Coupled librational and orbital motions of a large-scale spacecraft

Mechanical characteristics of coupled librational and orbital motions of a large-scale spacecraft are investigated. A rigid body of an arbitrary shape is considered as a mathematical model, and a set of nonlinear equations of motion about the librational and orbital motions is formulated. Through Lindstedt's perturbation method, approximated analytical solutions are obtained. From the analytical solutions, the conditions of instability are clarified, and the characteristics of the orbital motion are shown. The total mechanical energy has the minimum value when the librational and orbital motions coincide with the periodic solution. The formula for the total mechanical energy proves that the periodic solution is the minimum energy solution. From the nonlinear numerical investigations, it is shown that the results stated above are valid even without any approximations. The results of this study provide us the fundamental understandings of the dynamics of large-scale spacecraft in space.