The finite element method is used to represent crucial dynamics of real systems. However, it requires considerable computation time in dynamic simulation. This thesis introduces a new order reduction method, called geometric reduced hybrid system given partially described eigen-information. It is designed to meet the triple goals of geometric representation, physical accuracy under some low frequency, and computational efficiency. The system will be separated into a hybrid one, including both rigid and flexible sub-bodies, based on partially described mode shapes, and geometrical and/or functional grouping. The flexible sub-body is modeled as rigid body or n-node point masses depending on the relative accuracy when comparing to the high-order original system. Such a reduced model facilitates investigating structural interaction among different components and time domain simulation.

Such a method is applied in the study of the attitude control system of a science satellite, SNAP. The geometric reduced satellite model is very helpful for revealing interaction among subsystems, and it allows the convenience of investigating internal structural vibrations and change in optical path in the satellite. Other benefits include, but are not limited to, the ability to design a robust and reliable digital controller, or check an old one, which is designed for a simple model, whether it can meet the requirements in control objectives or not. A comparison between this method and Craig-Bampton method, which is used in Hubble Space Telescope, is made and shows the superiority of the former.

Disturbance is a major source of instability or failure of satellites. In this thesis, a parametric worst case analysis is made on fuel sloshing, the model of which is not known clearly. The fuel-slosh-based satellite motion during observation is exposed, and the controllers' performance is checked in the worst case.