/* dvsep.f -- translated by f2c (version 19980913).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/

#include "f2c.h"

/* $Procedure DVSEP ( Derivative of separation angle ) */
doublereal dvsep_(doublereal *s1, doublereal *s2)
{
    /* System generated locals */
    doublereal ret_val;

    /* Local variables */
    logical safe;
    extern doublereal vdot_(doublereal *, doublereal *);
    doublereal numr;
    extern /* Subroutine */ int chkin_(char *, ftnlen);
    doublereal denom;
    extern /* Subroutine */ int dvhat_(doublereal *, doublereal *);
    extern doublereal dpmax_(void);
    extern /* Subroutine */ int vcrss_(doublereal *, doublereal *, doublereal 
	    *);
    extern doublereal vnorm_(doublereal *);
    extern logical vzero_(doublereal *);
    doublereal u1[6], u2[6];
    extern /* Subroutine */ int sigerr_(char *, ftnlen), chkout_(char *, 
	    ftnlen), setmsg_(char *, ftnlen);
    doublereal pcross[3];
    extern logical return_(void);

/* $ Abstract */

/*     Calculate the time derivative of the separation angle between */
/*     two input states, S1 and S2. */

/* $ Disclaimer */

/*     THIS SOFTWARE AND ANY RELATED MATERIALS WERE CREATED BY THE */
/*     CALIFORNIA INSTITUTE OF TECHNOLOGY (CALTECH) UNDER A U.S. */
/*     GOVERNMENT CONTRACT WITH THE NATIONAL AERONAUTICS AND SPACE */
/*     ADMINISTRATION (NASA). THE SOFTWARE IS TECHNOLOGY AND SOFTWARE */
/*     PUBLICLY AVAILABLE UNDER U.S. EXPORT LAWS AND IS PROVIDED "AS-IS" */
/*     TO THE RECIPIENT WITHOUT WARRANTY OF ANY KIND, INCLUDING ANY */
/*     WARRANTIES OF PERFORMANCE OR MERCHANTABILITY OR FITNESS FOR A */
/*     PARTICULAR USE OR PURPOSE (AS SET FORTH IN UNITED STATES UCC */
/*     SECTIONS 2312-2313) OR FOR ANY PURPOSE WHATSOEVER, FOR THE */
/*     SOFTWARE AND RELATED MATERIALS, HOWEVER USED. */

/*     IN NO EVENT SHALL CALTECH, ITS JET PROPULSION LABORATORY, OR NASA */
/*     BE LIABLE FOR ANY DAMAGES AND/OR COSTS, INCLUDING, BUT NOT */
/*     LIMITED TO, INCIDENTAL OR CONSEQUENTIAL DAMAGES OF ANY KIND, */
/*     INCLUDING ECONOMIC DAMAGE OR INJURY TO PROPERTY AND LOST PROFITS, */
/*     REGARDLESS OF WHETHER CALTECH, JPL, OR NASA BE ADVISED, HAVE */
/*     REASON TO KNOW, OR, IN FACT, SHALL KNOW OF THE POSSIBILITY. */

/*     RECIPIENT BEARS ALL RISK RELATING TO QUALITY AND PERFORMANCE OF */
/*     THE SOFTWARE AND ANY RELATED MATERIALS, AND AGREES TO INDEMNIFY */
/*     CALTECH AND NASA FOR ALL THIRD-PARTY CLAIMS RESULTING FROM THE */
/*     ACTIONS OF RECIPIENT IN THE USE OF THE SOFTWARE. */

/* $ Required_Reading */

/*     None. */

/* $ Keywords */

/*     GEOMETRY */

/* $ Declarations */
/* $ Brief_I/O */

/*     VARIABLE  I/O  DESCRIPTION */
/*     --------  ---  -------------------------------------------------- */
/*     S1         I   State vector of the first body */
/*     S2         I   State vector of the second  body */

/* $ Detailed_Input */

/*     S1         the state vector of the first target body as seen from */
/*                the observer */

