CSPICE_DVCRSS calculates the cross product of the position components of
two state vectors and the time derivative of this cross product.
s1 a SPICE state(s);
s1 = (r1, dr1 ).
[6,n] = size(s1); double = class(s1)
s2 a second SPICE state(s);
s2 = (r2, dr2 ).
[6,n] = size(s2); double = class(s2)
An implicit assumption exists that 's1' and 's2' are specified
in the same reference frame. If this is not the case, the numerical
result has no meaning.
dvcrss = cspice_dvcrss ( s1, s2 )
dvcrss the cross product(s) associated with the position components
of 's1' and 's2' and the derivative of the cross product(s)
with respect to time.
'dvcrss' returns with the same vectorization measure (N)
as 's1' and 's2'
[6,n] = size(dvcrss); double = class(dvcrss)
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.
One can construct non-inertial coordinate frames from apparent
positions of objects or defined directions. However, if one wants
to convert states in this non-inertial frame to states in an inertial
reference frame, the derivatives of the axes of the non-inertial
frame are required.
Define a reference frame with the apparent direction of the sun
as seen from earth as the primary axis (x). Use the earth pole vector
to define with the primary axis a primary plane of the frame.
% Load SPK, PCK, and LSK kernels, use a meta kernel for convenience.
cspice_furnsh( 'standard.tm' )
% Define the earth body-fixed pole vector (z). The pole
% has no velocity in the earth fixed frame "IAU_EARTH."
z_earth = [ 0, 0, 1, 0, 0, 0 ]';
% Calculate the state transformation between IAU_EARTH and J2000
% at an arbitrary epoch.
utc = 'Jan 1, 2009';
et = cspice_str2et( utc );
trans = cspice_sxform( 'IAU_EARTH', 'J2000', et );
% Transform the earth pole vector from the IAU_EARTH frame to J2000.
z_j2000 = trans * z_earth;
% Calculate the apparent state of the sun from earth at the epoch
% 'et' in the J2000 frame.
target = 'Sun';
observer = 'Earth';
[state, ltime] = cspice_spkezr( target, et, 'J2000', 'LT+S', observer );
% Define the z axis of the new frame as the cross product between
% the apparent direction of the sun and the earth pole. 'z_new' cross
% 'x_new' defines the y axis of the derived frame.
x_new = cspice_dvhat( state )
% Calculate the z direction in the new reference frame then
% calculate the normal of the vector and derivative of
% the normal to determine the z unit vector.
z_new = cspice_dvcrss( state, z_j2000 );
z_new = cspice_dvhat( z_new )
% As for z_new, calculate the y direction in the new reference
% frame then calculate the normal of the vector and derivative
% of the normal to determine they unit vector.
y_new = cspice_dvcrss( z_new, state );
y_new = cspice_dvhat( y_new )
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
These vectors define the transformation between the new frame and J2000.
| : |
| R : 0 |
M = | ......:......|
| : |
| dRdt : R |
| : |
R = [ x_new(1:3): y_new(1:3); z_new(1:3) ]
dRdt = [ x_new(4:6): y_new(4:6); z_new(4:6) ]
In this discussion, the notation
V1 x V2
indicates the cross product of vectors V1 and V2.
With s1 = (r1,v1) and s2 = (r2,v2) then
dvcrss = [ r1 x r2 , -- (r1 x r2) ]
For important details concerning this module's function, please refer to
the CSPICE routine dvcrss_c.
-Mice Version 1.0.0, 09-NOV-2010, EDW (JPL)
compute the derivative of a cross product