Table of contents
CSPICE_TWOVXF finds the state transformation from a base frame to the
right-handed frame defined by two state vectors: one state
vector defining a specified axis and a second state vector
defining a specified coordinate plane.
Given:
axdef a "generalized" state vector defining one of the principal
axes of a reference frame.
[6,1] = size(axdef); double = class(axdef)
This vector consists of three components of a vector-valued
function of one independent variable `t' followed by the
derivatives of the components with respect to that variable:
( a, b, c, da/dt, db/dt, dc/dt )
This routine treats the input states as unitless, but
in most applications the input states represent
quantities that have associated units. The first three
components must have the same units, and the units of
the last three components must be compatible with
those of the first three: if the first three
components of `axdef'
( a, b, c )
have units U and `t' has units T, then the units of
`axdef' normally would be
( U, U, U, U/T, U/T, U/T )
Note that the direction and angular velocity defined
by `axdef' are actually independent of U, so scaling
`axdef' doesn't affect the output of this routine.
`axdef' could represent position and velocity; it could
also represent velocity and acceleration. `axdef' could
for example represent the velocity and acceleration of
a time-dependent position vector ( x(t), y(t), z(t) ),
in which case `axdef' would be defined by
a = dx/dt
b = dy/dt
c = dz/dt
2 2
da/dt = d x / dt
2 2
db/dt = d y / dt
2 2
dc/dt = d z / dt
Below, we'll call the normalized (unit length) version
of
( a, b, c )
the "direction" of `axdef'.
We call the frame relative to which `axdef' is specified
the "base frame." The input state `plndef' must be
specified relative to the same base frame.
indexa the index of the reference frame axis that is parallel to the
direction of `axdef'.
[1,1] = size(indexa); int32 = class(indexa)
indexa Axis
------ ----
1 X
2 Y
3 Z
plndef a state vector defining (with `axdef') a principal plane of
the reference frame.
[6,1] = size(plndef); double = class(plndef)
This vector consists of three components followed by their
derivatives with respect to the independent variable `t'
associated with `axdef', so `plndef' is
( e, f, g, de/dt, df/dt, dg/dt )
Below, we'll call the unitized version of
( e, f, g )
the "direction" of `plndef'.
The second axis of the principal plane containing the
direction vectors of `axdef' and `plndef' is perpendicular
to the first axis and has positive dot product with
the direction vector of `plndef'.
The first three components of `plndef' must have the
same units, and the units of the last three components
must be compatible with those of the first three: if
the first three components of `plndef'
( e, f, g )
have units U2 and `t' has units T, then the units of
`plndef' normally would be
( U2, U2, U2, U2/T, U2/T, U2/T )
Note that ***for meaningful results, the angular
velocities defined by `axdef' and `plndef' must both have
units of 1/T.***
As with `axdef', scaling `plndef' doesn't affect the
output of this routine.
`axdef' and `plndef' must be specified relative to a
common reference frame, which we call the "base
frame."
indexp the index of second axis of the principal frame determined by
`axdef' and `plndef'.
[1,1] = size(indexp); int32 = class(indexp)
The association of integer values and axes is the same as
for `indexa'.
the call:
[xform] = cspice_twovxf( axdef, indexa, plndef, indexp )
returns:
xform the 6x6 matrix that transforms states from the frame relative
to which `axdef' and `plndef' are specified (the "base
frame") to the frame whose axes and derivative are determined
by `axdef', `plndef', `indexa' and `indexp'.
[6,6] = size(xform); double = class(xform)
The matrix `xform' has the structure shown below:
.- -.
| : |
| r : 0 |
| : |
| .......:.......|
| : |
| dr/dt : r |
| : |
`- -'
where `r' is a rotation matrix that is a function of
the independent variable associated with `axdef' and
`plndef', and where dr/dt is the derivative of `r'
with respect to that independent variable.
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 time-dependent Sun-Canopus reference frame associated with
a spacecraft uses the spacecraft-sun state to define the Z axis
and the Canopus direction to define the X-Z plane.
Find the apparent position of the Earth as seen from the Mars
Reconnaissance Orbiter spacecraft (MRO) at a specified time,
relative to the Sun-Canopus reference frame associated with
MRO.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File: twovxf_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
--------- --------
naif0012.tls Leapseconds
de430.bsp Planetary ephemeris
mro_psp4_ssd_mro95a.bsp MRO ephemeris
\begindata
KERNELS_TO_LOAD = ( 'naif0012.tls',
'de430.bsp',
'mro_psp4_ssd_mro95a.bsp' )
\begintext
End of meta-kernel
Example code begins here.
function twovxf_ex1()
%
% Local parameters
%
META = 'twovxf_ex1.tm';
%
% Local variables
%
stcano = zeros(6,1);
%
% Define the Right Ascension and Declination, and the
% proper motion in both coordinates, of Canopus, relative
% to the J2000 frame at J2000 epoch, in degrees and
% arcsecond/yr respectively. Note that the values used here
% may not be suitable for real applications.
