On the numerical integration of the dynamic attitude equations

The authors describe a new class of numerical integration algorithms. The main aim of the algorithms is to numerically integrate differential equations which evolve on geometric objects, such as the rotation group. The algorithms provide iterates which lie on the prescribed geometric object, either exactly, or to some prescribed accuracy, independent of the order of the algorithm. In this sense the algorithms can be called exact integration algorithms. The application of these new algorithms to the differential equations describing the evolution of the attitude of a rigid body such as spacecraft, when the body is modeled by the corresponding dynamical equations is described. Such exact integration algorithms can be important in control applications, and their analysis has employed exactly the same tools used in contemporary analysis of nonlinear control systems