drdazl |
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ProcedureDRDAZL ( Derivative of rectangular w.r.t. AZ/EL ) SUBROUTINE DRDAZL ( RANGE, AZ, EL, AZCCW, ELPLSZ, JACOBI ) AbstractCompute the Jacobian matrix of the transformation from azimuth/elevation to rectangular coordinates. Required_ReadingNone. KeywordsCOORDINATES DERIVATIVES MATRIX DeclarationsIMPLICIT NONE DOUBLE PRECISION RANGE DOUBLE PRECISION AZ DOUBLE PRECISION EL LOGICAL AZCCW LOGICAL ELPLSZ DOUBLE PRECISION JACOBI ( 3, 3 ) Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- RANGE I Distance of a point from the origin. AZ I Azimuth of input point in radians. EL I Elevation of input point in radians. AZCCW I Flag indicating how azimuth is measured. ELPLSZ I Flag indicating how elevation is measured. JACOBI O Matrix of partial derivatives. Detailed_InputRANGE is the distance from the origin of the input point specified by RANGE, AZ, and EL. Negative values for RANGE are not allowed. Units are arbitrary and are considered to match those of the rectangular coordinate system associated with the output matrix JACOBI. AZ is the azimuth of the point. This is the angle between the projection onto the XY plane of the vector from the origin to the point and the +X axis of the reference frame. AZ is zero at the +X axis. The way azimuth is measured depends on the value of the logical flag AZCCW. See the description of the argument AZCCW for details. The range (i.e., the set of allowed values) of AZ is unrestricted. See the $Exceptions section for a discussion on the AZ range. Units are radians. EL is the elevation of the point. This is the angle between the vector from the origin to the point and the XY plane. EL is zero at the XY plane. The way elevation is measured depends on the value of the logical flag ELPLSZ. See the description of the argument ELPLSZ for details. The range (i.e., the set of allowed values) of EL is [-pi/2, pi/2], but no error checking is done to ensure that EL is within this range. See the $Exceptions section for a discussion on the EL range. Units are radians. AZCCW is a flag indicating how the azimuth is measured. If AZCCW is .TRUE., the azimuth increases in the counterclockwise direction; otherwise AZ increases in the clockwise direction. ELPLSZ if a flag indicating how the elevation is measured. If ELPLSZ is .TRUE., the elevation increases from the XY plane toward +Z; otherwise toward -Z. Detailed_OutputJACOBI is the matrix of partial derivatives of the transformation from azimuth/elevation to rectangular coordinates. It has the form .- -. | DX/DRANGE DX/DAZ DX/DEL | | | | DY/DRANGE DY/DAZ DY/DEL | | | | DZ/DRANGE DZ/DAZ DZ/DEL | `- -' evaluated at the input values of RANGE, AZ and EL. X, Y, and Z are given by the familiar formulae X = RANGE * COS( AZ ) * COS( EL ) Y = RANGE * SIN( AZSNSE * AZ ) * COS( EL ) Z = RANGE * SIN( ELDIR * EL ) where AZSNSE is +1 when AZCCW is .TRUE. and -1 otherwise, and ELDIR is +1 when ELPLSZ is .TRUE. and -1 otherwise. ParametersNone. Exceptions1) If the value of the input parameter RANGE is negative, the error SPICE(VALUEOUTOFRANGE) is signaled. 2) If the value of the input argument EL is outside the range [-pi/2, pi/2], the results may not be as expected. 