dpgrdr_c

 Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input Detailed_Output Parameters Exceptions Files Particulars Examples Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

```   void dpgrdr_c ( ConstSpiceChar  * body,
SpiceDouble       x,
SpiceDouble       y,
SpiceDouble       z,
SpiceDouble       re,
SpiceDouble       f,
SpiceDouble       jacobi  )

```

#### Abstract

```
This routine computes the Jacobian matrix of the transformation
from rectangular to planetographic coordinates.
```

```
None.
```

```
COORDINATES
DERIVATIVES
MATRIX

```

#### Brief_I/O

```
Variable  I/O  Description
--------  ---  --------------------------------------------------
body       I   Body with which coordinate system is associated.
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

```
body       Name of the body with which the planetographic
coordinate system is associated.

`body' is used by this routine to look up from the
kernel pool the prime meridian rate coefficient giving
the body's spin sense.  See the Files and Particulars

x,
y,
z          are the rectangular coordinates of the point at
which the Jacobian of the map from rectangular
to planetographic coordinates is desired.

re         Equatorial radius of the reference spheroid.

f          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
from rectangular to planetographic coordinates.  It
has the form

.-                               -.
|  DLON/DX    DLON/DY   DLON/DZ   |
|  DLAT/DX    DLAT/DY   DLAT/DZ   |
|  DALT/DX    DALT/DY   DALT/DZ   |
`-                               -'

evaluated at the input values of `x', `y', and `z'.
```

```
None.
```

#### Exceptions

```
1) If the body name `body' cannot be mapped to a NAIF ID code,
and if `body' is not a string representation of an integer,
the error SPICE(IDCODENOTFOUND) will be signaled.

2) If the kernel variable

BODY<ID code>_PGR_POSITIVE_LON

is present in the kernel pool but has a value other
than one of

'EAST'
'WEST'

the error SPICE(INVALIDOPTION) will be signaled.  Case
and blanks are ignored when these values are interpreted.

3) If polynomial coefficients for the prime meridian of `body'
are not available in the kernel pool, and if the kernel
variable BODY<ID code>_PGR_POSITIVE_LON is not present in
the kernel pool, the error SPICE(MISSINGDATA) will be signaled.

4) If the equatorial radius is non-positive, the error
SPICE(VALUEOUTOFRANGE) is signaled.

5) If the flattening coefficient is greater than or equal to one,
the error SPICE(VALUEOUTOFRANGE) is signaled.

6) If the input point is on the Z-axis (X = 0 and Y = 0), the
Jacobian matrix is undefined.  The error will be diagnosed
by routines in the call tree of this routine.

7) The error SPICE(EMPTYSTRING) is signaled if the input
string `body' does not contain at least one character, since the
input string cannot be converted to a Fortran-style string in
this case.

8) The error SPICE(NULLPOINTER) is signaled if the input string
pointer `body' is null.
```

#### Files

```
This routine expects a kernel variable giving body's prime
meridian angle as a function of time to be available in the
file.  The required kernel variable is named

BODY<body ID>_PM

where <body ID> represents a string containing the NAIF integer
ID code for `body'.  For example, if `body' is "JUPITER", then
the name of the kernel variable containing the prime meridian
angle coefficients is

BODY599_PM

See the PCK Required Reading for details concerning the prime
meridian kernel variable.

