Modeling of Spinning Plates: Geometric Stiffening and Modal Approximation for GNC Applications

This work presents a modal formulation for flexible rectangular plates, accounting for nonlinear geometric effects arising from in-plane foreshortening and centrifugal stiffening. The model is linearized with respect to elastic deformations while retaining the full dependence on spacecraft angular velocities and accelerations. System matrices depend nonlinearly on spacecraft states through squared and cross-product terms, capturing gyroscopic coupling and dynamic stiffening phenomena for arbitrary rotational maneuvers. Polynomial approximation of mode shapes enables efficient computation while preserving accuracy. Model predictions are validated against finite element simulations and literature data for transient response under prescribed hub motion.