drdsph_c

Index Page drdsph_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 drdsph_c ( SpiceDouble    r,
                       SpiceDouble    colat,
                       SpiceDouble    lon,
                       SpiceDouble    jacobi[3][3] )
#### Abstract
       This routine computes the Jacobian of the transformation from
       spherical 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.
       colat      I   Angle of the point from the positive z-axis.
       lon        I   Angle of the point from the xy plane.
       jacobi     O   Matrix of partial derivatives.
#### Detailed_Input
       r          Distance of a point from the origin.

       colat      Angle between the point and the positive z-axis, in
                  radians.

       lon        Angle of the point from the xz plane in radians.
                  The angle increases in the counterclockwise sense
                  about the +z axis.
#### Detailed_Output
       jacobi     is the matrix of partial derivatives of the conversion
                  between spherical and rectangular coordinates,
                  evaluated at the input coordinates.  This matrix has
                  the form

                      .-                                 -.
                      |  dx/dr     dx/dcolat     dx/dlon  |
                      |                                   |
                      |  dy/dr     dy/dcolat     dy/dlon  |
                      |                                   |
                      |  dz/dr     dz/dcolat     dz/dlon  |
                      `-                                 -'

                 evaluated at the input values of r, lon and lat.
                 Here x, y, and z are given by the familiar formulae

                     x = r*cos(lon)*sin(colat)
                     y = r*sin(lon)*sin(colat)
                     z = r*cos(colat)
#### Parameters
       None.
#### Exceptions
       Error free.
#### Files
       None.
#### Particulars
       It is often convenient to describe the motion of an object in
       the spherical coordinate system.  However, when performing
       vector computations its hard to beat rectangular coordinates.

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

       Given a state in spherical coordinates

          ( r, colat, lon, dr, dcolat, dlon )

       the velocity in rectangular coordinates is given by the matrix
       equation:
                      t          |                                   t
          (dx, dy, dz)   = jacobi|              * (dr, dcolat, dlon )
                                 |(r,colat,lon)

       This routine computes the matrix

                |
          jacobi|
                |(r,colat,lon)
#### Examples
       Suppose that one has a model that gives the radius, colatitude
       and longitude as a function of time (r(t), colat(t), lon(t)),
       for which the derivatives ( dr/dt, dcolat/dt, dlon/dt ) are
       computable.

       To find the velocity of the object in bodyfixed rectangular
       coordinates, one simply multiplies the Jacobian of the
       transformation from spherical to rectangular coordinates
       (evaluated at r(t), colat(t), lon(t) ) by the vector of
       derivatives of the spherical coordinates.

       In code this looks like:

          #include "SpiceUsr.h"
                .
                .
                .
          /.
          Load the derivatives of r, colat, and lon into the
          spherical velocity vector sphv.
          ./
          sphv[0] = dr_dt     ( t );
          sphv[1] = dcolat_dt ( t );
          sphv[2] = dlon_dt   ( t );

          /.
          Determine the Jacobian of the transformation from
          cylindrical to rectangular at the coordinates at the
          given cylindrical coordinates at time t.
          ./
          drdsph_c ( r(t), colat(t), lon(t), jacobi );

          /.
          Multiply the Jacobian on the left by the spherical
          velocity to obtain the rectangular velocity recv.
          ./
          mxv_c ( jacobi, sphv, recv );
#### Restrictions
       None.
#### Literature_References
       None.
#### Author_and_Institution
       W.L. Taber     (JPL)
       I.M. Underwood (JPL)
       N.J. Bachman   (JPL)
#### Version
       -CSPICE Version 1.0.0, 19-JUL-2001 (WLT) (IMU) (NJB)
#### Index_Entries
       Jacobian of rectangular w.r.t. spherical coordinates
#### Link to routine drdsph_c source file drdsph_c.c

    Thu Apr 16 08:57:47 2009