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Table of contents
Procedure
TIPBOD ( Transformation, inertial position to bodyfixed )
SUBROUTINE TIPBOD ( REF, BODY, ET, TIPM )
Abstract
Return a 3x3 matrix that transforms positions in inertial
coordinates to positions in body-equator-and-prime-meridian
coordinates.
Required_Reading
FRAMES
PCK
NAIF_IDS
ROTATION
TIME
Keywords
ROTATION
TRANSFORMATION
Declarations
IMPLICIT NONE
CHARACTER*(*) REF
INTEGER BODY
DOUBLE PRECISION ET
DOUBLE PRECISION TIPM ( 3, 3 )
Brief_I/O
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
REF I ID of inertial reference frame to transform from.
BODY I ID code of body.
ET I Epoch of transformation.
TIPM O Position transformation matrix, inertial to prime
meridian.
Detailed_Input
REF is the NAIF name for an inertial reference frame.
Acceptable names include:
Name Description
-------- --------------------------------
'J2000' Earth mean equator, dynamical
equinox of J2000
'B1950' Earth mean equator, dynamical
equinox of B1950
'FK4' Fundamental Catalog (4)
'DE-118' JPL Developmental Ephemeris (118)
'DE-96' JPL Developmental Ephemeris ( 96)
'DE-102' JPL Developmental Ephemeris (102)
'DE-108' JPL Developmental Ephemeris (108)
'DE-111' JPL Developmental Ephemeris (111)
'DE-114' JPL Developmental Ephemeris (114)
'DE-122' JPL Developmental Ephemeris (122)
'DE-125' JPL Developmental Ephemeris (125)
'DE-130' JPL Developmental Ephemeris (130)
'GALACTIC' Galactic System II
'DE-200' JPL Developmental Ephemeris (200)
'DE-202' JPL Developmental Ephemeris (202)
See the Frames Required Reading frames.req for a full
list of inertial reference frame names built into
SPICE.
The output TIPM will give the transformation
from this frame to the bodyfixed frame specified by
BODY at the epoch specified by ET.
BODY is the integer ID code of the body for which the
position transformation matrix is requested. Bodies
are numbered according to the standard NAIF numbering
scheme. The numbering scheme is explained in the NAIF
IDs Required Reading naif_ids.req.
ET is the epoch at which the position transformation
matrix is requested. (This is typically the
epoch of observation minus the one-way light time
from the observer to the body at the epoch of
observation.)
Detailed_Output
TIPM is a 3x3 coordinate transformation matrix. It is
used to transform positions from inertial
coordinates to body fixed (also called equator and
prime meridian --- PM) coordinates.
Given a position P in the inertial reference frame
specified by REF, the corresponding bodyfixed
position is given by the matrix vector product:
TIPM * S
The X axis of the PM system is directed to the
intersection of the equator and prime meridian.
The Z axis points along the spin axis and points
towards the same side of the invariable plane of
the solar system as does earth's north pole.
Parameters
None.
Exceptions
1) If the kernel pool does not contain all of the data required
for computing the transformation matrix, TIPM, the error
SPICE(INSUFFICIENTANGLES) is signaled.
2) If the reference frame, REF, is not recognized, an error is
signaled by a routine in the call tree of this routine.
3) If the specified body code, BODY, is not recognized, an error
is signaled by a routine in the call tree of this routine.
Files
None.
Particulars
TIPBOD takes PCK information as input, either in the
form of a binary or text PCK file. High precision
binary files are searched for first (the last loaded
file takes precedence); then it defaults to the text
PCK file. If binary information is found for the
requested body and time, the Euler angles are
evaluated and the transformation matrix is calculated
from them. Using the Euler angles PHI, DELTA and W
we compute
TIPM = [W] [DELTA] [PHI]
3 1 3
If no appropriate binary PCK files have been loaded,
the text PCK file is used. Here information is found
as RA, DEC and W (with the possible addition of nutation
and libration terms for satellites). Again, the Euler
angles are found, and the transformation matrix is
calculated from them. The transformation from inertial to
body-fixed coordinates is represented as:
TIPM = [W] [HALFPI-DEC] [RA+HALFPI]
3 1 3
These are basically the Euler angles, PHI, DELTA and W:
RA = PHI - HALFPI
DEC = HALFPI - DELTA
W = W
The angles RA, DEC, and W are defined as follows in the
text PCK file:
2 .-----
RA1*t RA2*t \
RA = RA0 + ------- + ------- + ) a(i) * sin( theta(i) )
T 2 /
T '-----
i
2 .-----
DEC1*t DEC2*t \
DEC = DEC0 + -------- + -------- + ) d(i) * cos( theta(i) )
T 2 /
T '-----
i
2 .-----
W1*t W2*t \
W = W0 + ------ + ------- + ) w(i) * sin( theta(i) )
d 2 /
d '-----
i
where `d' is in seconds/day; T in seconds/Julian century;
a(i), d(i), and w(i) arrays apply to satellites only; and
theta(i), defined as
THETA1(i)*t
theta(i) = THETA0(i) + -------------
T
are specific to each planet.
