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

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 17:59

*Enlace a Spanish version

Summary:

This video discusses calculation of equilibrium points, their linearization and the local stability analysis, of the simplified phugoid dynamics models (2nd order) of an aircraft (also ‘fugoid mode’). The detail of obtaining the model based on principles of Physics is discussed in the video [fugoid1EN], and different simulations with ode45 and animations are covered in the video [fugsimEN]. 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 ($𝜃=0$) as particular cases.

Stability is analyzed by obtaining a normalized state variable representation $ẋ=Ax$ for constant thrust, and evaluating the real part of the eigenvalues of $A$, solutions of the characteristic equation $\text{det}<!--FUNCTION\; APPLICATION-->(sI-A)=0$. Of course, as with any linearized system, its stability only proves “local” stability of the original non-linear system.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.