| The present thesis addresses the stability problem of a force free dual spin satellite which comprises an asymmetric rigid rotor and a flexible platform. Two cases are investigated, the case where the rotor is free from axial torques, and the case where the spin rate of the rotor relative to the platform is maintained constant.;A minimum number of the nonlinear equations of motion are derived directly by a hybrid method, which combines Euler and Lagrange equations, without the necessity to deal explicitly with internal forces and to consider forces of constraints.;Conditions for the existence of pure spin motion are obtained, and the equations of motion are linearized about this motion. The linearized equations of motion of such a system are characterized by periodic coefficients which appear also in the mass matrix and by gyroscopic terms. A special type of satellite is found, in which the number of the linearized equations may be reduced.;It is shown that the relation between the stability of the linearized system and the local stability of the actual non-linear system differs from the relation of satellites with axisymmetric rotor in case the rotor is axially torque free.;Because of the special form of the linearized equations, hitherto available methods for stability analysis are not appropriate. Hence, two methods for stability analysis are developed. The first method is a modification of Hsu's numerical scheme for computing the transition matrix over a period, and the second method is a perturbation method, based on the multiple scales method.;Three numerical examples are investigated. The platform in the first example is rigid. In the second example, the platform is composed of a rigid core and a point mass damper, and in the third example, of a rigid core and a beam like antenna. Phenomena, such as the effect of damping, parametric resonances, rotor location, and asymmetry of the platform are demonstrated and discussed, and the two methods for stability analysis are compared. |
