eul2xf_c |

Table of contents## Procedureeul2xf_c ( Euler angles and derivative to transformation ) void eul2xf_c ( ConstSpiceDouble eulang[6], SpiceInt axisa, SpiceInt axisb, SpiceInt axisc, SpiceDouble xform [6][6] ) ## AbstractCompute a state transformation from an Euler angle factorization of a rotation and the derivatives of those Euler angles. ## Required_ReadingROTATION ## KeywordsANGLES DERIVATIVES STATE ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- eulang I An array of Euler angles and their derivatives. axisa I Axis A of the Euler angle factorization. axisb I Axis B of the Euler angle factorization. axisc I Axis C of the Euler angle factorization. xform O A state transformation matrix. ## Detailed_Inputeulang is the set of Euler angles corresponding to the specified factorization. If we represent `r' as shown here: r = [ alpha ] [ beta ] [ gamma ] axisa axisb axisc then eulang[0] = alpha eulang[1] = beta eulang[2] = gamma eulang[3] = dalpha/dt eulang[4] = dbeta/dt eulang[5] = dgamma/dt axisa, axisb, axisc are the axes desired for the factorization of `r'. All must be in the range from 1 to 3. Moreover it must be the case that `axisa' and `axisb' are distinct and that `axisb' and `axisc' are distinct. Every rotation matrix can be represented as a product of three rotation matrices about the principal axes of a reference frame. r = [ alpha ] [ beta ] [ gamma ] axisa axisb axisc The value 1 corresponds to the X axis. The value 2 corresponds to the Y axis. The value 3 corresponds to the Z axis. ## Detailed_Outputxform is the state transformation matrix corresponding to `r' and dr/dt as described above. Pictorially, .- -. | | | | r | 0 | | | | |-------+-------| | | | | dr/dt | r | | | | `- -' where `r' is a rotation matrix that varies with respect to time and dr/dt is its time derivative. ## ParametersNone. ## Exceptions1) If any of `axisa', `axisb', or `axisc' do not have values in { 1, 2, 3 } an error is signaled by a routine in the call tree of this routine. ## FilesNone. ## ParticularsA word about notation: the symbol [ x ] i indicates a coordinate system rotation of x radians about the ith coordinate axis. To be specific, the symbol [ x ] 1 indicates a coordinate system rotation of x radians about the first, or x-, axis; the corresponding matrix is .- -. | 1 0 0 | | | | 0 cos(x) sin(x) | | | | 0 -sin(x) cos(x) | `- -' Remember, this is a COORDINATE SYSTEM rotation by x radians; this matrix, when applied to a vector, rotates the vector by -x radians, not x radians. Applying the matrix to a vector yields the vector's representation relative to the rotated coordinate system. The analogous rotation about the second, or y-, axis is represented by [ x ] 2 which symbolizes the matrix .- -. | cos(x) 0 -sin(x) | | | | 0 1 0 | | | | sin(x) 0 cos(x) | `- -' and the analogous rotation about the third, or z-, axis is represented by [ x ] 3 which symbolizes the matrix .- -. | cos(x) sin(x) 0 | | | | -sin(x) cos(x) 0 | | | | 0 0 1 | `- -' The input matrix is assumed to be the product of three rotation matrices, each one of the form .- -. | 1 0 0 | | | | 0 cos(r) sin(r) | (rotation of r radians about the | | x-axis), | 0 -sin(r) cos(r) | `- -' .- -. | cos(s) 0 -sin(s) | | | | 0 1 0 | (rotation of s radians about the | | y-axis), | sin(s) 0 cos(s) | `- -' or .- -. | cos(t) sin(t) 0 | | | | -sin(t) cos(t) 0 | (rotation of t radians about the | | z-axis), | 0 0 1 | `- -' where the second rotation axis is not equal to the first or third. Any rotation matrix can be factored as a sequence of three such rotations, provided that this last criterion is met. This routine is intended to provide an inverse for xf2eul_c. The two function calls shown here will not change `xform' except for round off errors. xf2eul_c ( xform, axisa, axisb, axisc, eulang, &unique ); ## 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) Suppose you have a set of Euler angles and their derivatives for a 3 1 3 rotation, and that you would like to determine the equivalent angles and derivatives for a 1 2 3 rotation. r = [alpha] [beta] [gamma] 3 1 3 r = [roll] [pitch] [yaw] 1 2 3 The following code example will perform the desired computation. Example code begins here. /. Program eul2xf_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main( ) { /. Local variables. ./ SpiceDouble abgang [6]; SpiceDouble rpyang [6]; SpiceDouble xform [6][6]; SpiceBoolean unique; /. Define the initial set of Euler angles. ./ abgang[0] = 0.01; abgang[1] = 0.03; abgang[2] = 0.09; abgang[3] = -0.001; abgang[4] = -0.003; abgang[5] = -0.009; /. Compute the equivalent angles and derivatives for a 1-2-3 rotation. ./ ## RestrictionsNone. ## Literature_ReferencesNone. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) W.L. Taber (JPL) E.D. Wright (JPL) ## Version-CSPICE Version 2.0.2, 10-AUG-2021 (JDR) Edited the header to comply with NAIF standard. Added complete code example based on existing example. -CSPICE Version 2.0.1, 25-APR-2007 (EDW) Corrected code in -Examples section, example showed a xf2eul_c call: xf2eul_c( xform, 1, 2, 3, rpyang); The proper form of the call: xf2eul_c( xform, 1, 2, 3, rpyang, &unique ); -CSPICE Version 2.0.0, 31-OCT-2005 (NJB) Restriction that second axis must differ from the first and third was removed. -CSPICE Version 1.0.1, 03-JUN-2003 (EDW) Correct typo in Procedure line. -CSPICE Version 1.0.0, 18-MAY-1999 (WLT) (NJB) ## Index_EntriesState transformation from Euler angles and derivatives |

Fri Dec 31 18:41:06 2021