| tisbod_c |
|
Table of contents
Procedure
tisbod_c ( Transformation, inertial state to bodyfixed )
void tisbod_c ( ConstSpiceChar * ref,
SpiceInt body,
SpiceDouble et,
SpiceDouble tsipm[6][6] )
AbstractReturn a 6x6 matrix that transforms states in inertial coordinates to states in body-equator-and-prime-meridian coordinates. Required_ReadingFRAMES PCK NAIF_IDS ROTATION TIME KeywordsROTATION TRANSFORMATION Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- ref I ID of inertial reference frame to transform from body I ID code of body et I Epoch of transformation tsipm O Transformation (state), 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 `tsipm' 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
state 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 state 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
tsipm is a 6x6 transformation matrix. It is used to
transform states from inertial coordinates to body
fixed (also called equator and prime meridian ---
PM) coordinates.
Given a state `s' in the inertial reference frame
specified by `ref', the corresponding bodyfixed state
is given by the matrix vector product:
tsipm * 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.
NOTE: The inverse of `tsipm' is NOT its transpose.
The matrix, `tsipm', has a structure as shown below:
.- -.
| : |
| r : 0 |
| ......:......|
| : |
| dr/dt : r |
| : |
`- -'
where `r' is a time varying rotation matrix and dr/dt is
its derivative. The inverse of this matrix is:
.- -.
| T : |
| r : 0 |
| .......:.......|
| : |
| T : T |
| dr/dt : r |
| : |
`- -'
The CSPICE routine invstm_c is available for producing
this inverse.
ParametersNone. Exceptions
1) If data required to define the body-fixed frame associated
with `body' are not found in the binary PCK system or the kernel
pool, the error SPICE(FRAMEDATANOTFOUND) is signaled by a
routine in the call tree of this routine. In the case of IAU
style body-fixed frames, the absence of prime meridian
polynomial data (which are required) is used as an indicator
of missing data.
2) If the test for exception (1) passes, but in fact requested
data are not available in the kernel pool, an error is
signaled by a routine in the call tree of this routine.
3) If the kernel pool does not contain all of the data required
to define the number of nutation precession angles
corresponding to the available nutation precession
coefficients, the error SPICE(INSUFFICIENTANGLES) is
signaled by a routine in the call tree of this routine.
4) If the reference frame `ref' is not recognized, an error is
signaled by a routine in the call tree of this routine.
5) If the specified body code `body' is not recognized, an error is
signaled by a routine in the call tree of this routine.
6) If, for a given body, both forms of the kernel variable names
BODY<body ID>_CONSTANTS_JED_EPOCH
BODY<body ID>_CONSTS_JED_EPOCH
are found in the kernel pool, the error
SPICE(COMPETINGEPOCHSPEC) is signaled by a routine in the call
tree of this routine. This is done regardless of whether the
values assigned to the kernel variable names match.
7) If, for a given body, both forms of the kernel variable names
BODY<body ID>_CONSTANTS_REF_FRAME
BODY<body ID>_CONSTS_REF_FRAME
are found in the kernel pool, the error
SPICE(COMPETINGFRAMESPEC) is signaled by a routine in the call
tree of this routine. This is done regardless of whether the
values assigned to the kernel variable names match.
8) If the central body associated with the input `body', whether a
system barycenter or `body' itself, has associated phase angles
(aka nutation precession angles), and the kernel variable
BODY<body ID>_MAX_PHASE_DEGREE for the central body is present
but has a value outside the range 1:3, the error
SPICE(DEGREEOUTOFRANGE) is signaled by a routine in the call
tree of this routine.
9) If the `ref' input string pointer is null, the error
SPICE(NULLPOINTER) is signaled.
10) If the `ref' input string has zero length, the error
SPICE(EMPTYSTRING) is signaled.