These angles ---typically nodal rates--- vary in number and
definition from one planetary system to the next.
Examples
The numerical results shown for this example may differ across
platforms. The results depend on the SPICE kernels used as
input, the compiler and supporting libraries, and the machine
specific arithmetic implementation.
1) Calculate the matrix to rotate a position vector from the
J2000 frame to the Saturn fixed frame at a specified
time, and use it to compute the position of Titan in
Saturn's body-fixed frame.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: tipbod_ex1.tm
This meta-kernel is intended to support operation of SPICE
example programs. The kernels shown here should not be
assumed to contain adequate or correct versions of data
required by SPICE-based user applications.
In order for an application to use this meta-kernel, the
kernels referenced here must be present in the user's
current working directory.
The names and contents of the kernels referenced
by this meta-kernel are as follows:
File name Contents
--------- --------
sat375.bsp Saturn satellite ephemeris
pck00010.tpc Planet orientation and
radii
naif0012.tls Leapseconds
\begindata
KERNELS_TO_LOAD = ( 'sat375.bsp',
'pck00010.tpc',
'naif0012.tls' )
\begintext
End of meta-kernel
Example code begins here.
PROGRAM TIPBOD_EX1
IMPLICIT NONE
C
C Local variables
C
DOUBLE PRECISION ET
DOUBLE PRECISION LT
DOUBLE PRECISION POS ( 3 )
DOUBLE PRECISION SATVEC ( 3 )
DOUBLE PRECISION TIPM ( 3, 3 )
INTEGER SATID
C
C Load the kernels.
C
CALL FURNSH ( 'tipbod_ex1.tm' )
C
C The body ID for Saturn.
C
SATID = 699
C
C Retrieve the transformation matrix at some time.
C
CALL STR2ET ( 'Jan 1 2005', ET )
CALL TIPBOD ( 'J2000', SATID, ET, TIPM )
C
C Retrieve the position of Titan as seen from Saturn
C in the J2000 frame at ET.
C
CALL SPKPOS ( 'TITAN', ET, 'J2000', 'NONE',
. 'SATURN', POS, LT )
WRITE(*,'(A)') 'Titan as seen from Saturn:'
WRITE(*,'(A,3F13.3)') ' in J2000 frame :', POS
C
C Rotate the position 3-vector POS into the
C Saturn body-fixed reference frame.
C
CALL MXV ( TIPM, POS, SATVEC )
WRITE(*,'(A,3F13.3)') ' in IAU_SATURN frame:', SATVEC
END
When this program was executed on a Mac/Intel/gfortran/64-bit
platform, the output was:
Titan as seen from Saturn:
in J2000 frame : 1071928.661 -505781.970 -60383.976
in IAU_SATURN frame: 401063.338 -1116965.364 -5408.806
Note that the complete example could be replaced by a single
SPKPOS call:
CALL SPKPOS ( 'TITAN', ET, 'IAU_SATURN', 'NONE',
. 'SATURN', POS, LT )
Restrictions
1) The kernel pool must be loaded with the appropriate
coefficients (from a text or binary PCK file) prior to
calling this routine.
Literature_References
None.
Author_and_Institution
N.J. Bachman (JPL)
J. Diaz del Rio (ODC Space)
H.A. Neilan (JPL)
B.V. Semenov (JPL)
W.L. Taber (JPL)
K.S. Zukor (JPL)
Version
SPICELIB Version 1.4.0, 06-JUL-2021 (JDR)
Added IMPLICIT NONE statement.
Edited the header to comply with NAIF standard. Removed
unnecessary entries in $Revisions section.
Added complete code example.
Added frames.req to $Required_Reading.
SPICELIB Version 1.3.0, 02-MAR-2016 (BVS)
Updated to use the 3x3 top-left corner of the 6x6 matrix
returned by TISBOD instead of fetching kernel data and doing
computations in-line.
Fixed indentation of some header sections.
SPICELIB Version 1.2.0, 23-OCT-2005 (NJB)
Updated to remove non-standard use of duplicate arguments
in MXM call. Replaced header references to LDPOOL with
references to FURNSH.
SPICELIB Version 1.1.0, 05-JAN-2005 (NJB)
Tests of routine FAILED() were added.
SPICELIB Version 1.0.3, 10-MAR-1994 (KSZ)
Underlying BODMAT code changed to look for binary PCK
data files, and use them to get orientation information if
they are available. Only the comments to TIPBOD changed.
SPICELIB Version 1.0.2, 06-JUL-1993 (HAN)
Example in header was corrected. Previous version had
incorrect matrix dimension specifications passed to MXVG.
SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)
Comment section for permuted index source lines was added
following the header.
SPICELIB Version 1.0.0, 05-AUG-1991 (NJB) (WLT)
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Fri Dec 31 18:37:02 2021