Numerical schemes for the solution of two-point boundary value problems arising from the application of optimal control theory to mathematical models of dynamic systems, are discussed. Optimal control problems are formulated for rotational maneuvers of multiple rigid body, asymmetric spacecraft configurations with both external torques and/or internal torques. Necessary conditions for optimality are derived through Pontryagin’s principle; solutions to the problems are obtained numerically. Comparison studies using competing numerical methods and various choices of performance indices are reported. / Ph. D.