Flexible satellite orientation, using the modal-analysis method for gyroscopic systems

A procedure for the solution of the eigenvalue problems related to gyroscopic systems using the modal-analysis method is described. The equations of motion represent a class of dynamic systems known as gyroscopic systems. A transformation is made in the state space, which allows the decoupling of theses equations, determining the eigenvalues and eigenvector corresponding to the vibration modes of this type of system. The procedure is applied to a satellite with two flexible appendages, and the eigenvalues and eigenvectors related to rotational and vibrational motions are determined. Also the system time response is obtained in the form of analytical expressions. This is of particular interest for on-board autonomous attitude control of satellites.