In recent years substantial progress has been made in the development of an improved understanding of unsteady aerodynamics and aeroelasticity in the transonic flow regime. This flow regime is often the most critical for aeroelastic phenomena; yet it has proven the most difficult to master in terms of basic understanding of physical phenomena and the development of predictive mathematical models. The difficulty is primarily a result of the nonlinearities which may be important in transonic flow. Emerging mathematical models have relied principally on finite difference solutions to the governing nonlinear partial differential equations of fluid mechanics. Here are addressed fundamental questions of current interest which will provide the reader with a basis for understanding the recent and current literature in the field. Four principal questions are discussed: (1) Under what conditions are the aerodynamic forces essentially linear functions of the airfoil motion? (2) Are there viable alternative methods to finite difference procedures for solving the relevant fluid dynamical equations? (3) Under conditions when the aerodynamic forces are nonlinear functions of the airfoil motion, what is the significance of the multiple (nonunique) solutions which are sometimes observed? (4) What are effective, efficient computational procedures for using unsteady transonic aerodynamic computer codes in aeroelastic (e.g., flutter) analyses?

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