Computer algorithms for computation of kinematical relations for three attitude angle systems
Abstract
A spacecraft attitude is usually described by a set of three attitude angles (typically Euler angles) through which a sequence of successive planar rotations is specified. In this description, a planar rotation is represented by a 3 by 3 orthogonal matrix called transformation matrix. A unified algorithm is developed for computation of the general transformation matrix on a digital computer; the transformation matrix is general in the sense that if a sequence of any order is given, the transformation matrix is generated automatically without any manual calculation. Another algorithm is developed for the general kinematical relations between angular velocities and the time derivatives of three attitude angles. Algorithms for inverse transformations are also established. A complete set of the kinematical relations is therefore obtained for use in digital computer simulation. Elimination of unnecessary multiplications which would otherwise cause excessive computational time is stressed.
 Publication:

AIAA Journal
 Pub Date:
 August 1976
 DOI:
 10.2514/3.7202
 Bibcode:
 1976AIAAJ..14.1135O
 Keywords:

 Algorithms;
 Attitude (Inclination);
 Digital Simulation;
 Kinematics;
 Spacecraft Motion;
 Angular Velocity;
 Attitude Stability;
 Matrices (Mathematics);
 Transformations (Mathematics);
 Astrodynamics