Table of contents
CSPICE_TIPBOD returns a 3x3 matrix that transforms positions in inertial
coordinates to positions in body-equator-and-prime-meridian
coordinates.
Given:
ref the NAIF name for an inertial reference frame.
[1,c1] = size(ref); char = class(ref)
or
[1,1] = size(ref); cell = class(ref)
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 the integer ID code of the body for which the position
transformation matrix is requested.
[1,1] = size(body); int32 = class(body)
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 the epoch at which the position transformation matrix is
requested.
[1,1] = size(et); double = class(et)
(This is typically the epoch of observation minus the
one-way light time from the observer to the body at the epoch
of observation.)
the call:
[tipm] = cspice_tipbod( ref, body, et )
returns:
tipm a 3x3 coordinate transformation matrix.
[3,3] = size(tipm); double = class(tipm)
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.
None.
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
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.
function tipbod_ex1()
%
% Load the kernels.
%
cspice_furnsh( 'tipbod_ex1.tm' );
%
% The body ID for Saturn.
%
satid = 699;
%
% Retrieve the transformation matrix at some time.
%
[et] = cspice_str2et( 'Jan 1 2005' );
[tipm] = cspice_tipbod( 'J2000', satid, et );
%
% Retrieve the position of Titan as seen from Saturn
% in the J2000 frame at `et'.
%
[pos, lt] = cspice_spkpos( 'TITAN', et, 'J2000', ...
'NONE', 'SATURN' );
fprintf( 'Titan as seen from Saturn:\n' )
fprintf( ' in J2000 frame : %12.3f %12.3f %12.3f\n', pos )
%
% Rotate the position 3-vector `pos' into the
% Saturn body-fixed reference frame.
%
satvec = tipm * pos;
fprintf( ' in IAU_SATURN frame: %12.3f %12.3f %12.3f\n', satvec )
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave5.x/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
cspice_spkpos call:
[pos, lt] = cspice_spkpos( 'TITAN', et, 'IAU_SATURN', ...
'NONE', 'SATURN' );
cspice_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] [cspice_halfpi-dec] [ra+cspice_halfpi]
3 1 3
These are basically the Euler angles, `phi', `delta' and `w':
ra = phi - cspice_halfpi
dec = cspice_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.
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 by a routine in the call
tree of this routine.
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.
4) If any of the input arguments, `ref', `body' or `et', is
undefined, an error is signaled by the Matlab error handling
system.
5) If any of the input arguments, `ref', `body' or `et', is not
of the expected type, or it does not have the expected
dimensions and size, an error is signaled by the Mice
interface.
None.
1) The kernel pool must be loaded with the appropriate
coefficients (from a text or binary PCK file) prior to
calling this routine.
FRAMES.REQ
MICE.REQ
NAIF_IDS.REQ
PCK.REQ
ROTATION.REQ
TIME.REQ
None.
J. Diaz del Rio (ODC Space)
-Mice Version 1.0.0, 07-SEP-2020 (JDR)
transformation from inertial position to bodyfixed
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