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drdcyl_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

```   drdcyl_c (Derivative of rectangular w.r.t. cylindrical)

void drdcyl_c ( SpiceDouble    r,
SpiceDouble    clon,
SpiceDouble    z,
SpiceDouble    jacobi[3][3] )

```

#### Abstract

```   Compute the Jacobian matrix of the transformation from
cylindrical to rectangular coordinates.
```

```   None.
```

#### Keywords

```   COORDINATES
DERIVATIVES
MATRIX

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
r          I   Distance of a point from the origin.
clon       I   Angle of the point from the XZ plane in radians.
z          I   Height of the point above the XY plane.
jacobi     O   Matrix of partial derivatives.
```

#### Detailed_Input

```   r           is the distance of the point of interest from Z axis.

clon        is the cylindrical angle (in radians) of the point of
interest from XZ plane. The angle increases in the
counterclockwise sense about the +Z axis.

z           is the height of the point above XY plane.
```

#### Detailed_Output

```   jacobi      is the matrix of partial derivatives of the conversion
between cylindrical and rectangular coordinates. It
has the form

.-                                -.
|  dx/dr     dx/dclon     dx/dz    |
|                                  |
|  dy/dr     dy/dclon     dy/dz    |
|                                  |
|  dz/dr     dz/dclon     dz/dz    |
`-                                -'

evaluated at the input values of `r', `clon' and `z'.
Here `x', `y', and `z' are given by the familiar formulae

x = r*cos(clon)
y = r*sin(clon)
z = z
```

#### Parameters

```   None.
```

#### Exceptions

```   Error free.
```

#### Files

```   None.
```

#### Particulars

```   It is often convenient to describe the motion of an object in
the cylindrical coordinate system. However, when performing
vector computations its hard to beat rectangular coordinates.

To transform states given with respect to cylindrical coordinates
to states with respect to rectangular coordinates, one uses
the Jacobian of the transformation between the two systems.

Given a state in cylindrical coordinates

( r, clon, z, dr, dclon, dz )

the velocity in rectangular coordinates is given by the matrix
equation:
t          |                           t
(dx, dy, dz)   = jacobi|          * (dr, dclon, dz)
|(r,clon,z)

This routine computes the matrix

|
jacobi|
|(r,clon,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 cylindrical 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: drdcyl_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
naif0009.tls                  Leapseconds

\begindata

'pck00010.tpc',
'naif0009.tls'  )

\begintext

End of meta-kernel

Example code begins here.

/.
Program drdcyl_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables
./
SpiceDouble          clon;
SpiceDouble          drectn [3];
SpiceDouble          et;
SpiceDouble          jacobi [3][3];
SpiceDouble          lt;
SpiceDouble          cylvel [3];
SpiceDouble          rectan [3];
SpiceDouble          r;
SpiceDouble          state  [6];
SpiceDouble          z;

/.
Load SPK, PCK and LSK kernels, use a meta kernel for
convenience.
./
furnsh_c ( "drdcyl_ex1.tm" );

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

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

/.
Convert position to cylindrical coordinates.
./
reccyl_c ( state, &r, &clon, &z );

/.
Convert velocity to cylindrical coordinates.
./

dcyldr_c ( state[0], state[1], state[2], jacobi );

mxv_c ( jacobi, state+3, cylvel );

/.
As a check, convert the cylindrical state back to
rectangular coordinates.
./
cylrec_c ( r, clon, z, rectan );

drdcyl_c ( r, clon, z, jacobi );

mxv_c ( jacobi, cylvel, drectn );

printf( " \n" );
printf( "Rectangular coordinates:\n" );
printf( " \n" );
printf( " X (km)                 =  %17.8e\n", state[0] );
printf( " Y (km)                 =  %17.8e\n", state[1] );
printf( " Z (km)                 =  %17.8e\n", state[2] );
printf( " \n" );
printf( "Rectangular velocity:\n" );
printf( " \n" );
printf( " dX/dt (km/s)           =  %17.8e\n", state[3] );
printf( " dY/dt (km/s)           =  %17.8e\n", state[4] );
printf( " dZ/dt (km/s)           =  %17.8e\n", state[5] );
printf( " \n" );
printf( "Cylindrical coordinates:\n" );
printf( " \n" );
printf( " Radius    (km)         =  %17.8e\n", r );
printf( " Longitude (deg)        =  %17.8e\n", clon/rpd_c() );
printf( " Z         (km)         =  %17.8e\n", z );
printf( " \n" );
printf( "Cylindrical velocity:\n" );
printf( " \n" );
printf( " d Radius/dt    (km/s)  =  %17.8e\n", cylvel[0] );
printf( " d Longitude/dt (deg/s) =  %17.8e\n", cylvel[1]/rpd_c() );
printf( " d Z/dt         (km/s)  =  %17.8e\n", cylvel[2] );
printf( " \n" );
printf( "Rectangular coordinates from inverse mapping:\n" );
printf( " \n" );
printf( " X (km)                 =  %17.8e\n", rectan[0] );
printf( " Y (km)                 =  %17.8e\n", rectan[1] );
printf( " Z (km)                 =  %17.8e\n", rectan[2] );
printf( " \n" );
printf( "Rectangular velocity from inverse mapping:\n" );
printf( " \n" );
printf( " dX/dt (km/s)           =  %17.8e\n", drectn[0] );
printf( " dY/dt (km/s)           =  %17.8e\n", drectn[1] );
printf( " dZ/dt (km/s)           =  %17.8e\n", drectn[2] );
printf( " \n" );

return ( 0 );
}

When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:

Rectangular coordinates:

X (km)                 =    -7.60961826e+07
Y (km)                 =     3.24363805e+08
Z (km)                 =     4.74704840e+07

Rectangular velocity:

dX/dt (km/s)           =     2.29520749e+04
dY/dt (km/s)           =     5.37601112e+03
dZ/dt (km/s)           =    -2.08811490e+01

Cylindrical coordinates:

Longitude (deg)        =     1.03202903e+02
Z         (km)         =     4.74704840e+07

Cylindrical velocity:

d Longitude/dt (deg/s) =    -4.05392876e-03
d Z/dt         (km/s)  =    -2.08811490e+01

Rectangular coordinates from inverse mapping:

X (km)                 =    -7.60961826e+07
Y (km)                 =     3.24363805e+08
Z (km)                 =     4.74704840e+07

Rectangular velocity from inverse mapping:

dX/dt (km/s)           =     2.29520749e+04
dY/dt (km/s)           =     5.37601112e+03
dZ/dt (km/s)           =    -2.08811490e+01
```

#### Restrictions

```   None.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

```   N.J. Bachman        (JPL)
J. Diaz del Rio     (ODC Space)
W.L. Taber          (JPL)
I.M. Underwood      (JPL)
```

#### Version

```   -CSPICE Version 1.1.0, 01-NOV-2021 (JDR)

Changed the input argument name "lon" to "clon" for consistency
with other routines.

Edited the header to comply with NAIF standard.
```   Jacobian of rectangular w.r.t. cylindrical coordinates
`Fri Dec 31 18:41:04 2021`