FilesNone. ParticularsNote: NAIF recommends the use of spkezr_c with the appropriate frames kernels when possible over tisbod_c. The matrix for transforming inertial states to bodyfixed states is the 6x6 matrix shown below as a block structured matrix. .- -. | : | | tipm : 0 | | ......:......| | : | | dtipm : tipm | | : | `- -' This can also be expressed in terms of Euler angles `phi', `delta' and `w'. The transformation from inertial to bodyfixed coordinates is represented in the SPICE kernel pool as: tipm = [w] [delta] [phi] 3 1 3 Thus dtipm = d[w] /dt [delta] [phi] 3 1 3 + [w] d[delta] /dt [phi] 3 1 3 + [w] [delta] d[phi] /dt 3 1 3 If a binary PCK file record can be used for the time and body requested, it will be used. The most recently loaded binary PCK file has first priority, followed by previously loaded binary PCK files in backward time order. If no binary PCK file has been loaded, the text P_constants kernel file is used. If there is only text PCK kernel information, it is expressed in terms of `ra', `dec' and `w', where ra = phi - halfpi_c dec = halfpi_c - 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. Thus .----- ra1 2*ra2*t \ a[i]*theta1[i]*cos(theta[i]) dra/dt = ----- + --------- + ) ------------------------------ T 2 / T T '----- i .----- dec1 2*dec2*t \ d[i]*theta1[i]*sin(theta[i]) ddec/dt = ------ + ---------- - ) ------------------------------ T 2 / T T '----- i .----- w1 2*w2*t \ w[i]*theta1[i]*cos(theta[i]) dw/dt = ---- + -------- + ) ------------------------------ d 2 / T d '----- i Examples
The numerical results shown for these examples 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 state vector from the
J2000 frame to the Saturn fixed frame at a specified
time, and use it to compute the geometric position and
velocity of Titan in Saturn's body-fixed frame.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: tisbod_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 tisbod_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"
int main( )
{
/.
Local variables
./
SpiceDouble et;
SpiceDouble lt;
SpiceDouble state [6];
SpiceDouble satvec [6];
SpiceDouble tsipm [6][6];
SpiceInt satid;
/.
Load the kernels.
./
furnsh_c ( "tisbod_ex1.tm" );
/.
The body ID for Saturn.
./
satid = 699;
/.
Retrieve the transformation matrix at some time.
./
str2et_c ( "Jan 1 2005", &et );
tisbod_c ( "J2000", satid, et, tsipm );
/.
Retrieve the state of Titan as seen from Saturn
in the J2000 frame at `et'.
./
spkezr_c ( "TITAN", et, "J2000", "NONE", "SATURN", state, < );
printf( "Titan as seen from Saturn (J2000 frame):\n" );
printf( " position (km): %12.3f %12.3f %12.3f\n",
state[0], state[1], state[2] );
printf( " velocity (km/s): %12.3f %12.3f %12.3f\n",
state[3], state[4], state[5] );
/.
Rotate the 6-vector `state' into the
Saturn body-fixed reference frame.
./
mxvg_c ( tsipm, state, 6, 6, satvec );
printf( "Titan as seen from Saturn (IAU_SATURN frame):\n" );
printf( " position (km): %12.3f %12.3f %12.3f\n",
satvec[0], satvec[1], satvec[2] );
printf( " velocity (km/s): %12.3f %12.3f %12.3f\n",
satvec[3], satvec[4], satvec[5] );
return ( 0 );
}
When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:
Titan as seen from Saturn (J2000 frame):
position (km): 1071928.661 -505781.970 -60383.976
velocity (km/s): 2.404 5.176 -0.560
Titan as seen from Saturn (IAU_SATURN frame):
position (km): 401063.338 -1116965.364 -5408.806
velocity (km/s): -177.547 -63.745 0.028
Note that the complete example could be replaced by a single
spkezr_c call:
spkezr_c ( "TITAN", et, "IAU_SATURN", "NONE",
"SATURN", state, < );
2) Use tisbod_c is used to compute the angular velocity vector (with
respect to the J2000 inertial frame) of the specified body at
given time.
Use the meta-kernel from Example 1 above.
Example code begins here.
/.
Program tisbod_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"
int main( )
{
/.