%
RAJ2K = 90.3991968556;
DECJ2K = -52.6956610556;
PMRA = 19.93e-3;
PMDEC = 23.24e-3;
%
% Load kernel files via the meta-kernel.
%
cspice_furnsh( META );
%
% Convert the TDB input time string to seconds past
% J2000, TDB.
%
[et] = cspice_str2et( '2007 SEP 30 00:00:00 TDB' );
%
% Define an approximate "state vector" for Canopus using
% the J2000-relative, unit direction vector toward Canopus
% at a specified time `et' (time is needed to compute proper
% motion) as position and the zero vector as velocity.
%
[rpmra] = cspice_convrt( PMRA, 'ARCSECONDS', 'RADIANS' );
[rpmdec] = cspice_convrt( PMDEC, 'ARCSECONDS', 'RADIANS' );
ra = RAJ2K * cspice_rpd + rpmra * et/cspice_jyear;
dec = DECJ2K * cspice_rpd + rpmdec * et/cspice_jyear;
[pcano] = cspice_radrec( 1.0, ra, dec );
%
% Compute MRO geometric velocity w.r.t. the Solar System
% Barycenter, and use it to correct the Canopus direction
% for stellar aberration.
%
[state, lt] = cspice_spkezr( 'MRO', et, 'J2000', 'NONE', 'SSB' );
[stelab] = cspice_stelab( pcano, state(4:6) );
stcano(1:3) = stelab';
stcano(4:6) = [ 0.0, 0.0, 0.0 ]';
%
% Let `stsun' be the J2000-relative apparent state of the Sun
% relative to the spacecraft at `et'.
%
[stsun, lt] = cspice_spkezr( 'SUN', et, 'J2000', 'CN+S', 'MRO' );
%
% The matrix `xfisc' transforms states from J2000 frame
% to the Sun-Canopus reference frame at `et'.
%
[xfisc] = cspice_twovxf( stsun, 3, stcano, 1 );
%
% Compute the apparent state of the Earth as seen from MRO
% in the J2000 frame at `et' and transform that vector into
% the Sun-Canopus reference frame.
%
[state, lt] = cspice_spkezr( 'EARTH', et, 'J2000', 'CN+S', 'MRO' );
sterth = xfisc * state;
%
% Display the results.
%
fprintf( [ 'Earth as seen from MRO in Sun-Canopus frame (km', ...
' and km/s):\n' ] )
fprintf( ' position: %15.3f %15.3f %15.3f\n', sterth(1:3) )
fprintf( ' velocity: %15.3f %15.3f %15.3f\n', sterth(4:6) )
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave5.x/64-bit
platform, the output was:
Earth as seen from MRO in Sun-Canopus frame (km and km/s):
position: -16659764.322 97343706.915 106745539.738
velocity: 2.691 -10.345 -7.877
Given two linearly independent state vectors `axdef' and `plndef',
define vectors `dir1' and `dir2' by
dir1 = ( axdef(1), axdef(2), axdef(3) )
dir2 = ( plndef(1), plndef(2), plndef(3) )
Then there is a unique right-handed reference frame `f' having:
`dir1' lying along the `indexa' axis.
`dir2' lying in the indexa-indexp coordinate plane, such that
the dot product of `dir2' with the positive `indexp' axis is
positive.
This routine determines the 6x6 matrix that transforms states
from the base frame used to represent the input vectors to the
the frame `f' determined by `axdef' and `plndef'. Thus a state vector
s = ( x, y, z, dx/dt, dy/dt, dz/dt )
base
in the input reference frame will be transformed to
s = xform * s
f base
in the frame `f' determined by `axdef' and `plndef'.
1) If `indexa' or `indexp' is not in the set {1,2,3}, the error
SPICE(BADINDEX) is signaled by a routine in the call tree of
this routine.
2) If `indexa' and `indexp' are the same, the error
SPICE(UNDEFINEDFRAME) is signaled by a routine in the call
tree of this routine.
3) If the cross product of the vectors `axdef' and `plndef' is zero,
the error SPICE(DEPENDENTVECTORS) is signaled by a routine in
the call tree of this routine.
4) If any of the input arguments, `axdef', `indexa', `plndef' or
`indexp', is undefined, an error is signaled by the Matlab
error handling system.
5) If any of the input arguments, `axdef', `indexa', `plndef' or
`indexp', is not of the expected type, or it does not have the
expected dimensions and size, an error is signaled by the Mice
interface.
None.
None.
MICE.REQ
None.
J. Diaz del Rio (ODC Space)
-Mice Version 1.0.0, 08-FEB-2021 (JDR)
define a state transformation matrix from two states
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