The equations of motion for an elastically-supported airfoil are first derived. This is followed by a extensive review of the classical results of linear unsteady aerodynamics. State-space realizations are then introduced for those solutions, which result in time-domain formulations in dynamic aeroelasticity. They are used to introduce basic aeroelastic concepts, including flutter, divergence, and response to discrete gusts and continuous turbulence.

The dynamic interactions between aeroelasticity and flight dynamics are discussed, under the assumption of small-amplitude vibrations of the elastic aircraft. Firstly, the equations of the dynamics of a flexible aircraft are described using quasi-coordinates. Linear normal modes are then defined, and used to project the dynamics of the flexible aircraft. Next, linear methods for unsteady aerodynamics are introduced with a particular focus in the doublet-lattice method. The linear dynamic response of the aircraft is finally assembled using rational-function approximations of the frequency-domain aerodynamics.

This chapter describes the various situations in which the incoming flow on an aircraft may be non-stationary, as well as the mathematical models typically used to incorporate them in engineering analysis. Starting from the standard atmosphere, it discusses continuous turbulence, discrete wind gusts and flight in atmospheric boundary layers and wakes.

The classical theory of atmospheric flight mechanics is introduced. The kinematic description of a rigid aircraft is first described using Euler angles. This is followed by the derivation of the Newton-Euler equations describing the aircraft dynamics, with a discussion on the external forces appearing on the vehicle. Steady-state flight conditions are discussed next and used to introduce the concept of load factor and the maneuvering envelope of an aircraft. Finally, dynamic stability is described for both the longitudinal and lateral problem.

The basic control architecture for flexible aircraft is introduced. Both linear and nonlinear optimal control methods are considered in a sequential manner. First, the theory of linear-quadratic regulators is described, and applied to simple aeroelastic problems. A linear estimator is then introduced thus resulting in linear quadratic Gaussian (LQG) control, which is also exemplified. Finally, the approach is expanded to nonlinear problems with a short introduction to model predictive control theory and its application to flexible aircraft. Some recent numerical results are included to illustrate the potential of this technique.

Here we study flows that possess steady solutions that may not persist in time if subjected to small perturbations. Often the behavior of a fluid with no time-dependency is dramatically different than one with time-dependency. Understanding what type of perturbation induces persistent time-dependency is essential for scientific and practical understanding of fluid behavior. An example that we will consider here as well as in later chapters is that of warm air rising or not rising; see Fig. 12.1.

This book considers the mechanics of a fluid, defined as a material that continuously deforms under the influence of an applied shear stress, as depicted in Fig. 1.1. Here the fluid, initially at rest, lies between a stationary wall and a moving plate. Nearly all common fluids stick to solid surfaces. Thus, at the bottom, the fluid remains at rest; at the top, it moves with the velocity of the plate.

This chapter will focus on one-dimensional flow of a compressible fluid. The emphasis will be on inviscid problems, with one brief excursion into viscous compressible flow that will serve as a transition to a study of viscous flow in following chapters. The compressibility we will study here is that which is induced when the fluid particle velocity is of similar magnitude to the fluid sound speed.

This chapter will expand upon potential flow, introduced in Section 7.7, and will mainly be restricted to steady, two-dimensional planar, incompressible potential flow. Such flows can be characterized by a scalar potential field. An example of such a field along with associated streamlines is given in Fig. 8.1.

The primary goal of this chapter is to convert verbal notions that embody the basic axioms of nonrelativistic continuum mechanics into usable mathematical expressions. They will have generality beyond fluid mechanics in that they apply to any continuum material, for example solids. First, we must list those axioms. These axioms will speak to the evolution in time of mass, linear momenta, angular momenta, energy, and entropy.