void ckw02_c ( SpiceInt handle,
SpiceDouble begtim,
SpiceDouble endtim,
SpiceInt inst,
ConstSpiceChar * ref,
ConstSpiceChar * segid,
SpiceInt nrec,
ConstSpiceDouble start [],
ConstSpiceDouble stop [],
ConstSpiceDouble quats [][4],
ConstSpiceDouble avvs [][3],
ConstSpiceDouble rates [] )
Write a type 2 segment to a C-kernel.
CK
DAF
SCLK
POINTING
UTILITY
Variable I/O Description
-------- --- --------------------------------------------------
handle I Handle of an open CK file.
begtim I The beginning encoded SCLK of the segment.
endtim I The ending encoded SCLK of the segment.
inst I The NAIF instrument ID code.
ref I The reference frame of the segment.
segid I Segment identifier.
nrec I Number of pointing records.
start I Encoded SCLK interval start times.
stop I Encoded SCLK interval stop times.
quats I Quaternions representing instrument pointing.
avvs I Angular velocity vectors.
rates I Number of seconds per tick for each interval.
handle is the handle of the CK file to which the segment will
be written. The file must have been opened with write
access.
begtim is the beginning encoded SCLK time of the segment. This
value should be less than or equal to the first START
time in the segment.
endtim is the encoded SCLK time at which the segment ends.
This value should be greater than or equal to the last
STOP time in the segment.
inst is the NAIF integer ID code for the instrument.
ref is a character string that specifies the
reference frame of the segment. This should be one of
the frames supported by the SPICELIB routine NAMFRM
which is an entry point of FRAMEX.
segid is the segment identifier. A CK segment identifier may
contain up to 40 characters.
nrec is the number of pointing intervals that will be
written to the segment.
start are the start times of each interval in encoded
spacecraft clock. These times must be strictly
increasing.
stop are the stop times of each interval in encoded
spacecraft clock. These times must be greater than
the START times that they correspond to but less
than or equal to the START time of the next interval.
quats are the quaternions representing the C-matrices
associated with the start times of each interval. See the
discussion of "Quaternion Styles" in the Particulars
section below.
AVVS are the angular velocity vectors for each interval.
RATES are the number of seconds per encoded spacecraft clock
tick for each interval.
In most applications this value will be the same for
each interval within a segment. For example, when
constructing a predict C-kernel for Mars Observer, the
rate would be 1/256 for each interval since this is
the smallest time unit expressible by the MO clock. The
nominal seconds per tick rates for Galileo and Voyager
are 1/120 and 0.06 respectively.
None. See Files section.
None.
1) If handle is not the handle of a C-kernel opened for writing
the error will be diagnosed by routines called by this
routine.
2) If segid is more than 40 characters long, the error
SPICE(SEGIDTOOLONG) is signaled.
3) If segid contains any nonprintable characters, the error
SPICE(NONPRINTABLECHARS) is signaled.
4) If the first START time is negative, the error
SPICE(INVALIDSCLKTIME) is signaled. If any of the subsequent
START times are negative the error SPICE(TIMESOUTOFORDER)
will be signaled.
5) If any of the STOP times are negative, the error
SPICE(DEGENERATEINTERVAL) is signaled.
6) If the STOP time of any of the intervals is less than or equal
to the START time, the error SPICE(DEGENERATEINTERVAL) is
signaled.
7) If the START times are not strictly increasing, the
error SPICE(TIMESOUTOFORDER) is signaled.
8) If the STOP time of one interval is greater than the START
time of the next interval, the error SPICE(BADSTOPTIME)
is signaled.
9) If begtim is greater than START[0] or endtim is less than
STOP[NREC-1], the error SPICE(INVALIDDESCRTIME) is
signaled.
10) If the name of the reference frame is not one of those
supported by the routine NAMFRM, the error
SPICE(INVALIDREFFRAME) is signaled.
11) If nrec, the number of pointing records, is less than or
equal to 0, the error SPICE(INVALIDNUMRECS) is signaled.
12) If any quaternion has magnitude zero, the error
SPICE(ZEROQUATERNION) is signaled.
This routine adds a type 2 segment to a C-kernel. The C-kernel
may be either a new one or an existing one opened for writing.
For a detailed description of a type 2 CK segment please see the
CK Required Reading.
This routine relieves the user from performing the repetitive
calls to the DAF routines necessary to construct a CK segment.
Quaternion Styles
-----------------
There are different "styles" of quaternions used in
science and engineering applications. Quaternion styles
are characterized by
- The order of quaternion elements
- The quaternion multiplication formula
- The convention for associating quaternions
with rotation matrices
Two of the commonly used styles are
- "SPICE"
> Invented by Sir William Rowan Hamilton
> Frequently used in mathematics and physics textbooks
- "Engineering"
> Widely used in aerospace engineering applications
CSPICE function interfaces ALWAYS use SPICE quaternions.
Quaternions of any other style must be converted to SPICE
quaternions before they are passed to CSPICE functions.
Relationship between SPICE and Engineering Quaternions
------------------------------------------------------
Let M be a rotation matrix such that for any vector V,
M*V
is the result of rotating V by theta radians in the
counterclockwise direction about unit rotation axis vector A.
Then the SPICE quaternions representing M are
(+/-) ( cos(theta/2),
sin(theta/2) A(1),
sin(theta/2) A(2),
sin(theta/2) A(3) )
while the engineering quaternions representing M are
(+/-) ( -sin(theta/2) A(1),
-sin(theta/2) A(2),
-sin(theta/2) A(3),
cos(theta/2) )
For both styles of quaternions, if a quaternion q represents
a rotation matrix M, then -q represents M as well.
