| dgeodr |
|
Table of contents
Procedure
DGEODR ( Derivative of geodetic w.r.t. rectangular )
SUBROUTINE DGEODR ( X, Y, Z, RE, F, JACOBI )
Abstract
Compute the Jacobian matrix of the transformation from
rectangular to geodetic coordinates.
Required_Reading
None.
Keywords
COORDINATES
DERIVATIVES
MATRIX
Declarations
IMPLICIT NONE
DOUBLE PRECISION X
DOUBLE PRECISION Y
DOUBLE PRECISION Z
DOUBLE PRECISION RE
DOUBLE PRECISION F
DOUBLE PRECISION JACOBI ( 3, 3 )
Brief_I/O
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
X I X-coordinate of point.
Y I Y-coordinate of point.
Z I Z-coordinate of point.
RE I Equatorial radius of the reference spheroid.
F I Flattening coefficient.
JACOBI O Matrix of partial derivatives.
Detailed_Input
X,
Y,
Z are the rectangular coordinates of the point at
which the Jacobian of the map from rectangular
to geodetic coordinates is desired.
RE is the equatorial radius of the reference spheroid.
F is the flattening coefficient = (RE-RP) / RE, where RP
is the polar radius of the spheroid. (More importantly
RP = RE*(1-F).)
Detailed_Output
JACOBI is the matrix of partial derivatives of the conversion
between rectangular and geodetic coordinates. It
has the form
.- -.
| DLONG/DX DLONG/DY DLONG/DZ |
| DLAT/DX DLAT/DY DLAT/DZ |
| DALT/DX DALT/DY DALT/DZ |
`- -'
evaluated at the input values of X, Y, and Z.
Parameters
None.
Exceptions
1) If the input point is on the z-axis (X = 0 and Y = 0), the
Jacobian is undefined, the error SPICE(POINTONZAXIS) is
signaled.
2) If the flattening coefficient is greater than or equal to
one, the error SPICE(VALUEOUTOFRANGE) is signaled.
3) If the equatorial radius is not positive, the error
SPICE(BADRADIUS) is signaled.
Files
None.
Particulars
When performing vector calculations with velocities it is
usually most convenient to work in rectangular coordinates.
However, once the vector manipulations have been performed,
it is often desirable to convert the rectangular representations
into geodetic coordinates to gain insights about phenomena
in this coordinate frame.
To transform rectangular velocities to derivatives of coordinates
in a geodetic system, one uses the Jacobian of the transformation
between the two systems.
Given a state in rectangular coordinates
( x, y, z, dx, dy, dz )
the velocity in geodetic coordinates is given by the matrix
equation:
t | t
(dlon, dlat, dalt) = JACOBI| * (dx, dy, dz)
|(x,y,z)
This routine computes the matrix
|
JACOBI|
|(x, y, z)
Examples
The 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 geodetic state of the earth as seen from
Mars in the IAU_MARS reference frame at January 1, 2005 TDB.
Map this state back to rectangular coordinates as a check.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: dgeodr_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
--------- --------
de421.bsp Planetary ephemeris
pck00010.tpc Planet orientation and
radii
naif0009.tls Leapseconds
\begindata
KERNELS_TO_LOAD = ( 'de421.bsp',
'pck00010.tpc',
'naif0009.tls' )
\begintext
End of meta-kernel
Example code begins here.
PROGRAM DGEODR_EX1
IMPLICIT NONE
C
C SPICELIB functions
C
DOUBLE PRECISION RPD
C
C Local parameters
C
CHARACTER*(*) FMT1
PARAMETER ( FMT1 = '(A,E18.8)' )
C
C Local variables
C
DOUBLE PRECISION ALT
DOUBLE PRECISION DRECTN ( 3 )
DOUBLE PRECISION ET
DOUBLE PRECISION F
DOUBLE PRECISION JACOBI ( 3, 3 )
DOUBLE PRECISION LAT
DOUBLE PRECISION LON
DOUBLE PRECISION LT
DOUBLE PRECISION GEOVEL ( 3 )
DOUBLE PRECISION RADII ( 3 )
DOUBLE PRECISION RE
DOUBLE PRECISION RECTAN ( 3 )
DOUBLE PRECISION RP
DOUBLE PRECISION STATE ( 6 )
INTEGER N
C
C Load SPK, PCK, and LSK kernels, use a meta kernel for
C convenience.
C
CALL FURNSH ( 'dgeodr_ex1.tm' )
C
C Look up the radii for Mars. Although we
C omit it here, we could first call BADKPV
C to make sure the variable BODY499_RADII
C has three elements and numeric data type.