3) If the value of the input argument AZ is outside the range [0, 2*pi], the value will be mapped to a value inside the range that differs from the input value by an integer multiple of 2*pi. FilesNone. ParticularsIt is often convenient to describe the motion of an object in azimuth/elevation coordinates. It is also convenient to manipulate vectors associated with the object in rectangular coordinates. The transformation of a azimuth/elevation state into an equivalent rectangular state makes use of the Jacobian matrix of the transformation between the two systems. Given a state in latitudinal coordinates, ( r, az, el, dr, daz, del ) the velocity in rectangular coordinates is given by the matrix equation t | t (dx, dy, dz) = JACOBI| * (dr, daz, del) |(r,az,el) This routine computes the matrix | JACOBI| |(r,az,el) In the azimuth/elevation coordinate system, several conventions exist on how azimuth and elevation are measured. Using the AZCCW and ELPLSZ flags, users indicate which conventions shall be used. See the descriptions of these input arguments for details. ExamplesThe numerical results shown for this example may differ across platforms. The results depend on the SPICE kernels used as input, the compiler and supporting libraries, and the machine specific arithmetic implementation. 1) Find the azimuth/elevation state of Venus as seen from the DSS-14 station at a given epoch. Map this state back to rectangular coordinates as a check. Task description ================ In this example, we will obtain the apparent state of Venus as seen from the DSS-14 station in the DSS-14 topocentric reference frame. We will use a station frames kernel and transform the resulting rectangular coordinates to azimuth, elevation and range and its derivatives using RECAZL and DAZLDR. We will map this state back to rectangular coordinates using AZLREC and DRDAZL. In order to introduce the usage of the logical flags AZCCW and ELPLSZ, we will request the azimuth to be measured clockwise and the elevation positive towards +Z axis of the DSS-14_TOPO reference frame. Kernels ======= Use the meta-kernel shown below to load the required SPICE kernels. KPL/MK File name: drdazl_ex1.tm This meta-kernel is intended to support operation of SPICE example programs. The kernels shown here should not be assumed to contain adequate or correct versions of data required by SPICE-based user applications. In order for an application to use this meta-kernel, the kernels referenced here must be present in the user's current working directory. The names and contents of the kernels referenced by this meta-kernel are as follows: File name Contents --------- -------- de430.bsp Planetary ephemeris naif0011.tls Leapseconds earth_720101_070426.bpc Earth historical binary PCK earthstns_itrf93_050714.bsp DSN station SPK earth_topo_050714.tf DSN station FK \begindata KERNELS_TO_LOAD = ( 'de430.bsp', 'naif0011.tls', 'earth_720101_070426.bpc', 'earthstns_itrf93_050714.bsp', 'earth_topo_050714.tf' ) \begintext End of meta-kernel. Example code begins here. PROGRAM DRDAZL_EX1 IMPLICIT NONE C C SPICELIB functions C DOUBLE PRECISION DPR C C Local parameters C CHARACTER*(*) FMT1 PARAMETER ( FMT1 = '(A,F20.8)' ) CHARACTER*(*) META PARAMETER ( META = 'drdazl_ex1.tm' ) INTEGER BDNMLN PARAMETER ( BDNMLN = 36 ) INTEGER CORLEN PARAMETER ( CORLEN = 10 ) INTEGER FRNMLN PARAMETER ( FRNMLN = 32 ) INTEGER TIMLEN PARAMETER ( TIMLEN = 40 ) C C Local variables C CHARACTER*(CORLEN) ABCORR CHARACTER*(BDNMLN) OBS CHARACTER*(TIMLEN) OBSTIM CHARACTER*(FRNMLN) REF CHARACTER*(BDNMLN) TARGET DOUBLE PRECISION AZ DOUBLE PRECISION AZLVEL ( 3 ) DOUBLE PRECISION DRECTN ( 3 ) DOUBLE PRECISION