dsphdr_c

Index Page dsphdr_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 dsphdr_c ( SpiceDouble   x,
                       SpiceDouble   y,
                       SpiceDouble   z,
                       SpiceDouble   jacobi[3][3] )
#### Abstract
       This routine computes the Jacobian of the transformation from
       rectangular to spherical 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 spherical coordinates is desired.
#### Detailed_Output
       jacobi     is the matrix of partial derivatives of the conversion
                  between rectangular and spherical coordinates.  It
                  has the form

                     .-                                  -.
                     |  dr/dx       dr/dy      dr/dz      |
                     |  dcolat/dx   dcolat/dy  dcolat/dz  |
                     |  dlon/dx     dlon/dy    dlon/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 spherical coordinates to gain insights about phenomena
       in this coordinate frame.

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

                            t          |                    t
          (dr, dcolat, dlon)   = 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 spherical coordinates, one simply multiplies the
       Jacobian of the transformation from rectangular to spherical
       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
          spherical coordinates at the rectangular coordinates at time t.
          ./
          dsphdr_c ( x(t), y(t), z(t), jacobi );

          /.
          Multiply the Jacobian on the right by the rectangular
          velocity to obtain the spherical coordinate derivatives
          sphv.
          ./
          mxv_c ( jacobi, recv, sphv );
#### Restrictions
       None.
#### Literature_References
       None.
#### Author_and_Institution
       W.L. Taber     (JPL)
       N.J. Bachman   (JPL)
#### Version
       -CSPICE Version 1.0.0, 20-JUL-2001 (WLT) (NJB)
#### Index_Entries
       Jacobian of spherical w.r.t. rectangular coordinates
#### Link to routine dsphdr_c source file dsphdr_c.c

    Thu Apr 16 08:57:47 2009