/*     S2         the state vector of the second target body as seen from */
/*                the observer */

/*     An implicit assumption exists that both states lie in the same */
/*     refrence frame with the same observer for the same epoch. If this */
/*     is not the case, the numerical result has no meaning. */

/* $ Detailed_Output */

/*     The function returns the double precision value of the time */
/*     derivative of the angular separation between S1 and S2. */

/* $ Parameters */

/*      None. */

/* $ Exceptions */

/*     1) The error SPICE(NUMERICOVERFLOW) signals if the inputs S1, S2 */
/*        define states with an angular separation rate ~ DPMAX(). */

/*     2) If called in RETURN mode, the return has value 0. */

/*     3) Linear dependent position components of S1 and S1 constitutes */
/*        a non-error exception. The function returns 0 for this case. */

/* $ Files */

/*      None. */

/* $ Particulars */

/*     In this discussion, the notation */

/*        < V1, V2 > */

/*     indicates the dot product of vectors V1 and V2. The notation */

/*        V1 x V2 */

/*     indicates the cross product of vectors V1 and V2. */

/*     To start out, note that we need consider only unit vectors, */
/*     since the angular separation of any two non-zero vectors */
/*     equals the angular separation of the corresponding unit vectors. */
/*     Call these vectors U1 and U2; let their velocities be V1 and V2. */

/*     For unit vectors having angular separation */

/*        THETA */

/*     the identity */

/*        || U1 x U1 || = ||U1|| * ||U2|| * sin(THETA)                (1) */

/*     reduces to */

/*        || U1 x U2 || = sin(THETA)                                  (2) */

/*     and the identity */

/*        | < U1, U2 > | = || U1 || * || U2 || * cos(THETA)           (3) */

/*     reduces to */

/*        | < U1, U2 > | = cos(THETA)                                 (4) */

/*     Since THETA is an angular separation, THETA is in the range */

/*        0 : Pi */

/*     Then letting s be +1 if cos(THETA) > 0 and -1 if cos(THETA) < 0, */
/*     we have for any value of THETA other than 0 or Pi */


/*                                  2          1/2 */
/*        cos(THETA) = s * ( 1 - sin (THETA)  )                       (5) */

/*     or */

/*                                  2          1/2 */
/*        < U1, U2 > = s * ( 1 - sin (THETA)  )                       (6) */


/*     At this point, for any value of THETA other than 0 or Pi, */
/*     we can differentiate both sides with respect to time (T) */
/*     to obtain */

/*                                                      2        -1/2 */
/*        < U1, V2 > + < V1, U2 > =    s * (1/2)(1 - sin (THETA)) */

/*                                   * (-2) sin(THETA)*cos(THETA) */

/*                                   * d(THETA)/dT                   (7a) */


/*     Using equation (5), and noting that s = 1/s, we can cancel */
/*     the cosine terms on the right hand side */

/*                                                      -1 */
/*        < U1, V2 > + < V1, U2 > =    (1/2)(cos(THETA)) */

/*                                   * (-2) sin(THETA)*cos(THETA) */

/*                                   * d(THETA)/dT                   (7b) */

/*     With (7b) reducing to */

/*        < U1, V2 > + < V1, U2 > = - sin(THETA) * d(THETA)/dT        (8) */

/*     Using equation (2) and switching sides, we obtain */

/*        || U1 x U2 || * d(THETA)/dT  =  - < U1, V2 > - < V1, U2 >   (9) */

/*     or, provided U1 and U2 are linearly independent, */

/*        d(THETA)/dT = ( - < U1, V2 > - < V1, U2 > ) / ||U1 x U2||  (10) */

/*     Note for times when U1 and U2 have angular separation 0 or Pi */
/*     radians, the derivative of angular separation with respect to */
/*     time doesn't exist. (Consider the graph of angular separation */
/*     with respect to time; typically the graph is roughly v-shaped at */
/*     the singular points.) */

