Table of contents
CSPICE_INVSTM returns the inverse of a state transformation matrix.
Given:
mat a state transformation matrix for converting states relative
to one frame to states relative to another.
help, mat
DOUBLE = Array[6,6]
The state transformation of a state vector, `s', is performed
by the matrix-vector product.
mat * s.
For `mat' to be a "true" state transformation matrix
it must have the form
.- -.
| : |
| r : 0 |
|.......:......|
| : |
| w*r : r |
| : |
`- -'
where `r' is a 3x3 rotation matrix, 0 is the 3x3 zero
matrix and `w' is a 3x3 skew-symmetric matrix.
NOTE: no checks are performed on `mat' to ensure that it
does indeed have the form described above.
the call:
cspice_invstm, mat, invmat
returns:
invmat the inverse of `mat' under the operation of matrix
multiplication.
help, invmat
DOUBLE = Array[6,6]
If `mat' has the form described above, then `invmat' has
the form shown below.
.- -.
| t : |
| r : 0 |
|........:......|
| t : t |
| (w*r) : r |
| : |
`- -'
(The superscript "t" denotes the matrix transpose
operation.)
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) Suppose you have a geometric state of a spacecraft in Earth
body-fixed reference frame and wish to express this state
relative to an Earth centered J2000 frame. The following
example code illustrates how to carry out this computation.
Use the PCK kernel below to load the required high precision
orientation of the ITRF93 Earth body-fixed reference frame.
Note that the body ID code used in this file for the Earth is
3000.
earth_720101_070426.bpc
Example code begins here.
PRO invstm_ex1
;;
;; Define the state of the spacecraft, in km and
;; km/s, and the `et' epoch, in seconds past J2000.
;;
et = 0.D0
state = [ 175625246.2910042D0, 164189388.1254006D0, $
-62935198.26067264D0, 11946.73372264D0, $
-12771.29732556D0, 13.84902914D0 ]
;;
;; Load the required high precision Earth PCK.
;;
cspice_furnsh, 'earth_720101_070426.bpc'
;;
;; First get the state transformation from J2000 frame
;; to Earth body-fixed frame at the time of interest `et'.
;; The body ID code used in high precision PCK files for
;; the Earth is 3000; this number indicates that the
;; terrestrial frame used is ITRF93.
;;
earth = 3000L
cspice_tisbod, 'J2000', earth, et, mat
;;
;; Get the inverse of `mat'.
;;
cspice_invstm, mat, invmat
;;
;; Transform from bodyfixed state to inertial state.
;;
istat1 = transpose( invmat ) # state
;;
;; Print the resulting state.
;;
print, format='(A)', 'Input state in Earth centered J2000' + $
' frame, using cspice_invstm:'
print, format='(A,3F16.3)', ' Position:', istat1[0:2]
print, format='(A,3F16.3)', ' Velocity:', istat1[3:5]
;;
;; Compute the same state using cspice_sxform.
;;
cspice_sxform, 'ITRF93', 'J2000', et, xmat
istat2 = transpose( xmat ) # state
print
print, format='(A)', 'Input state in Earth centered J2000' + $
' frame, using cspice_sxform:'
print, format='(A,3F16.3)', ' Position:', istat2[0:2]
print, format='(A,3F16.3)', ' Velocity:', istat2[3:5]
;;
;; It's always good form to unload kernels after use,
;; particularly in IDL due to data persistence.
;;
cspice_kclear
END
When this program was executed on a Mac/Intel/IDL8.x/64-bit
platform, the output was:
Input state in Earth centered J2000 frame, using cspice_invstm:
Position: 192681395.921 -143792821.383 -62934296.473
Velocity: 30.312 32.007 13.876
Input state in Earth centered J2000 frame, using cspice_sxform:
Position: 192681395.921 -143792821.383 -62934296.473
Velocity: 30.312 32.007 13.876
Given a matrix for transforming states relative frame 1 to
states relative frame 2, the routine produces the inverse
matrix. That is, it returns the matrix for transforming states
relative to frame 2 to states relative to frame 1.
This special routine exists because unlike the inverse of a
rotation matrix, the inverse of a state transformation matrix,
is NOT simply the transpose of the matrix.
1) No checks are performed to ensure that the input matrix is
indeed a state transformation matrix.
2) If the input argument `mat' is undefined, an error is signaled
by the IDL error handling system.
3) If the input argument `mat' is not of the expected type, or it
does not have the expected dimensions and size, an error is
signaled by the Icy interface.
4) If the output argument `invmat' is not a named variable, an
error is signaled by the Icy interface.
None.
None.
ICY.REQ
ROTATION.REQ
None.
J. Diaz del Rio (ODC Space)
-Icy Version 1.0.0, 25-NOV-2021 (JDR)
inverse of state transformation matrix
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