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Recent publications have documented the development and successful application of weighting function techniques for analytically modeling discretely measurable two-dimensional irregular surfaces. The weighting function techniques produce an analytic functional model valid over the entire input data set. The globally valid function is comprised of an arbitrarily large family of locally valid functions which join together with m-th order continuity assured. The locally valid functions are typically low order polynomials, so that analysis of the functional model is efficient and inexpensive. The theory of the weighting function techniques has been extended to N-dimensional functions, allowing mathematical modeling of discretely measurable functions of an arbitrary number of independent parameters, with m-th order continuity assured. Analytic formula for the weighting function coefficients for N-dimensional, m-th order continuity have been developed. This technique has been employed to store and analyze mass remotely sensed topographic data for contour maps and three-dimensional graphical displays.

An open loop control law is applied to a flexible spacecraft that admits translational, as well as rotational and flexural motion. The translational degrees of freedom are coupled to the rotation and deformation through the active controls applied to the structure. The objective of any maneuver is to control the attitude of the craft as well as to dissipate any vibrations of the structure. Depending on the type of maneuver specified, the equations of motion may be divided into two distinct optimal control problems. Single-axis rotational maneuvers (with small flexural deformations) constitute a strictly linear problem. The solution of the resulting two Q point boundary value problem is accomplished through the use of matrix exponential functions. Maneuvers which involve the translational degrees of freedom, are described by nonlinear equations. The solution method presented is a algorithm that generates successive approximations similar to quasi-linearization. A perturbed linear optimal control problem is solved for each approximation. Examples are presented which illustrate the effectiveness of the solution methods for both types of maneuvers. Master of Science