/* $ Examples */

/*           PROGRAM DVSEP_T */
/*           IMPLICIT              NONE */

/*           DOUBLE PRECISION      ET */
/*           DOUBLE PRECISION      LT */
/*           DOUBLE PRECISION      DSEPT */
/*           DOUBLE PRECISION      STATEE (6) */
/*           DOUBLE PRECISION      STATEM (6) */

/*           INTEGER               STRLEN */
/*           PARAMETER           ( STRLEN = 64 ) */

/*           CHARACTER*(STRLEN)    BEGSTR */

/*           DOUBLE PRECISION      DVSEP */

/*     C */
/*     C     Load kernels. */
/*     C */
/*           CALL FURNSH ('standard.tm') */

/*     C */
/*     C     Ab arbitrary time. */
/*     C */
/*           BEGSTR = 'JAN 1 2009' */
/*           CALL STR2ET( BEGSTR, ET ) */

/*     C */
/*     C     Calculate the state vectors sun to Moon, sun to earth at ET. */
/*     C */
/*     C */
/*           CALL SPKEZR ( 'EARTH', ET, 'J2000', 'NONE', 'SUN', */
/*          .               STATEE, LT) */

/*           CALL SPKEZR ( 'MOON', ET, 'J2000', 'NONE', 'SUN', */
/*          .               STATEM, LT) */

/*     C */
/*     C     Calculate the time derivative of the angular separation of */
/*     C     the earth and Moon as seen from the sun at ET. */
/*     C */
/*           DSEPT = DVSEP( STATEE, STATEM ) */
/*           WRITE(*,*) 'Time derivative of angular separation: ', DSEPT */

/*           END */

/*   The program compiled on OS X with g77 outputs (radians/sec): */

/*      Time derivative of angular separation:   3.81211936E-09 */

/* $ Restrictions */

/*     None. */

/* $ Literature_References */

/*     None. */

/* $ Author_and_Institution */

/*     E.D. Wright    (JPL) */
/*     N.J. Bachman   (JPL) */

/* $ Version */

/* -    SPICELIB Version 1.0.0, 31-MAR-2009 (EDW) */

/* -& */
/* $ Index_Entries */

/*   time derivative of angular separation */

/* -& */

/*     SPICELIB functions */


/*     Local variables */

    if (return_()) {
	ret_val = 0.;
	return ret_val;
    }
    chkin_("DVSEP", (ftnlen)5);

/*     Compute the unit vectors and corresponding time derivatives */
/*     for the input state vectors. */

    dvhat_(s1, u1);
    dvhat_(s2, u2);

/*     Calculate the cross product vector of U1 and U2. As both vectors */
/*     have magnitude one, the magnitude of the cross product equals */
/*     sin(THETA), with THETA the angle between S1 and S2. */

    vcrss_(u1, u2, pcross);

/*     Now calculate the time derivate of the angular separation between */
/*     S1 and S2. */

/*     The routine needs to guard against both division by zero */
/*     and numeric overflow. Before carrying out the division */
/*     indicated by equation (10), the routine should verify that */

/*     || U1 x U2 || >  fudge factor * | numerator | / DPMAX() */

/*     A fudge factor of 10.D0 should suffice. */

/*     Note that the inequality is strict. */


/*     Handle the parallel and anti-parallel cases. */

    if (vzero_(pcross)) {
	ret_val = 0.;
	chkout_("DVSEP", (ftnlen)5);
	return ret_val;
    }

/*     Now check for possible overflow. */

    numr = vdot_(u1, &u2[3]) + vdot_(&u1[3], u2);
    denom = vnorm_(pcross);
    safe = denom > abs(numr) / dpmax_() * 10.;
    if (! safe) {
	ret_val = 0.;
	setmsg_("Numerical overflow event.", (ftnlen)25);
	sigerr_("SPICE(NUMERICOVERFLOW)", (ftnlen)22);
	chkout_("DVSEP", (ftnlen)5);
	return ret_val;
    }
    ret_val = -numr / denom;
    chkout_("DVSEP", (ftnlen)5);
    return ret_val;
} /* dvsep_ */

