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Index Page drdcyl_c

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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.

#### Required_Reading

       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
                                              radii
                naif0009.tls                  Leapseconds

             \begindata

                KERNELS_TO_LOAD = ( 'de421.bsp',
                                    '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:

           Radius    (km)         =     3.33170387e+08
           Longitude (deg)        =     1.03202903e+02
           Z         (km)         =     4.74704840e+07

          Cylindrical velocity:

           d Radius/dt    (km/s)  =    -8.34966283e+00
           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.
           Added complete code example.

       -CSPICE Version 1.0.0, 19-JUL-2001 (WLT) (IMU) (NJB)

#### Index_Entries

       Jacobian of rectangular w.r.t. cylindrical coordinates

#### Link to routine drdcyl_c source file drdcyl_c.c

    Fri Dec 31 18:41:04 2021