- A nonsingular formulation of the necessary conditions for optimal large-angle rotational maneuvers is presented. By optimal we mean that some integral measure of the system performance is minimized. The formulation is for the case of a rigid asymmetric vehicle having a control system capable of generating a continuous torque history; it is valid for an arbitrary specification of terminal orientation and angular velocity states. Analytical solutions of the two-point boundary-value problem are extracted for single-axis maneuvers, and a relaxation process is proposed for reliable numerical solutions for arbitrary boundary conditions. The validity of the necessary condition formulation is supported by analytical solutions for special cases; the relaxation process or general boundary conditions is illustrated by numerical examples. 1980 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.