This lesson covers the concept of finite state models in aerodynamics, focusing on the arbitrary motion of thin airfoils in incompressible flow. The lesson explains the derivation of lift for harmonic oscillation and introduces Theodorsen's lift deficiency function. It also discusses the concept of upwash at the three-quarter chord and the impact of frequency on lift. The lesson further explores the application of Fourier transform to convert time-dependent functions into the frequency domain. The lesson concludes with the explanation of finite state models of unsteady aerodynamics, providing a new approach to modeling unsteady aerodynamics and demonstrating how to obtain a time domain model for any arbitrary motion of the airfoil.

- The lift for harmonic oscillation is derived using Theodorsen's lift deficiency function.
- The concept of upwash at the three-quarter chord is crucial in understanding the aerodynamics of airfoils.
- Fourier transform is used to convert time-dependent functions into the frequency domain, enabling the analysis of arbitrary motion.
- Finite state models provide a new approach to modeling unsteady aerodynamics, allowing for the analysis of arbitrary motion of the airfoil in the time domain.

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