General expression for a threeangle rotation matrix
Abstract
A general transformation matrix can be expressed as the product of three singleaxis rotation matrices, and this paper derives a general expression for such a transformation matrix R from which the nine elements of R can be read off as functions of the three rotation angles and the three rotation axes. The expression is valid for the 12 possible nondegenerate types of the 27 possible distinct types. The derivation uses the fact that the set of all 3 x 3 matrices constitutes a vector space of dimension 9. The expressions for the elements of R can be programmed as a simple FORTRAN subroutine, which needs to be called only once.
 Publication:

Journal of Guidance Control Dynamics
 Pub Date:
 April 1979
 DOI:
 10.2514/3.55853
 Bibcode:
 1979JGCD....2..156W
 Keywords:

 Body Kinematics;
 Computerized Simulation;
 Equations Of Motion;
 Matrices (Mathematics);
 Spacecraft Motion;
 Three Axis Stabilization;
 Algorithms;
 Axes Of Rotation;
 Digital Computers;
 Fortran;
 Triangles;
 Physics (General)