It is considered the forming of Strapdown Inertial Navigation System (SINS) which is the base of spacecraft control system. The main problem is accuracy one so it is necessary to use and implement integrated navigation systems. During outer space flight onboard devices measurements and external navigation aids can be introduced. It is shown how to organize software algorithms for orientation system relying on so called kinematic principle. Different control modes may be easily realized within the scope of suggested structure. Here the kinematic loop mainly kinematic equations is the subject of investigation. So a specific attention is given to integration methods examination for kinematic equations of angular motion and ways of improving it. The results (methods, models, software and algorithmic support) can be used when developing strapdown systems orientation and navigation of a new generation of small-sized spacecraft, as well as the development of new and modifying of existing software of small-sized spacecraft SINS.