Given an engineering quaternion
QENG = ( q0, q1, q2, q3 )
the equivalent SPICE quaternion is
QSPICE = ( q3, -q0, -q1, -q2 )
Associating SPICE Quaternions with Rotation Matrices
----------------------------------------------------
Let FROM and TO be two right-handed reference frames, for
example, an inertial frame and a spacecraft-fixed frame. Let the
symbols
V , V
FROM TO
denote, respectively, an arbitrary vector expressed relative to
the FROM and TO frames. Let M denote the transformation matrix
that transforms vectors from frame FROM to frame TO; then
V = M * V
TO FROM
where the expression on the right hand side represents left
multiplication of the vector by the matrix.
Then if the unit-length SPICE quaternion q represents M, where
q = (q0, q1, q2, q3)
the elements of M are derived from the elements of q as follows:
+- -+
| 2 2 |
| 1 - 2*( q2 + q3 ) 2*(q1*q2 - q0*q3) 2*(q1*q3 + q0*q2) |
| |
| |
| 2 2 |
M = | 2*(q1*q2 + q0*q3) 1 - 2*( q1 + q3 ) 2*(q2*q3 - q0*q1) |
| |
| |
| 2 2 |
| 2*(q1*q3 - q0*q2) 2*(q2*q3 + q0*q1) 1 - 2*( q1 + q2 ) |
| |
+- -+
Note that substituting the elements of -q for those of q in the
right hand side leaves each element of M unchanged; this shows
that if a quaternion q represents a matrix M, then so does the
quaternion -q.
To map the rotation matrix M to a unit quaternion, we start by
decomposing the rotation matrix as a sum of symmetric
and skew-symmetric parts:
2
M = [ I + (1-cos(theta)) OMEGA ] + [ sin(theta) OMEGA ]
symmetric skew-symmetric
OMEGA is a skew-symmetric matrix of the form
+- -+
| 0 -n3 n2 |
| |
OMEGA = | n3 0 -n1 |
| |
| -n2 n1 0 |
+- -+
The vector N of matrix entries (n1, n2, n3) is the rotation axis
of M and theta is M's rotation angle. Note that N and theta
are not unique.
Let
C = cos(theta/2)
S = sin(theta/2)
Then the unit quaternions Q corresponding to M are
Q = +/- ( C, S*n1, S*n2, S*n3 )
The mappings between quaternions and the corresponding rotations
are carried out by the CSPICE routines
q2m_c {quaternion to matrix}
m2q_c {matrix to quaternion}
m2q_c always returns a quaternion with scalar part greater than
or equal to zero.
SPICE Quaternion Multiplication Formula
---------------------------------------
Given a SPICE quaternion
Q = ( q0, q1, q2, q3 )
corresponding to rotation axis A and angle theta as above, we can
represent Q using "scalar + vector" notation as follows:
s = q0 = cos(theta/2)
v = ( q1, q2, q3 ) = sin(theta/2) * A
Q = s + v
Let Q1 and Q2 be SPICE quaternions with respective scalar
and vector parts s1, s2 and v1, v2:
Q1 = s1 + v1
Q2 = s2 + v2
We represent the dot product of v1 and v2 by
<v1, v2>
and the cross product of v1 and v2 by
v1 x v2
Then the SPICE quaternion product is
Q1*Q2 = s1*s2 - <v1,v2> + s1*v2 + s2*v1 + (v1 x v2)
If Q1 and Q2 represent the rotation matrices M1 and M2
respectively, then the quaternion product
Q1*Q2
represents the matrix product
M1*M2
This example writes a predict type 2 C-kernel segment for
the Mars Observer spacecraft bus to a previously opened CK file
attached to handle.
/.
Assume arrays of quaternions, angular velocities, and interval
start and stop times are produced elsewhere.
./
.
.
.
/.
The nominal number of seconds in a tick for MO is 1/256.
./
sectik = 1. / 256.;
for ( i = 0; i < nrec; i++ )
{
rate[i] = sectik;
}
/.
The subroutine ckw02_c needs the following components of the
segment descriptor:
1) SCLK limits of the segment.
2) Instrument code.
3) Reference frame.
./
begtim = start [ 0 ];
endtim = stop [nrec-1];
inst = -94000;
ref = "j2000";
segid = "mo predict seg type 2";
/.
Write the segment.
./
ckw02_c ( handle, begtim, endtim, inst, ref, segid,
nrec, start, stop, quat, avv, rates );
None.
None.
N.J. Bachman (JPL)
K.R. Gehringer (JPL)
J.M. Lynch (JPL)
-CSPICE Version 2.0.0, 01-JUN-2010 (NJB)
The check for non-unit quaternions has been replaced
with a check for zero-length quaternions. (The
implementation of the check is located in ckw02_.)
-CSPICE Version 1.2.1, 27-FEB-2008 (NJB)
Updated header; added information about SPICE
quaternion conventions.
-CSPICE Version 1.2.0, 28-AUG-2001 (NJB)
Changed prototype: inputs start, stop, sclkdp, quats,
and avvs are now const-qualified. Implemented interface
macros for casting these inputs to const.
-CSPICE Version 1.1.0, 08-FEB-1998 (NJB)
References to C2F_CreateStr_Sig were removed; code was
cleaned up accordingly. String checks are now done using
the macro CHKFSTR.
-CSPICE Version 1.0.0, 25-OCT-1997 (NJB)
Based on SPICELIB Version 2.0.0, 28-DEC-1993 (WLT)
write ck type_2 pointing data segment
Link to routine ckw02_c source file ckw02_c.c
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