Index Page drdcyl_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 drdcyl_c ( SpiceDouble    r,
                       SpiceDouble    lon,
                       SpiceDouble    z,
                       SpiceDouble    jacobi[3][3] )

#### Abstract

       This routine computes the Jacobian of the transformation from
       cylindrical 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.
       lon        I   Angle of the point from the xz plane in radians.
       z          I   Height of the point above the xy plane.
       jacobi     O   Matrix of partial derivatives.

#### Detailed_Input

       r          Distance of the point of interest from z axis.

       lon        Cylindrical angle (in radians) of the point of
                  interest from xz plane.  The angle increases in the
                  counterclockwise sense about the +z axis.

       z          Height of the point above xy plane.

#### Detailed_Output

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

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

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

                     x = r*cos(lon)
                     y = r*sin(lon)
                     z = z

#### Parameters

       None.

#### Exceptions

       Error free.

#### Files

       None.

#### Particulars

       It is often convenient to describe the motion of an object in
       the cylindrical coordinate system.  However, when performing
       vector computations its hard to beat rectangular coordinates.

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

       Given a state in cylindrical coordinates

          ( r, lon, z, dr, dlon, dz )

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

       This routine computes the matrix

                |
          jacobi|
                |(r,lon,z)

#### Examples

       Suppose that one has a model that gives radius, longitude and
       height as a function of time (r(t), lon(t), z(t)) for
       which the derivatives ( dr/dt, dlon/dt, dz/dt ) are computable.

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

       In code this looks like:

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

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

          /.
          Multiply the Jacobian on the left by the cylindrical
          velocity to obtain the rectangular velocity recv.
          ./
          mxv_c ( jacobi, cylv, 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. cylindrical coordinates

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

    Wed Apr  5 17:54:32 2017