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The aim of this work is to study the relation between two invariants of water flow in a channel of finite depth. The first invariant is the height of the water wave and the second one is the flow force. We restrict ourselves to water waves of small amplitude. Using asymptotic technique together with the method of separation of variables, we construct all water waves of small amplitude which are parameterized by a small parameter. Then we demonstrate numerically that the flow force depends monotonically on the height.

This dissertation integrates in a single mathematical formulation the disciplines pertinent to the flight of flexible aircraft, namely, analytical dynamics, structural dynamics, aerodynamics and controls. The unified formulation is based on fundamental principles and incorporates in a natural manner both rigid body motions of the aircraft as a whole and elastic deformations of the flexible components (fuselage, wing and empennage), as well as the aerodynamic, propulsion, gravity and control forces. The aircraft motion is described in terms of three translations (forward motion, sideslip and plunge) and three rotations (roll, pitch and yaw) of a reference frame attached to the undeformed fuselage, and acting as aircraft body axes, and elastic displacements of each of the flexible components relative to corresponding body axes. The mathematical formulation consists of six ordinary differential equations for the rigid body motions and one set of ordinary differential equations for each elastic displacement. A perturbation approach permits division of the problem into a nonlinear "zero-order Problem" for the rigid body motions, corresponding to flight dynamics, and a linear "first-order problem" for the elastic deformations and perturbations in the rigid body translations and rotations, corresponding to "extended aeroelasticity." Due to computational speed advantages, the aerodynamic forces are derived by means of strip theory. The control forces for the flight dynamics problem are obtained by an "inverse" process. On the other hand, the feedback control forces for the extended aeroelasticity problem are derived by means of LQG theory. A numerical example corresponding to steady level flight and steady level turn maneuver is included. / Ph. D.