Use of Euler Transformations in the Determination of Rocket Orientation

摘要

An analytical treatment of data from rocket aspect sensors (such as magnetometers and solar sensors) was developed in terms of Euler angle coordinate systems and transformations, since the Euler angles represent the zenith, azimuth, and spin angular coordinates of the rocket. It was found that the relationships between the sensor outputs and the orientation of the rocket are exceedingly straightforward when considered in terms of these coordinate transformations. Three cases of aspect sensor combinations were considered; complete magnetometer data were assumed in each of the three cases (except for consideration of failure of one of the three magnetometers) with supplementary information in case 1 from continuous sun sensor coverage, in case 2 from partial sun sensor data, and in case 3 from horizon scanners. The equations are derived for ideal experimental conditions (instrumental errors are neglected). The solutions can easily be programmed on a computer. A general computer program was not developed, however, because the problems encountered in the reduction of aspect data vary considerably for each rocket flight. (Author)