license. Commercial use of the * Software is subject to the prior written agreement of the Board on * terms to be agreed. * * 4. The provision of any version of the 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. * * 5. The user may modify the Software for his/her own purposes. The * user may distribute the modified software provided that the Board * is informed and that a copy of the modified software is made * available to the Board on request. All modifications made by the * user shall be clearly identified to show how the modified software * differs from the original Software, and the name(s) of the * affected routine(s) shall be changed. The original SOFA Software * License text must be present. * * 6. In any published work produced by the user and which includes * results achieved by using the Software, the user shall acknowledge * that the Software was used in producing the information contained * in such publication. * * 7. The user may incorporate or embed the Software into other software * products which he/she may then give away free of charge but not * sell provided the user makes due acknowledgement of the use which * he/she has made of the Software in creating such software * products. Any redistribution of the Software in this way shall be * made under the same terms and conditions under which the user * received it from the SOFA Center. * * 8. The user shall not cause the Software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or by * inappropriate modification. * * 9. The Software is provided to the user "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 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. * * 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