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Established procedures of linear, quadratic, Gaussian optimal estimation and control are developed and interpreted for their application ion to the problem of attitude control of spacecraft with dycallyamially significant elastic appendages. Results are presented both in general terms and for specific application to a solar electric spacecraft. aft. Comparisons are made between alternative coordinattems, systems, and a realistic range of design parameters is considered. For single axis control, system evaluation is accomplished by simulation of a fifteenth-order spacecraft plant with alternative second-order, fourth-order, and sixth-order constant gain estimators. Results point out the importance of modeling errors.