C If the variable is not present in the kernel
C pool, BODVRD will signal an error.
C
CALL BODVRD ( 'MARS', 'RADII', 3, N, RADII )
C
C Compute flattening coefficient.
C
RE = RADII(1)
RP = RADII(3)
F = ( RE - RP ) / RE
C
C Look up the apparent state of earth as seen from Mars at
C January 1, 2005 TDB, relative to the IAU_MARS reference
C frame.
C
CALL STR2ET ( 'January 1, 2005 TDB', ET )
CALL SPKEZR ( 'Earth', ET, 'IAU_MARS', 'LT+S',
. 'Mars', STATE, LT )
C
C Convert position to geodetic coordinates.
C
CALL RECGEO ( STATE, RE, F, LON, LAT, ALT )
C
C Convert velocity to geodetic coordinates.
C
CALL DGEODR ( STATE(1), STATE(2), STATE(3),
. RE, F, JACOBI )
CALL MXV ( JACOBI, STATE(4), GEOVEL )
C
C As a check, convert the geodetic state back to
C rectangular coordinates.
C
CALL GEOREC ( LON, LAT, ALT, RE, F, RECTAN )
CALL DRDGEO ( LON, LAT, ALT, RE, F, JACOBI )
CALL MXV ( JACOBI, GEOVEL, DRECTN )
WRITE(*,*) ' '
WRITE(*,*) 'Rectangular coordinates:'
WRITE(*,*) ' '
WRITE(*,FMT1) ' X (km) = ', STATE(1)
WRITE(*,FMT1) ' Y (km) = ', STATE(2)
WRITE(*,FMT1) ' Z (km) = ', STATE(3)
WRITE(*,*) ' '
WRITE(*,*) '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(*,*) 'Ellipsoid shape parameters: '
WRITE(*,*) ' '
WRITE(*,FMT1) ' Equatorial radius (km) = ', RE
WRITE(*,FMT1) ' Polar radius (km) = ', RP
WRITE(*,FMT1) ' Flattening coefficient = ', F
WRITE(*,*) ' '
WRITE(*,*) 'Geodetic coordinates:'
WRITE(*,*) ' '
WRITE(*,FMT1) ' Longitude (deg) = ', LON / RPD()
WRITE(*,FMT1) ' Latitude (deg) = ', LAT / RPD()
WRITE(*,FMT1) ' Altitude (km) = ', ALT
WRITE(*,*) ' '
WRITE(*,*) 'Geodetic velocity:'
WRITE(*,*) ' '
WRITE(*,FMT1) ' d Longitude/dt (deg/s) = ',
. GEOVEL(1)/RPD()
WRITE(*,FMT1) ' d Latitude/dt (deg/s) = ',
. GEOVEL(2)/RPD()
WRITE(*,FMT1) ' d Altitude/dt (km/s) = ', GEOVEL(3)
WRITE(*,*) ' '
WRITE(*,*) '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(*,*) '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:
Rectangular coordinates:
X (km) = -0.76096183E+08
Y (km) = 0.32436380E+09
Z (km) = 0.47470484E+08
Rectangular velocity:
dX/dt (km/s) = 0.22952075E+05
dY/dt (km/s) = 0.53760111E+04
dZ/dt (km/s) = -0.20881149E+02
Ellipsoid shape parameters:
Equatorial radius (km) = 0.33961900E+04
Polar radius (km) = 0.33762000E+04
Flattening coefficient = 0.58860076E-02
Geodetic coordinates:
Longitude (deg) = 0.10320290E+03
Latitude (deg) = 0.81089876E+01
Altitude (km) = 0.33653182E+09
Geodetic velocity:
d Longitude/dt (deg/s) = -0.40539288E-02
d Latitude/dt (deg/s) = -0.33189934E-05
d Altitude/dt (km/s) = -0.11211601E+02
Rectangular coordinates from inverse mapping:
X (km) = -0.76096183E+08
Y (km) = 0.32436380E+09
Z (km) = 0.47470484E+08
Rectangular velocity from inverse mapping:
dX/dt (km/s) = 0.22952075E+05
dY/dt (km/s) = 0.53760111E+04
dZ/dt (km/s) = -0.20881149E+02
Restrictions
None.
Literature_References
None.
Author_and_Institution
J. Diaz del Rio (ODC Space)
W.L. Taber (JPL)
Version
SPICELIB Version 1.0.1, 26-OCT-2021 (JDR)
Edited the header to comply with NAIF standard.
Added complete code example.
SPICELIB Version 1.0.0, 20-JUL-2001 (WLT)
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Fri Dec 31 18:36:13 2021