Index Page dlatdr_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 dlatdr_c ( SpiceDouble   x,
                       SpiceDouble   y,
                       SpiceDouble   z,
                       SpiceDouble   jacobi[3][3] )

#### Abstract

       This routine computes the Jacobian of the transformation from
       rectangular to latitudinal 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.
       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 latitudinal coordinates is desired.

#### Detailed_Output

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

                     .-                             -.
                     |  dr/dx     dr/dy     dr/dz    |
                     |  dlon/dx   dlon/dy   dlon/dz  |
                     |  dlat/dx   dlat/dy   dlat/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.

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

       To transform rectangular velocities to derivatives of coordinates
       in a latitudinal 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 corresponding latitudinal coordinate derivatives are given by
       the matrix equation:

                           t          |                     t
          (dr, dlon, dlat)   = 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 latitudinal coordinates, one simply multiplies the
       Jacobian of the transformation from rectangular to latitudinal
       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 ( t );
          recv[1] = dy ( t );
          recv[2] = dz ( t );

          /.
          Determine the Jacobian of the transformation from rectangular to
          latitudinal coordinates at the rectangular coordinates at time t.
          ./
          dlatdr_c ( x(t), y(t), z(t), jacobi );

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

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

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

#### Version

       -CSPICE Version 1.0.0, 13-JUL-2001 (WLT) (NJB)

#### Index_Entries

       Jacobian of rectangular w.r.t. latitudinal coordinates

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

    Wed Apr  5 17:54:31 2017