Pontryagin's principle is applied to several significant problems associated with optimal large angle spacecraft rotational maneuvers. Both rigid and flexible body dynamical models for these vehicles are considered. Three relaxation/analytic continuation methods are developed for iteratively solving the two-point-boundary value problem which results in the treatment of these problems. The solutions obtained are required to rigorously satisfy the necessary conditions derived from Pontryagin's principle. These methods include: (1) boundary condition relaxation processes; (2) differential equation relaxation processes; and (3) hybrid relaxation processes, combining (1) and (2) above. In the literature these relaxation processes are closely related to a number of methods for solving nonlinear equations, known as Davidenko's method, imbedding, and homotopy chain methods. For rigid vehicles a general nonsingular optimal maneuver formulation is obtained, treating all kinematic and dynamical nonlinearities, for general orientation and angular velocity boundary conditions. For flexible vehicles restricted to single axis maneuvers and anti-symmetric elastic deflection modes, a general optimal maneuver formulation is obtained; treating all kinematic, dynamical, and first order structural nonlinearities. In the case of general motion for a flexible vehicle a general formulation is provided, though a solution is not obtained; due to a previously unidentified and as yet unresolved computational difficulty associated symmetry in the dynamical model for the spacecraft. / Ph. D.