The optional kernel variable

BODY<body ID>_PGR_POSITIVE_LON

variable is present in the kernel pool, the prime meridian
coefficients for `body' are not required by this routine. See the
Particulars section below for details.
```

#### 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
planetographic coordinates to gain insights about phenomena in
this coordinate frame.

To transform rectangular velocities to derivatives of coordinates
in a planetographic 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 planetographic 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)

The planetographic definition of latitude is identical to the
planetodetic (also called "geodetic" in SPICE documentation)
definition. In the planetographic coordinate system, latitude is
defined using a reference spheroid.  The spheroid is
point P on the spheroid, latitude is defined as the angle between
the X-Y plane and the outward surface normal at P.  For a point P
off the spheroid, latitude is defined as the latitude of the
nearest point to P on the spheroid.  Note if P is an interior
point, for example, if P is at the center of the spheroid, there
may not be a unique nearest point to P.

In the planetographic coordinate system, longitude is defined
using the spin sense of the body.  Longitude is positive to the
west if the spin is prograde and positive to the east if the spin
is retrograde.  The spin sense is given by the sign of the first
degree term of the time-dependent polynomial for the body's prime
meridian Euler angle "W":  the spin is retrograde if this term is
negative and prograde otherwise.  For the sun, planets, most
natural satellites, and selected asteroids, the polynomial
expression for W may be found in a SPICE PCK kernel.

The earth, moon, and sun are exceptions: planetographic longitude
is measured positive east for these bodies.

If you wish to override the default sense of positive longitude
for a particular body, you can do so by defining the kernel
variable

BODY<body ID>_PGR_POSITIVE_LON

where <body ID> represents the NAIF ID code of the body. This
variable may be assigned either of the values

'WEST'
'EAST'

For example, you can have this routine treat the longitude
of the earth as increasing to the west using the kernel
variable assignment

BODY399_PGR_POSITIVE_LON = 'WEST'

Normally such assignments are made by placing them in a text

The definition of this kernel variable controls the behavior of
the CSPICE planetographic routines

pgrrec_c
recpgr_c
dpgrdr_c
drdpgr_c

It does not affect the other CSPICE coordinate conversion
routines.
```

