The modal frequencies and shape functions for a thin square orbiting free-free platform are calculated in this paper. The platform is assumed to be a composite graphite/epoxy -homogenous and laminate type-material. The mathematical modeling of the system is comprised of matrices that are heavily populated and dependent on these modal values. Application of the integrated linear quadratic Gaussian/loop transfer rceovery technique in a stochastic, discretized environment provides digital shape and attitude control for this platform structure.
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