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Abstract
I/O
Examples
Particulars
Required Reading
Version
Index_Entries

Abstract


   CSPICE_DPGRDR computes the Jacobian matrix of the transformation
   from rectangular to planetographic coordinates.

I/O


   Given:

      body   name of the body with which the planetographic coordinate system
             is associated.

             [1,m] = size(body); char = class(body)

             `body' is used by this routine to look up from the
             kernel pool the prime meridian rate coefficient giving
             the body's spin sense.

      x      [1,n] = size(x); double = class(x)

      y      [1,n] = size(y); double = class(y)

      z      [1,n] = size(z); double = class(z)

             the rectangular coordinates of the point at which the Jacobian of
             the map from rectangular to planetographic coordinates is
             desired.

      re     equatorial radius of a reference spheroid. This spheroid is a
             volume of revolution: its horizontal cross sections are circular.
             The shape of the spheroid is defined by an equatorial radius `re'
             and a polar radius `rp'.

             [1,1] = size(re); double = class(re)

      f      the flattening coefficient

             [1,1] = size(f); double = class(f)

                f = (re-rp) / re

             where rp is the polar radius of the spheroid. (More importantly
             rp = re*(1-f).)

   the call:

      jacobi = cspice_dpgrdr( body, x, y, z, re, f)

   returns:

      jacobi   the matrix of partial derivatives of the conversion from
               rectangular to planetographic coordinates. It has the form

               If [1,1] = size(x) then [3,3]   = size(jacobi).
               If [1,n] = size(x) then [3,3,n] = size(jacobi).
               double = class(jacobi)

                   -                               -
                  |  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'.

Examples


   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
   planetographic coordinates to gain insights about phenomena in
   this coordinate frame.

   To transform rectangular velocities to derivatives of coordinates
   in a planetographic 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 planetographic 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)


   The planetographic definition of latitude is identical to the
   planetodetic (also called "geodetic" in SPICE documentation)
   definition. In the planetographic coordinate system, latitude is
   defined using a reference spheroid.  The spheroid is
   characterized by an equatorial radius and a polar radius. For a
   point P on the spheroid, latitude is defined as the angle between
   the X-Y plane and the outward surface normal at P.  For a point P
   off the spheroid, latitude is defined as the latitude of the
   nearest point to P on the spheroid.  Note if P is an interior
   point, for example, if P is at the center of the spheroid, there
   may not be a unique nearest point to P.

   In the planetographic coordinate system, longitude is defined
   using the spin sense of the body.  Longitude is positive to the
   west if the spin is prograde and positive to the east if the spin
   is retrograde.  The spin sense is given by the sign of the first
   degree term of the time-dependent polynomial for the body's prime
   meridian Euler angle "W":  the spin is retrograde if this term is
   negative and prograde otherwise.  For the sun, planets, most
   natural satellites, and selected asteroids, the polynomial
   expression for W may be found in a SPICE PCK kernel.

   The earth, moon, and sun are exceptions: planetographic longitude
   is measured positive east for these bodies.

   If you wish to override the default sense of positive longitude
   for a particular body, you can do so by defining the kernel
   variable

      BODY<body ID>_PGR_POSITIVE_LON

   where <body ID> represents the NAIF ID code of the body. This
   variable may be assigned either of the values

      'WEST'
      'EAST'

   For example, you can have this routine treat the longitude
   of the earth as increasing to the west using the kernel
   variable assignment

      BODY399_PGR_POSITIVE_LON = 'WEST'

   Normally such assignments are made by placing them in a text
   kernel and loading that kernel via cspice_furnsh.

   The definition of this kernel variable controls the behavior of
   the CSPICE planetographic routines

      cspice_pgrrec
      cspice_recpgr
      cspice_dpgrdr
      cspice_drdpgr

   It does not affect the other CSPICE coordinate conversion
   routines.

Required Reading


   For important details concerning this module's function, please refer to
   the CSPICE routine dpgrdr_c.

   MICE.REQ

Version


   -Mice Version 1.0.0, 11-NOV-2013, EDW (JPL), SCK (JPL)

Index_Entries


   Jacobian of planetographic  w.r.t. rectangular coordinates


Wed Apr  5 18:00:30 2017