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Table of contents
Procedure
BODEUL ( Return Euler angles for a body )
SUBROUTINE BODEUL ( BODY, ET, RA, DEC, W, LAMBDA )
Abstract
Return the Euler angles needed to compute the transformation from
inertial to body-fixed coordinates for any body in the kernel
pool.
Required_Reading
PCK
NAIF_IDS
TIME
Keywords
CONSTANTS
ROTATION
TRANSFORMATION
Declarations
IMPLICIT NONE
INTEGER BODY
DOUBLE PRECISION ET
DOUBLE PRECISION RA
DOUBLE PRECISION DEC
DOUBLE PRECISION W
DOUBLE PRECISION LAMBDA
Brief_I/O
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
BODY I ID code of body.
ET I Epoch of transformation.
RA O Right ascension of the (IAU) north pole.
DEC O Declination of the (IAU) north pole of the body.
W O Prime meridian rotation angle.
LAMBDA O Angle between the prime meridian and longitude of
longest axis.
Detailed_Input
BODY is the integer ID code of the body for which the
transformation is requested. Bodies are numbered
according to the standard NAIF numbering scheme.
ET is the epoch at which the transformation is
requested.
Detailed_Output
RA,
DEC are the right ascension and declination of the
(IAU) north pole of the body at the epoch of
transformation. RA and DEC are given in radians.
W is the angle between the ascending node of the
body-fixed equatorial plane on the inertial
equatorial plane and the prime meridian of the body.
The node is the cross product of the inertial
frame's Z-axis with the Z-axis of the body-fixed
frame. The angle is measured in the positive
(counterclockwise) sense about the body-fixed
Z-axis, from the node to the prime meridian. W is
given in radians.
LAMBDA is the angle between the prime meridian and the
longest axis of the tri-axial ellipsoid which
models the body. LAMBDA is given in radians.
See the $Particulars section below for further
discussion.
Parameters
None.
Exceptions
1) If any of the PCK keywords required to compute the angles are
not available in the kernel pool, an error is signaled by a
routine in the call tree of this routine.
2) If the number of phase terms is insufficient, the error
SPICE(INSUFFICIENTANGLES) is signaled.
3) 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. This is done
regardless of whether the values assigned to the kernel
variable names match.
4) 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. This is done
regardless of whether the values assigned to the kernel
variable names match.
5) 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.
Files
A text or binary PCK containing orientation data for the
body designated by BODY must be loaded at the time this
routine is called.
Normally PCK files are loaded during program initialization;
they need not be re-loaded prior to each call to this routine.
Particulars
Applications that need to compute the transformation between
body-fixed and inertial frames usually can call the higher-level
routine PXFORM instead of this routine.
If there exists high-precision binary PCK kernel information for
the body at the requested time, the angles, W, DELTA and PHI are
computed directly from that file. These angles are then used to
compute RA, DEC and W. 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 (PCK) is used.
If there is only text PCK kernel information, it is expressed in
terms of RA, DEC and W (same W as above), where
RA = PHI - HALFPI()
DEC = HALFPI() - DELTA
RA, DEC, and W are defined as follows in the text PCK file:
RA = RA0 + RA1*T + RA2*T*T + a sin theta
i i
DEC = DEC0 + DEC1*T + DEC2*T*T + d cos theta
i i
W = W0 + W1*d + W2*d*d + w sin theta
i i
where:
d = days past J2000.
T = Julian centuries past J2000.
a , d , and w arrays apply to satellites only.
i i i
theta = THETA0 * THETA1*T are specific to each planet.
i
These angles -- typically nodal rates -- vary in number and
definition from one planetary system to the next.
The prime meridian offset LAMBDA
================================
The offset LAMBDA is the value specified by the kernel variable
BODYnnn_LONG_AXIS
if such a variable is defined.
The offset LAMBDA is a constant for a given body. LAMBDA serves
to distinguish between the planetocentric prime meridian, which
is provided in the PCK file, and the meridian that passes through
the +X axis of a reference frame aligned with the axes of the
body's reference ellipsoid.
However, SPICE Toolkit makes no use of LAMBDA. In order to
perform geometry computations using a reference ellipsoid not
aligned with a body's planetocentric reference frame, a
fixed-offset (aka "TK") reference frame aligned with the
ellipsoid's axes should be specified in a frames kernel. Note
that a fixed-offset frame may be rotated from the planetocentric
frame about an arbitrary axis, not just the polar axis.
See the Frames Required Reading frames.req for details on
constructing a fixed-offset frame specification.
Examples
In the following code fragment, BODEUL is used to get the unit
vector (POLE) parallel to the north pole of a target body (BODY)
at a specific epoch (ET).
CALL BODEUL ( BODY, ET, RA, DEC, W, LAMBDA )
CALL RADREC ( 1.D0, RA, DEC, POLE )
Note that the items necessary to compute the Euler angles
must have been loaded into the kernel pool (by one or more
previous calls to LDPOOL).
Restrictions
None.
Literature_References
None.
Author_and_Institution
N.J. Bachman (JPL)
J. Diaz del Rio (ODC Space)
B.V. Semenov (JPL)
W.L. Taber (JPL)
I.M. Underwood (JPL)
K.S. Zukor (JPL)
Version
SPICELIB Version 5.0.0, 14-APR-2021 (NJB) (JDR)
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.
Error handling was upgraded to check FAILED() between kernel
data lookups and computations.
Now SAVEs all local variables.
Edited the header to comply with NAIF standard. Moved NAIF_IDS
required reading from $Literature_References to
$Required_Reading section.
SPICELIB Version 4.2.0, 02-MAR-2016 (BVS)
BUG FIX: changed available room in the BODVCD call
fetching 'NUT_PREC_ANGLES' from MAXANG to MAXANG*2.
Fixed indention in some header sections.
Removed BODEUL: prefix from the text of the long
error for insufficient angles.
Last update was 24-APR-2014 (NJB)
Corrected the brief and detailed descriptions of W.
SPICELIB Version 4.1.0, 24-OCT-2005 (NJB)
Calls to ZZBODVCD have been replaced with calls to
BODVCD.
SPICELIB Version 4.0.0, 13-FEB-2004 (NJB)
Code has been updated to support satellite ID codes in the
range 10000 to 99999 and to allow nutation precession angles
to be associated with any object.
Implementation changes were made to improve robustness
of the code.
SPICELIB Version 3.1.0, 21-MAR-1995 (KSZ)
REF frame is now passed correctly as a character string.
SPICELIB Version 3.0.0, 10-MAR-1994 (KSZ)
Ability to get Euler angles from binary PCK file added.
This uses the new routine PCKEUL.
SPICELIB Version 2.0.1, 10-MAR-1992 (WLT)
Comment section for permuted index source lines was added
following the header.
SPICELIB Version 2.0.0, 04-SEP-1991 (NJB)
Updated to handle P_constants referenced to different epochs
and inertial reference frames.
SPICELIB Version 1.1.0, 02-NOV-1990 (NJB)
Allowed number of nutation precession angles increased to
100.
SPICELIB Version 1.0.0, 31-JAN-1990 (WLT) (IMU)
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Fri Dec 31 18:35:59 2021