Table of contents
CSPICE_CKW02 adds a type 2 segment to a C-kernel.
Given:
handle the handle of the CK file to which the segment will be written.
help, handle
LONG = Scalar
The file must have been opened with write access.
begtim the beginning encoded SCLK time of the segment.
help, begtim
DOUBLE = Scalar
This value should be less than or equal to the first `start'
time in the segment.
endtim the encoded SCLK time at which the segment ends.
help, endtim
DOUBLE = Scalar
This value should be greater than or equal to the last `stop'
time in the segment.
inst the NAIF integer ID code for the instrument.
help, inst
LONG = Scalar
ref a character string that specifies the reference frame of the
segment.
help, ref
STRING = Scalar
This should be one of the frames supported by the Icy routine
cspice_namfrm.
segid the segment identifier.
help, segid
STRING = Scalar
A CK segment identifier may contain up to 40 characters.
start the start times of each interval in encoded spacecraft clock.
help, start
DOUBLE = Array[N]
These times must be strictly increasing.
stop the stop times of each interval in encoded spacecraft clock.
help, stop
DOUBLE = Array[N]
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 an array of SPICE-style quaternions representing the C-matrices
associated with the start times of each interval.
help, quats
DOUBLE = Array[4,N]
See the discussion of quaternion styles in -Particulars below.
avvs the angular velocity vectors for each interval.
help, avvs
DOUBLE = Array[3,N]
rates the number of seconds per encoded spacecraft clock tick for each
interval.
help, rates
DOUBLE = Array[N]
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.
the call:
cspice_ckw02, handle, begtim, endtim, inst, ref, segid, $
start, stop, quats, avvs, rates
writes the data for a type 2 segment to the open CK file
indicated by `handle'.
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) The following example creates a CK file with a type-2 segment,
with data for a simple time dependent rotation and angular
velocity.
Example code begins here.
PRO ckw02_ex1
;;
;; Create a CK type 2 segment; fill with data for a simple time
;; dependent rotation and angular velocity.
;;
;;
;; Define needed parameters
;;
CK2 = "ckw02_ex1.bc"
INST = -77702
MAXREC = 201
SECPERTICK = 0.001d
SPICETRUE = 1L
IFNAME = "Test CK type 2 segment created by cspice_ckw02"
SEGID = "Test type 2 CK segment"
;;
;; 'NCOMCH' is the number of characters to reserve for the kernel's
;; comment area. This example doesn't write comments, so set to
;; zero.
;;
NCOMCH = 0
;;
;; The base reference from for the rotation data.
;;
REF = "J2000"
;;
;; Time spacing in encoded ticks.
;;
SPACING_TICKS = 10.d
;;
;; Time spacing in seconds
;;
SPACING_SECS = SPACING_TICKS * SECPERTICK
;;
;; Declare an angular rate in radians per sec.
;;
RATE = 1.d-2
;;
;; Open a new kernel.
;;
cspice_ckopn, CK2, IFNAME, NCOMCH, handle
;;
;; Create a 4xMAXREC matrix for quaternions, and a
;; 3xMAXREC for expavs.
;;
quats = dblarr( 4, MAXREC )
av = dblarr( 3, MAXREC )
;;
;; Create a 3x3 double precision identity matrix.
;; The Icy call:
;;
;; cspice_ident, work_mat
;;
;; performs the same function.
;;
work_mat = identity( 3 )
;;
;; Convert the matrix to quaternion.
;;
cspice_m2q, work_mat, work_quat
;;
;; Copy the work quaternion to the first row of
;; `quats'.
;;
quats[0:3] = work_quat
;;
;; Create an angular velocity vector. Copy to the first row
;; of `av'. This vector is in the REF reference frame.
;;
av [0:2] = [0.d, 0.d, RATE ]
;;
;; Create arrays of interval start and stop times. The interval
;; associated with each quaternion will start at the epoch of
;; the quaternion and will extend 0.8 * SPACING_TICKS forward in
;; time, leaving small gaps between the intervals.
;;
starts = dblarr( MAXREC )
stops = dblarr( MAXREC )
;;
;; Fill in the clock rates array with a constant SECPERTICK for
;; all values.
;;
rates = dblarr( MAXREC ) + SECPERTICK
;;
;; Create an array of encoded tick values in increments of
;; SPACING_TICKS with an initial value of 1000 ticks...
;;
sclkdp = dindgen(MAXREC) * SPACING_TICKS
sclkdp = sclkdp + 1000.d
starts = sclkdp
stops = sclkdp + ( 0.8d * SPACING_TICKS )
;;
;; Fill the rest of the av and quats matrices
;; with simple data.
;;
for i = 1, (MAXREC-1) do begin
;;
;; Create the transformation matrix for a rotation of `theta'
;; about the Z axis. Calculate `theta' from the constant
;; angular rate RATE at increments of 'SPACING_SECS'.
;;
theta = ( double(i) * RATE * SPACING_SECS)
cspice_rotmat, work_mat, theta, 3, work_mat
;;
;; Convert the `work_mat' matrix to SPICE type quaternion.
