Abstract
Abstract : A perturbation formulation and the generalized method of averaging are used to investigated the attitude motion of a symmetric dual-spin spacecraft which contains two spherical dampers arbitrarily located on the axisymmetric rotor and platform (one damper on each). The spherical dampers are intended to represent fully filled fuel tanks. The motions of these spherical dampers are treated as sources of perturbations which affect the otherwise torque-free attitude motion. Approximate attitude motion equations, valid through first order in the ratios of the damper moments of inertia to the spacecraft moment of inertia, are obtained. The generalized method of averaging is used to find an approximate analytical expression for the nutation angle for the case of equal damper moments of inertia and a constant speed rotor. This approximate expression is used to investigate the stability of the spacecraft attitude motion. Conditions for stability are presented and are found to agree well with a previous linear and energy-sink analyses obtained for small nutation angles. Results obtained using the approximate analytical expression for the nutation angle are compared to corresponding numerical solution to the full set of nonlinear equations for several choices of system parameters and very good agreement is found, even for large nutation angles. (Author)
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