A generalization of the classical theory of flight dynamics is presented that includes quasi-steady aeroelastic effects using residualization approach. This is then used to investigate static stability of the aircraft, which may result in torsional divergence, as well as its controllability, which results in a metric for control effectiveness and potentially control reversal. Several illustrative problems are finally considered: a simplified model for the dynamics of a aircraft with a rigid fuselage, the aeroelastic trim of an aircraft with high-aspect ratio wings, and roll control with aeroelastic effects.

A modelling strategy based on geometrically-nonlinear composite beams and unsteady vortex-lattice aerodynamics is introduce for the computer simulation of very flexible aircraft dynamics. The key challenges of this approach are discussed, including spatial coupling of structural and aerodynamic models and time integration schemes. This is then exemplified using numerical results on several recent prototypes of highly-efficient wings and aircraft. Finally, some of the analysis methods used in aircraft design are reviewed to incorporate the more complex physics associated to increased flexibility.

This chapter first defines the scope for flexible aircraft dynamics. It reviews the historical evolution of airframe designs and of the analysis methods used to support them. It also reviews some basic concepts in dynamics, linear systems, and system identification that are of relevance to the book.

Vortex-lattice solutions for unsteady aerodynamics on lifting surfaces are introduced. They provide a general description for aeroelastic applications with low-speed aircraft undergoing large wing deformations. The basic solution process is first outlined for 2-D problems, using a discrete vortex model for the fluid, and then extended to 3-D models using vortex rings. It is shown how this general solution can then be linearized around an arbitrary reference, and recast in state-space form. A compact form of the linear aerodynamic model is then introduce using methods of model-order reduction, and in particular, balanced realizations are seen to give a computationally-efficiency solution.

This chapter oulines the curretn insutrial methods for experimental modal analysis of air vehicles. Both ground and flight vibration tests are discussed, with a focus on large transport airraft with moderately stiff wings.

Geometrically-nonlinear composite beam solutions are discussed as structural models for airframes with slender subcomponents. As this is intended for aircraft applications, the beam equations of motion are written with respect to a moving reference frame, which is rigidly-attached to a fixed point on the aircraft. Three different solution methods are then discussed, corresponding to a displacement-based formulation, a strain-based formulation, and a hybrid formulation in intrinsic variables. Key issues in numerical solution are discussed, including the parametrization of the finite rotations and linearization around arbitrary equilibrium conditions.

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.