EL DOUBLE PRECISION ET DOUBLE PRECISION JACOBI ( 3, 3 ) DOUBLE PRECISION LT DOUBLE PRECISION STATE ( 6 ) DOUBLE PRECISION R DOUBLE PRECISION RECTAN ( 3 ) LOGICAL AZCCW LOGICAL ELPLSZ C C Load SPICE kernels. C CALL FURNSH ( META ) C C Convert the observation time to seconds past J2000 TDB. C OBSTIM = '2003 OCT 13 06:00:00.000000 UTC' CALL STR2ET ( OBSTIM, ET ) C C Set the target, observer, observer frame, and C aberration corrections. C TARGET = 'VENUS' OBS = 'DSS-14' REF = 'DSS-14_TOPO' ABCORR = 'CN+S' C C Compute the observer-target state. C CALL SPKEZR ( TARGET, ET, REF, ABCORR, OBS, . STATE, LT ) C C Convert position to azimuth/elevation coordinates, C with azimuth increasing clockwise and elevation C positive towards +Z axis of the DSS-14_TOPO C reference frame C AZCCW = .FALSE. ELPLSZ = .TRUE. CALL RECAZL ( STATE, AZCCW, ELPLSZ, R, AZ, EL ) C C Convert velocity to azimuth/elevation coordinates. C CALL DAZLDR ( STATE(1), STATE(2), STATE(3), . AZCCW, ELPLSZ, JACOBI ) CALL MXV ( JACOBI, STATE(4), AZLVEL ) C C As a check, convert the azimuth/elevation state back to C rectangular coordinates. C CALL AZLREC ( R, AZ, EL, AZCCW, ELPLSZ, RECTAN ) CALL DRDAZL ( R, AZ, EL, AZCCW, ELPLSZ, JACOBI ) CALL MXV ( JACOBI, AZLVEL, DRECTN ) WRITE(*,*) WRITE(*,'(A)') 'AZ/EL coordinates:' WRITE(*,*) WRITE(*,FMT1) ' Range (km) = ', R WRITE(*,FMT1) ' Azimuth (deg) = ', AZ * DPR() WRITE(*,FMT1) ' Elevation (deg) = ', EL * DPR() WRITE(*,*) WRITE(*,'(A)') 'AZ/EL velocity:' WRITE(*,*) WRITE(*,FMT1) ' d Range/dt (km/s) = ', AZLVEL(1) WRITE(*,FMT1) ' d Azimuth/dt (deg/s) = ', AZLVEL(2) . * DPR() WRITE(*,FMT1) ' d Elevation/dt (deg/s) = ', AZLVEL(3) . * DPR() WRITE(*,*) WRITE(*,'(A)') 'Rectangular coordinates:' WRITE(*,*) WRITE(*,FMT1) ' X (km) = ', STATE(1) WRITE(*,FMT1) ' Y (km) = ', STATE(2) WRITE(*,FMT1) ' Z (km) = ', STATE(3) WRITE(*,*) WRITE(*,'(A)') 'Rectangular velocity:' WRITE(*,*) WRITE(*,FMT1) ' dX/dt (km/s) = ', STATE(4) WRITE(*,FMT1) ' dY/dt (km/s) = ', STATE(5) WRITE(*,FMT1) ' dZ/dt (km/s) = ', STATE(6) WRITE(*,*) WRITE(*,'(A)') 'Rectangular coordinates from inverse ' . // 'mapping:' WRITE(*,*) WRITE(*,FMT1) ' X (km) = ', RECTAN(1) WRITE(*,FMT1) ' Y (km) = ', RECTAN(2) WRITE(*,FMT1) ' Z (km) = ', RECTAN(3) WRITE(*,*) WRITE(*,'(A)') 'Rectangular velocity from inverse ' . // 'mapping:' WRITE(*,*) WRITE(*,FMT1) ' dX/dt (km/s) = ', DRECTN(1) WRITE(*,FMT1) ' dY/dt (km/s) = ', DRECTN(2) WRITE(*,FMT1) ' dZ/dt (km/s) = ', DRECTN(3) WRITE(*,*) END When this program was executed on a Mac/Intel/gfortran/64-bit platform, the output was: AZ/EL coordinates: Range (km) = 245721478.99272084 Azimuth (deg) = 294.48543372 Elevation (deg) = -48.94609726 AZ/EL velocity: d Range/dt (km/s) = -4.68189834 d Azimuth/dt (deg/s) = 0.00402256 d Elevation/dt (deg/s) = -0.00309156 Rectangular coordinates: X (km) = 66886767.37916667 Y (km) = 146868551.77222887 Z (km) = -185296611.10841590 Rectangular velocity: dX/dt (km/s) = 6166.04150307 dY/dt (km/s) = -13797.77164550 dZ/dt (km/s) = -8704.32385654 Rectangular coordinates from inverse mapping: X (km) = 66886767.37916658 Y (km) = 146868551.77222890 Z (km) = -185296611.10841590 Rectangular velocity from inverse mapping: dX/dt (km/s) = 6166.04150307 dY/dt (km/s) = -13797.77164550 dZ/dt (km/s) = -8704.32385654 RestrictionsNone. Literature_ReferencesNone. Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) VersionSPICELIB Version 1.0.0, 08-SEP-2021 (JDR) (NJB) |
Fri Dec 31 18:36:14 2021