Phugoid mode dynamics: equilibrium, linearization, stability (simplified 2nd order equations)

This video discusses calculation of equilibrium points, their linearization and the local stability analysis, of the simplified phugoid mode (or "fugoid") dynamics model (2nd order) of an aircraft.
The detail of obtaining the model based on principles of Physics is discussed in the video / m \_VhFU29nj4 , and different simulations with {ode45} and animations are covered in the video
• phugoid mode: simulati... . Some more animations are, nevertheless, shown here to illustrate concepts.
In this video, we discuss the relationships between angle, airspeed, and thrust needed to achieve equilibrium, as well as equilibrium point stability. Emphasis is placed on gliding (glider u=0) and horizontal level flight ( \theta=0 ) as particular cases.
Stability is analyzed by obtaining a normalized state variable representation \dot x=Ax for constant thrust, and evaluating the real part of the eigenvalues of A, solutions of the characteristic equation \det(sI-A)=0. Of course, as with any linearized system, its stability only proves "local" stability of the original non-linear system.
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#flightdynamics #stability #controlengineering #aerospaceengineering
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Antonio Sala
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