cspice_eul2m |
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## AbstractCSPICE_EUL2M constructs a 3x3, double precision rotation matrix from a set of Euler angles and the corresponding rotation axes. ## I/OGiven: angle3 angle2 angle1 set(s) rotation angles measured in radians. [1,n] = size(angle3); double = class(angle3) [1,n] = size(angle2); double = class(angle2) [1,n] = size(angle1); double = class(angle1) axis3 axis2 axis1 the indices defining the rotation axis corresponding to each angle. [1,1] = size(axis3); int32 = class(axis3) [1,1] = size(axis2); int32 = class(axis2) [1,1] = size(axis1); int32 = class(axis1) The values of axisX may be 1, 2, or 3, indicating the x, y, and z axes respectively. the call: r = ## ExamplesAny 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. % % Create the rotation matrix for a single coordinate % rotation of 90 degrees about the Z axis. As the % second and third angles are 0, the final two axes IDs, % 1, 1, have no effect for in this example. % rot = ## 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. ## Required ReadingFor important details concerning this module's function, please refer to the CSPICE routine eul2m_c. MICE.REQ ROTATION.REQ ## Version-Mice Version 1.0.1, 06-NOV-2014, EDW (JPL) Edited I/O section to conform to NAIF standard for Mice documentation. -Mice Version 1.0.0, 22-NOV-2005, EDW (JPL) ## Index_Entrieseuler angles to matrix |

Wed Apr 5 18:00:31 2017