Non-inertial structural effects in flexible spacecraft with spinning appendage

New-generation satellites often show innovative configurations, designed to fulfill increasingly demanding tasks in space operations. This work focuses on one of these configurations, which consists of an Earth observation spacecraft equipped with a large rotating payload, linked to the main bus by a flexible boom. The payload motion aims at expanding the scanned area, resulting in a reduction of the time required to complete a set of measurements, thus considerably enhancing the expected performance. On the other hand, this configuration implies greater complexity both in the analysis of the dynamical behavior and in the design of the control architecture. In fact, when flexible structures subject to rotational motion are designed and used, the stiffening effect resulting from inertial loads (in particular, from the centrifugal action) can play a crucial role. In this work, the dynamical equations of the multibody flexible spacecraft are derived using Kane's formulation, which provides a minimum set of ordinary differential equations, while simplifying their derivation. Because the link is regarded as an elastic beam, flexibility is introduced through a modal decomposition approach that takes the nonlinear elastic dynamics into account, so that the stress stiffening is included in the dynamical model. Stress stiffening is proven to be a fundamental effect that arises in spinning space structures, for which the contribution of the centrifugal force is remarkable. In fact, incorrect predictions, associated with unrealistic dynamical behavior, i.e. structural instability for high spinning rates, are found if this effect is neglected. Moreover, the error related to neglecting this physical phenomenon depends on the spinning rate, and kinematical conditions that make it negligible are identified, in relation to the fundamental deformation frequencies of the space system.