Local variables
./
SpiceDouble av [3];
SpiceDouble et;
SpiceDouble dtipm [3][3];
SpiceDouble omega [3][3];
SpiceDouble rot [3][3];
SpiceDouble tipm [3][3];
SpiceDouble tsipm [6][6];
SpiceDouble v [3];
SpiceInt i;
SpiceInt j;
SpiceInt satid;
/.
Load the kernels.
./
furnsh_c ( "tisbod_ex1.tm" );
/.
The body ID for Saturn.
./
satid = 699;
/.
First get the state transformation matrix.
./
str2et_c ( "Jan 1 2005", &et );
tisbod_c ( "J2000", satid, et, tsipm );
/.
This matrix has the form:
.- -.
| : |
| tipm : 0 |
| ......:......|
| : |
| dtipm : tipm |
| : |
`- -'
We extract `tipm' and `dtipm'
./
for ( i = 0; i < 3; i++ )
{
for ( j = 0; j < 3; j++ )
{
tipm[i] [j] = tsipm[i] [j];
dtipm[i][j] = tsipm[i+3][j];
}
}
/.
The transpose of `tipm' and `dtipm', (`tpmi' and `dtpmi'), gives
the transformation from bodyfixed coordinates to inertial
coordinates.
Here is a fact about the relationship between angular
velocity associated with a time varying rotation matrix
that gives the orientation of a body with respect to
an inertial frame.
The angular velocity vector can be read from the off
diagonal components of the matrix product:
t
omega = dtpmi * tpmi
t
= dtipm * tipm
the components of the angular velocity `v' will appear
in this matrix as:
.- -.
| |
| 0 -v[2] v[1] |
| |
| v[2] 0 -v[0] |
| |
| -v[1] v[0] 0 |
| |
`- -'
./
mtxm_c ( dtipm, tipm, omega );
v[0] = omega[2][1];
v[1] = omega[0][2];
v[2] = omega[1][0];
/.
Display the results.
./
printf( "Angular velocity (km/s):\n" );
printf( "%16.9f %15.9f %15.9f\n", v[0], v[1], v[2] );
/.
It is possible to compute the angular velocity using
a single call to xf2rav_c.
./
xf2rav_c ( tsipm, rot, av );
printf( "Angular velocity using xf2rav_c (km/s):\n" );
printf( "%16.9f %15.9f %15.9f\n", av[0], av[1], av[2] );
return ( 0 );
}
When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:
Angular velocity (km/s):
0.000014001 0.000011995 0.000162744
Angular velocity using xf2rav_c (km/s):
0.000014001 0.000011995 0.000162744
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_ReferencesNone. Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) W.L. Taber (JPL) E.D. Wright (JPL) K.S. Zukor (JPL) Version
-CSPICE Version 1.1.0, 10-AUG-2021 (JDR) (NJB)
The routine was updated to support user-defined maximum phase
angle degrees. The additional text kernel kernel variable name
BODYnnn_MAX_PHASE_DEGREE must be used when the phase angle
polynomials have degree higher than 1. The maximum allowed
degree is 3.
The kernel variable names
BODY#_CONSTS_REF_FRAME
BODY#_CONSTS_JED_EPOCH
are now recognized.
Edited the header to comply with NAIF standard. Added complete
code example.
Added note to -Particulars section.
-CSPICE Version 1.0.3, 16-JAN-2008 (EDW)
Corrected typos in header titles:
Detailed Input to -Detailed_Input
Detailed Output to -Detailed_Output
-CSPICE Version 1.0.2, 10-NOV-2006 (EDW)
Replace mention of ldpool_c and pcklof_c with furnsh_c.
Added -Keywords and -Parameters section headers.
Reordered section headers.
-CSPICE Version 1.0.1, 02-JUL-2003 (EDW)
Corrected trivial typo in the Version 1.0.0 line.
The typo caused an integrity check script to fail.
-CSPICE Version 1.0.0, 20-JUN-1999 (NJB) (WLT) (KSZ)
Initial release, based on SPICELIB Version 3.3.0, 29-MAR-1995
Index_Entriestransformation from inertial state to bodyfixed |
Fri Dec 31 18:41:14 2021