twovxf_c |

Table of contents## Proceduretwovxf_c ( Two states defining a frame transformation ) void twovxf_c ( ConstSpiceDouble axdef [6], SpiceInt indexa, ConstSpiceDouble plndef [6], SpiceInt indexp, SpiceDouble xform [6][6] ) ## AbstractFind 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. ## Required_ReadingNone. ## KeywordsAXES FRAMES MATRIX TRANSFORMATION ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- axdef I State defining a principal axis. indexa I Principal axis number of `axdef' (x=1, y=2, z=3). plndef I State defining (with `axdef') a principal plane. indexp I Second axis number (with `indexa') of principal plane. xform O Output state transformation matrix. ## Detailed_Inputaxdef is a "generalized" state vector defining one of the principal axes of a reference frame. 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 is the index of the reference frame axis that is parallel to the direction of `axdef'. indexa Axis ------ ---- 1 x 2 y 3 z plndef is a state vector defining (with `axdef') a principal plane of the reference frame. 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 is the index of second axis of the principal frame determined by `axdef' and `plndef'. The association of integer values and axes is the same as for `indexa'. ## Detailed_Outputxform is 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'. 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. ## ParametersNone. ## Exceptions1) 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. ## FilesNone. ## ParticularsGiven two linearly independent state vectors `axdef' and `plndef', define vectors `dir1' and `dir2' by dir1 = ( axdef[0], axdef[1], axdef[2] ) dir2 = ( plndef[0], plndef[1], plndef[2] ) 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'. ## ExamplesThe numerical results shown for this example may differ across platforms. The results depend on the SPICE kernels used as input, the compiler and supporting libraries, 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 geometric 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. /. Program twovxf_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main( ) { /. Local parameters ./ #define META "twovxf_ex1.tm" /. 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. ./ #define RAJ2K 90.3991968556 #define DECJ2K -52.6956610556 #define PMRA 19.93e-3 #define PMDEC 23.24e-3 /. Local variables ./ SpiceDouble dec; SpiceDouble et; SpiceDouble lt; SpiceDouble pcano [3]; SpiceDouble ra; SpiceDouble rpmra; SpiceDouble rpmdec; SpiceDouble state [6]; SpiceDouble stcano [6]; SpiceDouble sterth [6]; SpiceDouble stsun [6]; SpiceDouble xfisc [6][6]; /. Load kernel files via the meta-kernel. ./ furnsh_c ( META ); /. Convert the TDB input time string to seconds past J2000, TDB. ./ str2et_c ( "2007 SEP 30 00:00:00 TDB", &et ); /. 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. ./ convrt_c ( PMRA, "ARCSECONDS", "RADIANS", &rpmra ); convrt_c ( PMDEC, "ARCSECONDS", "RADIANS", &rpmdec ); ra = RAJ2K * rpd_c() + rpmra * et/jyear_c(); dec = DECJ2K * rpd_c() + rpmdec * et/jyear_c(); radrec_c ( 1.0, ra, dec, pcano ); /. Compute MRO geometric velocity w.r.t. the Solar System Barycenter, and use it to correct the Canopus direction for stellar aberration. ./ spkezr_c ( "MRO", et, "J2000", "NONE", "SSB", state, < ); stelab_c ( pcano, state+3, stcano ); vpack_c ( 0.0, 0.0, 0.0, stcano+3 ); /. Let `stsun' be the J2000-relative apparent state of the Sun relative to the spacecraft at `et'. ./ spkezr_c ( "SUN", et, "J2000", "CN+S", "MRO", stsun, < ); /. The matrix `xfisc' transforms states from J2000 frame to the Sun-Canopus reference frame at `et'. ./ ## RestrictionsNone. ## Literature_ReferencesNone. ## Author_and_InstitutionJ. Diaz del Rio (ODC Space) ## Version-CSPICE Version 1.0.0, 05-AUG-2021 (JDR) ## Index_Entriesdefine a state transformation matrix from two states |

Fri Dec 31 18:41:14 2021