#### Examples

```
Numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as
input and the machine specific arithmetic implementation.

Find the planetographic state of the earth as seen from
Mars in the J2000 reference frame at January 1, 2005 TDB.
Map this state back to rectangular coordinates as a check.

#include <stdio.h>
#include "SpiceUsr.h"

int main()
{
/.
Local variables
./
SpiceDouble             alt;
SpiceDouble             drectn ;
SpiceDouble             et;
SpiceDouble             f;
SpiceDouble             jacobi ;
SpiceDouble             lat;
SpiceDouble             lon;
SpiceDouble             lt;
SpiceDouble             pgrvel ;
SpiceDouble             re;
SpiceDouble             rectan ;
SpiceDouble             rp;
SpiceDouble             state  ;

SpiceInt                n;

/.
Load a PCK file containing a triaxial
ellipsoidal shape model and orientation
data for Mars.
./
furnsh_c ( "pck00008.tpc" );

/.
Load an SPK file giving ephemerides of earth and Mars.
./
furnsh_c ( "de405.bsp" );

/.
Load a leapseconds kernel to support time conversion.
./
furnsh_c ( "naif0007.tls" );

/.
Look up the radii for Mars.  Although we
omit it here, we could first call badkpv_c
to make sure the variable BODY499_RADII
has three elements and numeric data type.
If the variable is not present in the kernel
pool, bodvrd_c will signal an error.
./

/.
Compute flattening coefficient.
./
f   =  ( re - rp ) / re;

/.
Look up the geometric state of earth as seen from Mars at
January 1, 2005 TDB, relative to the J2000 reference
frame.
./
str2et_c ( "January 1, 2005 TDB", &et);

spkezr_c ( "Earth", et,    "J2000", "LT+S",
"Mars",  state, &lt              );

/.
Convert position to planetographic coordinates.
./
recpgr_c ( "mars", state, re, f, &lon, &lat, &alt );

/.
Convert velocity to planetographic coordinates.
./

dpgrdr_c ( "MARS",  state,  state,  state,
re,      f,         jacobi               );

mxv_c ( jacobi, state+3, pgrvel );

/.
As a check, convert the planetographic state back to
rectangular coordinates.
./
pgrrec_c ( "mars", lon, lat, alt, re, f, rectan );
drdpgr_c ( "mars", lon, lat, alt, re, f, jacobi );

mxv_c ( jacobi, pgrvel, drectn );

printf ( "\n"
"Rectangular coordinates:\n"
"\n"
"  X (km)                 = %18.9e\n"
"  Y (km)                 = %18.9e\n"
"  Z (km)                 = %18.9e\n"
"\n"
"Rectangular velocity:\n"
"\n"
"  dX/dt (km/s)           = %18.9e\n"
"  dY/dt (km/s)           = %18.9e\n"
"  dZ/dt (km/s)           = %18.9e\n"
"\n"
"Ellipsoid shape parameters:\n"
"\n"
"  Equatorial radius (km) = %18.9e\n"
"  Polar radius      (km) = %18.9e\n"
"  Flattening coefficient = %18.9e\n"
"\n"
"Planetographic coordinates:\n"
"\n"
"  Longitude (deg)        = %18.9e\n"
"  Latitude  (deg)        = %18.9e\n"
"  Altitude  (km)         = %18.9e\n"
"\n"
"Planetographic velocity:\n"
"\n"
"  d Longitude/dt (deg/s) = %18.9e\n"
"  d Latitude/dt  (deg/s) = %18.9e\n"
"  d Altitude/dt  (km/s)  = %18.9e\n"
"\n"
"Rectangular coordinates from inverse mapping:\n"
"\n"
"  X (km)                 = %18.9e\n"
"  Y (km)                 = %18.9e\n"
"  Z (km)                 = %18.9e\n"
"\n"
"Rectangular velocity from inverse mapping:\n"
"\n"
"  dX/dt (km/s)           = %18.9e\n"
"  dY/dt (km/s)           = %18.9e\n"
"  dZ/dt (km/s)           = %18.9e\n"
"\n",
state ,
state ,
state ,
state ,
state ,
state ,
re,
rp,
f,
lon / rpd_c(),
lat / rpd_c(),
alt,
pgrvel/rpd_c(),
pgrvel/rpd_c(),
pgrvel,
rectan ,
rectan ,
rectan ,
drectn ,
drectn ,
drectn                 );

return ( 0 );
}

Output from this program should be similar to the following
(rounding and formatting differ across platforms):

Rectangular coordinates:

X (km)                 =    1.460397325e+08
Y (km)                 =    2.785466068e+08
Z (km)                 =    1.197503153e+08

Rectangular velocity:

dX/dt (km/s)           =   -4.704288238e+01
dY/dt (km/s)           =    9.070217780e+00
dZ/dt (km/s)           =    4.756562739e+00

Ellipsoid shape parameters:

Flattening coefficient =    5.886007556e-03

Planetographic coordinates:

Longitude (deg)        =    2.976676591e+02
Latitude  (deg)        =    2.084450403e+01
Altitude  (km)         =    3.365318254e+08

Planetographic velocity:

d Longitude/dt (deg/s) =   -8.357386316e-06
d Latitude/dt  (deg/s) =    1.593493548e-06
d Altitude/dt  (km/s)  =   -1.121443268e+01

Rectangular coordinates from inverse mapping:

X (km)                 =    1.460397325e+08
Y (km)                 =    2.785466068e+08
Z (km)                 =    1.197503153e+08

Rectangular velocity from inverse mapping:

dX/dt (km/s)           =   -4.704288238e+01
dY/dt (km/s)           =    9.070217780e+00
dZ/dt (km/s)           =    4.756562739e+00
```

```
None.
```

```
None.
```

#### Author_and_Institution

```
N.J. Bachman   (JPL)
W.L. Taber     (JPL)
```

#### Version

```
-CSPICE Version 1.0.0, 26-DEC-2004 (NJB) (WLT)
```

#### Index_Entries

```
Jacobian of planetographic  w.r.t. rectangular coordinates
```
`Wed Apr  5 17:54:31 2017`