;;
cspice_m2q, work_mat, work_quat
;;
;; Store the quaternion in the `quats' matrix.
;; Store angular velocity in `av'. Both variables
;; represent arrays, but in IDL you can fill them
;; as vectors.
;;
;;
quats[ (i*4):((i*4)+3) ] = work_quat
av [ (i*3):((i*3)+2) ] = [ 0.d, 0.d, RATE ]
endfor
;;
;; Set the segment boundaries equal to the first and last
;; time in the segment.
;;
begtim = starts[ 0]
endtim = stops [MAXREC-1]
;;
;; All information ready to write. Write to a CK type 2 segment
;; to the file indicated by `handle'.
;;
cspice_ckw02, handle, $
begtim, $
endtim, $
INST, $
REF, $
SEGID , $
starts, $
stops, $
quats, $
av, $
rates
;;
;; SAFELY close the file.
;;
cspice_ckcls, handle
END
When this program is executed, no output is presented on
screen. After run completion, a new CK file exists in the
output directory.
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
Icy routine interfaces ALWAYS use SPICE quaternions.
Quaternions of any other style must be converted to SPICE
quaternions before they are passed to Icy routines.
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[0],
sin(theta/2) a[1],
sin(theta/2) a[2] )
while the engineering quaternions representing `m' are
(+/-) ( -sin(theta/2) a[0],
-sin(theta/2) a[1],
-sin(theta/2) a[2],
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 Icy routines
cspice_q2m {quaternion to matrix}
cspice_m2q {matrix to quaternion}
cspice_m2q 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
1) If `handle' is not the handle of a C-kernel opened for writing,
an error is signaled by a routine in the call tree of this
routine.
2) If `segid' is more than 40 characters long, the error
SPICE(SEGIDTOOLONG) is signaled by a routine in the call tree
of this routine.
3) If `segid' contains any nonprintable characters, the error
SPICE(NONPRINTABLECHARS) is signaled by a routine in the call
tree of this routine.
4) If the first `start' time is negative, the error
SPICE(INVALIDSCLKTIME) is signaled by a routine in the call
tree of this routine.
5) If the second or any subsequent `start' times are negative, the
error SPICE(TIMESOUTOFORDER) is signaled by a routine in the
call tree of this routine.
6) If any of the `stop' times are negative, the error
SPICE(DEGENERATEINTERVAL) is signaled by a routine in the call
tree of this routine.
7) If the `stop' time of any of the intervals is less than or equal
to the `start' time, the error SPICE(DEGENERATEINTERVAL) is
signaled by a routine in the call tree of this routine.
8) If the `start' times are not strictly increasing, the error
SPICE(TIMESOUTOFORDER) is signaled by a routine in the call
tree of this routine.
9) If the `stop' time of one interval is greater than the `start'
time of the next interval, the error SPICE(BADSTOPTIME)
is signaled by a routine in the call tree of this routine.
10) If `begtim' is greater than start[0] or `endtim' is less than
stop[nrec-1], where `nrec' is the number of pointing records,
the error SPICE(INVALIDDESCRTIME) is signaled by a routine in
the call tree of this routine.
11) If the name of the reference frame is not one of those
supported by the routine cspice_namfrm, the error
SPICE(INVALIDREFFRAME) is signaled by a routine in the call
tree of this routine.
12) If `nrec', the number of pointing records, is less than or
equal to 0, the error SPICE(INVALIDNUMRECS) is signaled by a
routine in the call tree of this routine.
13) If any quaternion has magnitude zero, the error
SPICE(ZEROQUATERNION) is signaled by a routine in the call
tree of this routine.
14) If any of the input arguments, `handle', `begtim', `endtim',
`inst', `ref', `segid', `start', `stop', `quats', `avvs' or
`rates', is undefined, an error is signaled by the IDL error
handling system.
15) If any of the input arguments, `handle', `begtim', `endtim',
`inst', `ref', `segid', `start', `stop', `quats', `avvs' or
`rates', is not of the expected type, or it does not have the
expected dimensions and size, an error is signaled by the Icy
interface.
16) If the input vector arguments `start', `stop', `quats', `avvs'
and `rates' do not have the same dimension (N), an error is
signaled by the Icy interface.
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.
None.
ICY.REQ
CK.REQ
DAF.REQ
SCLK.REQ
None.
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
-Icy Version 1.0.2, 25-AUG-2021 (JDR)
Edited the header to comply with NAIF standard. Added example's
problem statement.
Added -Parameters, -Particulars, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections.
Removed reference to the routine's corresponding CSPICE header from
-Abstract section.
Added arguments' type and size information in the -I/O section.
-Icy Version 1.0.1, 07-JAN-2008 (EDW)
Removed mention of "nrec" from the -I/O section. mention of
this argument constitutes a typo as the Icy interface
does not need to explicitly pass this value.
-Icy Version 1.0.0, 16-JUN-2003 (EDW)
write CK type_2 pointing data segment
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