eul2m |

## ProcedureEUL2M ( Euler angles to matrix ) SUBROUTINE EUL2M ( ANGLE3, ANGLE2, ANGLE1, . AXIS3, AXIS2, AXIS1, R ) ## AbstractConstruct a rotation matrix from a set of Euler angles. ## Required_ReadingROTATION ## KeywordsMATRIX ROTATION TRANSFORMATION ## DeclarationsDOUBLE PRECISION ANGLE3 DOUBLE PRECISION ANGLE2 DOUBLE PRECISION ANGLE1 INTEGER AXIS3 INTEGER AXIS2 INTEGER AXIS1 DOUBLE PRECISION R ( 3, 3 ) ## Brief_I/OVariable I/O Description -------- --- -------------------------------------------------- ANGLE3, ANGLE2, ANGLE1 I Rotation angles about third, second, and first rotation axes (radians). AXIS3, AXIS2, AXIS1 I Axis numbers of third, second, and first rotation axes. R O Product of the 3 rotations. ## Detailed_InputANGLE3, ANGLE2, ANGLE1, AXIS3, AXIS2, AXIS1 are, respectively, a set of three angles and three coordinate axis numbers; each pair ANGLEx and AXISx specifies a coordinate transformation consisting of a rotation by ANGLEx radians about the coordinate axis indexed by AXISx. These coordinate transformations are typically symbolized by [ ANGLEx ] . AXISx See the $ Particulars section below for details concerning this notation. Note that these coordinate transformations rotate vectors by -ANGLEx radians about the axis indexed by AXISx. The values of AXISx may be 1, 2, or 3, indicating the x, y, and z axes respectively. ## Detailed_OutputR is a rotation matrix representing the composition of the rotations defined by the input angle-axis pairs. Together, the three pairs specify a composite transformation that is the result of performing the rotations about the axes indexed by AXIS1, AXIS2, and AXIS3, in that order. So, R = [ ANGLE3 ] [ ANGLE2 ] [ ANGLE1 ] AXIS3 AXIS2 AXIS1 See the $ Particulars section below for details concerning this notation. The resulting matrix R may be thought of as a coordinate transformation; applying it to a vector yields the vector's coordinates in the rotated system. Viewing R as a coordinate transformation matrix, the basis that R transforms vectors to is created by rotating the original coordinate axes first by ANGLE1 radians about the coordinate axis indexed by AXIS1, next by ANGLE2 radians about the coordinate axis indexed by AXIS2, and finally by ANGLE3 radians about coordinate axis indexed by AXIS3. At the second and third steps of this process, the coordinate axes about which rotations are performed belong to the bases resulting from the previous rotations. ## ParametersNone. ## Exceptions1) If any of AXIS3, AXIS2, or AXIS1 do not have values in { 1, 2, 3 }, the error SPICE(BADAXISNUMBERS) is signalled. ## FilesNone. ## ParticularsA word about notation: the symbol [ x ] i indicates a 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 | +- -+ From time to time, (depending on one's line of work, perhaps) one may happen upon a pair of coordinate systems related by a sequence of rotations. For example, the coordinate system defined by an instrument such as a camera is sometime specified by RA, DEC, and twist; if alpha, delta, and phi are the rotation angles, then the series of rotations [ phi ] [ pi/2 - delta ] [ alpha ] 3 2 3 produces a transformation from inertial to camera coordinates. This routine is related to the SPICELIB routine M2EUL, which produces a sequence of Euler angles, given a rotation matrix. This routine is a `left inverse' of M2EUL: the sequence of calls CALL M2EUL ( R, AXIS3, AXIS2, AXIS1, . ANGLE3, ANGLE2, ANGLE1 ) CALL ## Examples1) Create a coordinate transformation matrix by rotating the original coordinate axes first by 30 degrees about the z axis, next by 60 degrees about the y axis resulting from the first rotation, and finally by -50 degrees about the z axis resulting from the first two rotations. C C Create the coordinate transformation matrix C C o o o C R = [ -50 ] [ 60 ] [ 30 ] C 3 2 3 C C All angles in radians, please. The SPICELIB C function RPD (radians per degree) gives the C conversion factor. C C The z axis is `axis 3'; the y axis is `axis 2'. C ANGLE1 = RPD() * 30.D0 ANGLE2 = RPD() * 60.D0 ANGLE3 = RPD() * -50.D0 AXIS1 = 3 AXIS2 = 2 AXIS3 = 3 CALL ## RestrictionsBeware: more than one definition of "RA, DEC and twist" exists. ## Literature_References[1] `Galileo Attitude and Camera Models', JPL IOM 314-323, W. M. Owen, Jr., Nov. 11, 1983. NAIF document number 204.0. ## Author_and_InstitutionN.J. Bachman (JPL) ## VersionSPICELIB Version 1.2.1, 26-DEC-2006 (NJB) Corrected header typo. SPICELIB Version 1.2.0, 25-AUG-2005 (NJB) Updated to remove non-standard use of duplicate arguments in ROTMAT calls. SPICELIB Version 1.1.2, 14-OCT-2004 (LSE) Corrected a typo in the header. SPICELIB Version 1.1.1, 10-MAR-1992 (WLT) Comment section for permuted index source lines was added following the header. SPICELIB Version 1.1.0, 02-NOV-1990 (NJB) Names of input arguments changed to reflect the order in which the rotations are applied when their product is computed. The header was upgraded to describe notation in more detail. Examples were added. SPICELIB Version 1.0.0, 30-AUG-1990 (NJB) |

Wed Apr 5 17:46:36 2017