Index Page dgeodr_c

A B C D E F G H I J K L M N O P Q R S T U V W X

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 dgeodr_c ( SpiceDouble   x,
                       SpiceDouble   y,
                       SpiceDouble   z,
                       SpiceDouble   re,
                       SpiceDouble   f,
                       SpiceDouble   jacobi[3][3] )

#### Abstract

       This routine computes the Jacobian of the transformation from
       rectangular to geodetic coordinates.

#### Required_Reading

       None.

#### Keywords

       COORDINATES
       DERIVATIVES
       MATRIX

#### 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         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
                  between rectangular and geodetic 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.

#### Parameters

       None.

#### Exceptions

        1) If the input point is on the z-axis (x and y = 0), the
           Jacobian is undefined.  The error SPICE(POINTONZAXIS)
           will be 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

       Suppose one is given the bodyfixed rectangular state of an object
       (x(t), y(t), z(t), dx(t), dy(t), dz(t)) as a function of time t.

       To find the derivatives of the coordinates of the object in
       bodyfixed geodetic coordinates, one simply multiplies the
       Jacobian of the transformation from rectangular to geodetic
       coordinates (evaluated at x(t), y(t), z(t)) by the rectangular
       velocity vector of the object at time t.

       In code this looks like:

          #include "SpiceUsr.h"
              .
              .
              .

          /.
          Load the rectangular velocity vector vector recv.
          ./
          recv[0] = dx_dt ( t );
          recv[1] = dy_dt ( t );
          recv[2] = dz_dt ( t );

          /.
          Determine the Jacobian of the transformation from
          rectangular to geodetic coordinates at the rectangular
          coordinates at time t.
          ./
          dgeodr_c ( x(t), y(t), z(t), re, f, jacobi );

          /.
          Multiply the Jacobian on the right by the rectangular
          velocity to obtain the geodetic coordinate derivatives
          geov.
          ./
          mxv_c ( jacobi, recv, geov );

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

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

#### Version

       -CSPICE Version 1.0.0, 18-JUL-2001 (WLT) (NJB)

#### Index_Entries

       Jacobian of geodetic  w.r.t. rectangular coordinates

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

    Wed Apr  5 17:54:31 2017