- The necessary conditions formulated from Pontryagins principle for optimal single-axis reorientations of a flexible vehicle having a control system capable of generating a continuous torque (on a rigid part of the structure) are discussed in this paper. The flexural deformations are modeled using the "assumed modes" method and only small (linear) flexural displacements are considered. A single-stage relaxation process is proposed for solution of the two-point boundary-value problem. Starting iteratives for initial costate variables are obtained by zeroing the kinematic nonlinearity in the state equation, leading to a closed-form solution algorithm. The relaxation process increases the participation of the nonlinearity in a sequence of neighboring optimal solutions, converging finally to the solution of the nonlinear problem. 1980 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.